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krahets 1 year ago
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chapter_dynamic_programming/dp_problem_features/index.html
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@ -3464,7 +3464,23 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDP</span><span class="p">}</span>
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 爬楼梯最小代价：动态规划 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minCostClimbingStairsDP</span><span class="p">(</span><span class="nx">cost</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">cost</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">n</span><span class="p">]</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// 初始化 dp 表，用于存储子问题的解</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 初始状态：预设最小子问题的解</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 状态转移：从较小子问题逐步求解较大子问题</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="nx">cost</span><span class="p">[</span><span class="nx">i</span><span class="p">])))</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">]</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3595,7 +3611,22 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">}</span>
<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 爬楼梯最小代价：状态压缩后的动态规划 */</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="nx">cost</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">cost</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="nx">n</span><span class="p">]</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="c1">// 初始状态：预设最小子问题的解</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="c1">// 状态转移：从较小子问题逐步求解较大子问题</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">b</span>
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">a</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">tmp</span><span class="o">+</span><span class="nx">cost</span><span class="p">[</span><span class="nx">i</span><span class="p">])))</span>
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span>
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3760,7 +3791,25 @@ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsConstraintDP</span><span class="p">}</span>
<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 带约束爬楼梯：动态规划 */</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsConstraintDP</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="c1">// 初始化 dp 表，用于存储子问题的解</span>
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][</span><span class="mi">3</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="c1">// 初始状态：预设最小子问题的解</span>
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="c1">// 状态转移：从较小子问题逐步求解较大子问题</span>
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

87
chapter_dynamic_programming/dp_solution_pipeline/index.html
Unescape View File

@ -3582,7 +3582,22 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDFS</span><span class="p">}</span>
<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最小路径和：暴力搜索 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 若为左上角单元格，则终止搜索</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// 若行列索引越界，则返回 +∞ 代价</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">MaxInt</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="c1">// 计算从左上角到 (i-1, j) 和 (i, j-1) 的最小路径代价</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="nx">up</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">minPathSumDFS</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="c1">// 返回从左上角到 (i, j) 的最小路径代价</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">left</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">up</span><span class="p">)))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3741,7 +3756,27 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDFSMem</span><span class="p">}</span>
<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 最小路径和：记忆化搜索 */</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="c1">// 若为左上角单元格，则终止搜索</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="c1">// 若行列索引越界，则返回 +∞ 代价</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">MaxInt</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="c1">// 若已有记录，则直接返回</span>
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="c1">// 左边和上边单元格的最小路径代价</span>
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span>
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w"> </span><span class="nx">up</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">minPathSumDFSMem</span><span class="p">(</span><span class="nx">grid</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w"> </span><span class="c1">// 记录并返回左上角到 (i, j) 的最小路径代价</span>
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">left</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">up</span><span class="p">)))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3914,7 +3949,31 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDP</span><span class="p">}</span>
<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 最小路径和：动态规划 */</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minPathSumDP</span><span class="p">(</span><span class="nx">grid</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">grid</span><span class="p">),</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="p">)</span>
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w"> </span><span class="c1">// 状态转移：首行</span>
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="c1">// 状态转移：首列</span>
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w"> </span><span class="c1">// 状态转移：其余行列</span>
<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="p">])))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">m</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4127,7 +4186,27 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDPComp</span><span class="p">}</span>
<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 最小路径和：状态压缩后的动态规划 */</span>
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">minPathSumDPComp</span><span class="p">(</span><span class="nx">grid</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">grid</span><span class="p">),</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="p">)</span>
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w"> </span><span class="c1">// 状态转移：首行</span>
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w"> </span><span class="c1">// 状态转移：其余行列</span>
<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w"> </span><span class="c1">// 状态转移：首列</span>
<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w"> </span><span class="c1">// 状态转移：其余列</span>
<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">])))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">grid</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

60
chapter_dynamic_programming/edit_distance_problem/index.html
Unescape View File

@ -3510,7 +3510,35 @@ dp[i, j] = dp[i-1, j-1]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">editDistanceDP</span><span class="p">}</span>
<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 编辑距离：动态规划 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">editDistanceDP</span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">s</span><span class="p">)</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">t</span><span class="p">)</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 状态转移：首行首列</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">j</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="c1">// 状态转移：其余行列</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">t</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="c1">// 若两字符相等，则直接跳过此两字符</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="c1">// 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1</span>
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]),</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">m</span><span class="p">]</span>
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3761,7 +3789,35 @@ dp[i, j] = dp[i-1, j-1]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">editDistanceDPComp</span><span class="p">}</span>
<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 编辑距离：状态压缩后的动态规划 */</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">editDistanceDPComp</span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">s</span><span class="p">)</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">t</span><span class="p">)</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="c1">// 状态转移：首行</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">j</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="c1">// 状态转移：其余行</span>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="c1">// 状态转移：首列</span>
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="nx">leftUp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="c1">// 暂存 dp[i-1, j-1]</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span>
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="c1">// 状态转移：其余列</span>
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">t</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w"> </span><span class="c1">// 若两字符相等，则直接跳过此两字符</span>
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">leftUp</span>
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w"> </span><span class="c1">// 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1</span>
<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]),</span><span class="w"> </span><span class="nx">leftUp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w"> </span><span class="nx">leftUp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="c1">// 更新为下一轮的 dp[i-1, j-1]</span>
<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span>
<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

110
chapter_dynamic_programming/intro_to_dynamic_programming/index.html
Unescape View File

@ -3503,9 +3503,36 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">climbing_stairs_backtrack.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsBacktrack</span><span class="p">}</span>
<div class="highlight"><span class="filename">climbing_stairs_backtrack.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 回溯 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 当爬到第 n 阶时，方案数量加 1</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 剪枝：不允许越过第 n 阶</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">state</span><span class="o">+</span><span class="nx">choice</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="o">+</span><span class="nx">choice</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="c1">// 回退</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="p">}</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="cm">/* 爬楼梯：回溯 */</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsBacktrack</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="c1">// 可选择向上爬 1 或 2 阶</span>
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">}</span>
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="c1">// 从第 0 阶开始爬</span>
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w"> </span><span class="nx">state</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w"> </span><span class="c1">// 使用 res[0] 记录方案数量</span>
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3689,9 +3716,21 @@ dp[i] = dp[i-1] + dp[i-2]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">climbing_stairs_dfs.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDFS</span><span class="p">}</span>
<div class="highlight"><span class="filename">climbing_stairs_dfs.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 搜索 */</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="c1">// 已知 dp[1] 和 dp[2] ，返回之</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="p">}</span>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="cm">/* 爬楼梯：搜索 */</span>
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsDFS</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span>
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3858,9 +3897,32 @@ dp[i] = dp[i-1] + dp[i-2]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDFSMem</span><span class="p">}</span>
<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 记忆化搜索 */</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfsMem</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="c1">// 已知 dp[1] 和 dp[2] ，返回之</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w"> </span><span class="c1">// 若存在记录 dp[i] ，则直接返回之</span>
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w"> </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dfsMem</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dfsMem</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">)</span>
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="c1">// 记录 dp[i]</span>
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="p">}</span>
<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a>
<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="cm">/* 爬楼梯：记忆化搜索 */</span>
<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsDFSMem</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w"> </span><span class="c1">// mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录</span>
<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dfsMem</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">)</span>
<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4028,7 +4090,22 @@ dp[i] = dp[i-1] + dp[i-2]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDP</span><span class="p">}</span>
<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 爬楼梯：动态规划 */</span>
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsDP</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span>
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w"> </span><span class="c1">// 初始化 dp 表，用于存储子问题的解</span>
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w"> </span><span class="c1">// 初始状态：预设最小子问题的解</span>
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w"> </span><span class="c1">// 状态转移：从较小子问题逐步求解较大子问题</span>
<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span>
<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">]</span>
<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4161,7 +4238,18 @@ dp[i] = dp[i-1] + dp[i-2]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDPComp</span><span class="p">}</span>
<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsDPComp</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span>
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w"> </span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w"> </span><span class="c1">// 状态转移：从较小子问题逐步求解较大子问题</span>
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w"> </span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">b</span><span class="p">,</span><span class="w"> </span><span class="nx">a</span><span class="o">+</span><span class="nx">b</span>
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">b</span>
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

80
chapter_dynamic_programming/knapsack_problem/index.html
Unescape View File

@ -3508,7 +3508,22 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDFS</span><span class="p">}</span>
<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 0-1 背包：暴力搜索 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 若已选完所有物品或背包无容量，则返回价值 0</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则只能不放入背包</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="c1">// 计算不放入和放入物品 i 的最大价值</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="nx">no</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="nx">yes</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">knapsackDFS</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="c1">// 返回两种方案中价值更大的那一个</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">no</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">yes</span><span class="p">)))</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3666,7 +3681,27 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDFSMem</span><span class="p">}</span>
<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 0-1 背包：记忆化搜索 */</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="c1">// 若已选完所有物品或背包无容量，则返回价值 0</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="c1">// 若已有记录，则直接返回</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则只能不放入背包</span>
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="c1">// 计算不放入和放入物品 i 的最大价值</span>
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w"> </span><span class="nx">no</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="p">)</span>
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w"> </span><span class="nx">yes</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">knapsackDFSMem</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">mem</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w"> </span><span class="c1">// 返回两种方案中价值更大的那一个</span>
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">no</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">yes</span><span class="p">)))</span>
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">mem</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span>
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3830,7 +3865,28 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDP</span><span class="p">}</span>
<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 0-1 背包：动态规划 */</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">knapsackDP</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">)</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="c1">// 状态转移</span>
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则不选物品 i</span>
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span>
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])))</span>
<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">cap</span><span class="p">]</span>
<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4053,7 +4109,23 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDPComp</span><span class="p">}</span>
<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 0-1 背包：状态压缩后的动态规划 */</span>
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">knapsackDPComp</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">)</span>
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w"> </span><span class="c1">// 状态转移</span>
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w"> </span><span class="c1">// 倒序遍历</span>
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])))</span>
<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">cap</span><span class="p">]</span>
<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

151
chapter_dynamic_programming/unbounded_knapsack_problem/index.html
Unescape View File

@ -3606,7 +3606,28 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDP</span><span class="p">}</span>
<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 完全背包：动态规划 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">unboundedKnapsackDP</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">)</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 状态转移</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则不选物品 i</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">c</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])))</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">cap</span><span class="p">]</span>
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3784,7 +3805,25 @@ dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDPComp</span><span class="p">}</span>
<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 完全背包：状态压缩后的动态规划 */</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">unboundedKnapsackDPComp</span><span class="p">(</span><span class="nx">wgt</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">)</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="c1">// 状态转移</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="p">;</span><span class="w"> </span><span class="nx">c</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则不选物品 i</span>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span>
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">c</span><span class="o">-</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">])))</span>
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">cap</span><span class="p">]</span>
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3984,7 +4023,36 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeDP</span><span class="p">}</span>
<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 零钱兑换：动态规划 */</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeDP</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w"> </span><span class="c1">// 状态转移：首行首列</span>
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">max</span>
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="c1">// 状态转移：其余行列</span>
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则不选硬币 i</span>
<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span>
<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="o">-</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="mi">1</span><span class="p">)))</span>
<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span>
<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4215,7 +4283,33 @@ dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeDPComp</span><span class="p">}</span>
<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 零钱兑换：动态规划 */</span>
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeDPComp</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span>
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">max</span>
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w"> </span><span class="c1">// 状态转移</span>
<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w"> </span><span class="c1">// 倒序遍历</span>
<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则不选硬币 i</span>
<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span>
<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="o">-</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span><span class="o">+</span><span class="mi">1</span><span class="p">)))</span>
<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-21" name="__codelineno-36-21" href="#__codelineno-36-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-22" name="__codelineno-36-22" href="#__codelineno-36-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-23" name="__codelineno-36-23" href="#__codelineno-36-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-24" name="__codelineno-36-24" href="#__codelineno-36-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span>
<a id="__codelineno-36-25" name="__codelineno-36-25" href="#__codelineno-36-25"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-36-26" name="__codelineno-36-26" href="#__codelineno-36-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-36-27" name="__codelineno-36-27" href="#__codelineno-36-27"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4405,7 +4499,32 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeIIDP</span><span class="p">}</span>
<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 零钱兑换 II：动态规划 */</span>
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeIIDP</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span>
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w"> </span><span class="c1">// 初始化首列</span>
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w"> </span><span class="c1">// 状态转移：其余行列</span>
<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则不选硬币 i</span>
<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span>
<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案的较小值</span>
<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">a</span><span class="o">-</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
<a id="__codelineno-47-22" name="__codelineno-47-22" href="#__codelineno-47-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-23" name="__codelineno-47-23" href="#__codelineno-47-23"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-24" name="__codelineno-47-24" href="#__codelineno-47-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-47-25" name="__codelineno-47-25" href="#__codelineno-47-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">amt</span><span class="p">]</span>
<a id="__codelineno-47-26" name="__codelineno-47-26" href="#__codelineno-47-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4575,7 +4694,27 @@ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeIIDPComp</span><span class="p">}</span>
<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 零钱兑换 II：状态压缩后的动态规划 */</span>
<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeIIDPComp</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span>
<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w"> </span><span class="c1">// 初始化 dp 表</span>
<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w"> </span><span class="c1">// 状态转移</span>
<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w"> </span><span class="c1">// 倒序遍历</span>
<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">amt</span><span class="p">;</span><span class="w"> </span><span class="nx">a</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w"> </span><span class="c1">// 若超过背包容量，则不选硬币 i</span>
<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span>
<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a><span class="w"> </span><span class="c1">// 不选和选硬币 i 这两种方案之和</span>
<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">a</span><span class="o">-</span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span>
<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">amt</span><span class="p">]</span>
<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

36
chapter_greedy/fractional_knapsack_problem/index.html
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@ -3534,9 +3534,39 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fractional_knapsack.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">II</span><span class="p">}</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">fractionalKnapsack</span><span class="p">}</span>
<div class="highlight"><span class="filename">fractional_knapsack.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 物品 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">Item</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="nx">w</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="c1">// 物品重量</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="c1">// 物品价值</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="p">}</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 分数背包：贪心 */</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">fractionalKnapsack</span><span class="p">(</span><span class="nx">wgt</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">float64</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 创建物品列表，包含两个属性：重量、价值</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="nx">items</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="nx">Item</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">))</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">wgt</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="nx">items</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">Item</span><span class="p">{</span><span class="nx">wgt</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">val</span><span class="p">[</span><span class="nx">i</span><span class="p">]}</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="c1">// 按照单位价值 item.v / item.w 从高到低进行排序</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="nx">sort</span><span class="p">.</span><span class="nx">Slice</span><span class="p">(</span><span class="nx">items</span><span class="p">,</span><span class="w"> </span><span class="kd">func</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">items</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">v</span><span class="p">)</span><span class="o">/</span><span class="nb">float64</span><span class="p">(</span><span class="nx">items</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">w</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">items</span><span class="p">[</span><span class="nx">j</span><span class="p">].</span><span class="nx">v</span><span class="p">)</span><span class="o">/</span><span class="nb">float64</span><span class="p">(</span><span class="nx">items</span><span class="p">[</span><span class="nx">j</span><span class="p">].</span><span class="nx">w</span><span class="p">)</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="p">})</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="c1">// 循环贪心选择</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mf">0.0</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">item</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">items</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w"> </span><span class="c1">// 若剩余容量充足，则将当前物品整个装进背包</span>
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">v</span><span class="p">)</span>
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span>
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w"> </span><span class="c1">// 若剩余容量不足，则将当前物品的一部分装进背包</span>
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">v</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">item</span><span class="p">.</span><span class="nx">w</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">cap</span><span class="p">)</span>
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w"> </span><span class="c1">// 已无剩余容量，因此跳出循环</span>
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="p">}</span>
</code></pre></div>
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<div class="tabbed-block">

22
chapter_greedy/greedy_algorithm/index.html
Unescape View File

@ -3489,7 +3489,27 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeGreedy</span><span class="p">}</span>
<div class="highlight"><span class="filename">coin_change_greedy.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 假设 coins 列表有序</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="nx">i</span><span class="o">--</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 选择 coins[i]</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

21
chapter_greedy/max_capacity_problem/index.html
Unescape View File

@ -3536,7 +3536,26 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">max_capacity.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">maxCapacity</span><span class="p">}</span>
<div class="highlight"><span class="filename">max_capacity.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最大容量：贪心 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">maxCapacity</span><span class="p">(</span><span class="nx">ht</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 初始化 i, j 分列数组两端</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">ht</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="c1">// 初始最大容量为 0</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// 循环贪心选择，直至两板相遇</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 更新最大容量</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="nx">capacity</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])))</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">res</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">capacity</span><span class="p">)))</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 向内移动短板</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="nx">i</span><span class="o">++</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="nx">j</span><span class="o">--</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

21
chapter_greedy/max_product_cutting_problem/index.html
Unescape View File

@ -3512,7 +3512,26 @@ n = 3 a + b
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">max_product_cutting.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">maxProductCutting</span><span class="p">}</span>
<div class="highlight"><span class="filename">max_product_cutting.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最大切分乘积：贪心 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">maxProductCutting</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 当 n &lt;= 3 时，必须切分出一个 1</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// 贪心地切分出 3 ，a 为 3 的个数，b 为余数</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="c1">// 当余数为 1 时，将一对 1 * 3 转化为 2 * 2</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">a</span><span class="o">-</span><span class="mi">1</span><span class="p">)))</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="c1">// 当余数为 2 时，不做处理</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">a</span><span class="p">)))</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="c1">// 当余数为 0 时，不做处理</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">a</span><span class="p">)))</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="p">}</span>
</code></pre></div>
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<div class="tabbed-block">

21
chapter_heap/top_k/index.html
Unescape View File

@ -3509,7 +3509,24 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">top_k.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">topKHeap</span><span class="p">}</span>
<div class="highlight"><span class="filename">top_k.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 基于堆查找数组中最大的 k 个元素 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">topKHeap</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">minHeap</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="nx">h</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">minHeap</span><span class="p">{}</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Init</span><span class="p">(</span><span class="nx">h</span><span class="p">)</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="c1">// 将数组的前 k 个元素入堆</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">h</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 从第 k+1 个元素开始，保持堆的长度为 k</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="c1">// 若当前元素大于堆顶元素，则将堆顶元素出堆、当前元素入堆</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">Top</span><span class="p">().(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">h</span><span class="p">)</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">h</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">h</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3521,7 +3538,7 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">top_k.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">topKHeap</span><span class="p">}</span>
<div class="highlight"><span class="filename">top_k.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">topKHeap</span><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

94
chapter_tree/array_representation_of_tree/index.html
Unescape View File

@ -3849,7 +3849,99 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
<div class="highlight"><span class="filename">array_binary_tree.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 数组表示下的二叉树类 */</span>
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">class</span> <span class="nc">ArrayBinaryTree</span> <span class="p">{</span>
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">tree</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">?]</span>
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a>
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a> <span class="cm">/* 构造方法 */</span>
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a> <span class="kd">init</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">?])</span> <span class="p">{</span>
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a> <span class="n">tree</span> <span class="p">=</span> <span class="n">arr</span>
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="p">}</span>
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a>
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a> <span class="cm">/* 节点数量 */</span>
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a> <span class="kd">func</span> <span class="nf">size</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a> <span class="n">tree</span><span class="p">.</span><span class="bp">count</span>
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a> <span class="p">}</span>
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a>
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a> <span class="cm">/* 获取索引为 i 节点的值 */</span>
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a> <span class="kd">func</span> <span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span><span class="p">?</span> <span class="p">{</span>
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a> <span class="c1">// 若索引越界，则返回 null ，代表空位</span>
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a> <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="n">size</span><span class="p">()</span> <span class="p">{</span>
<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a> <span class="k">return</span> <span class="kc">nil</span>
<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a> <span class="p">}</span>
<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a> <span class="k">return</span> <span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a> <span class="p">}</span>
<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a>
<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a> <span class="cm">/* 获取索引为 i 节点的左子节点的索引 */</span>
<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a> <span class="kd">func</span> <span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a> <span class="p">}</span>
<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a>
<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a> <span class="cm">/* 获取索引为 i 节点的右子节点的索引 */</span>
<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a> <span class="kd">func</span> <span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
<a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a> <span class="p">}</span>
<a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a>
<a id="__codelineno-19-34" name="__codelineno-19-34" href="#__codelineno-19-34"></a> <span class="cm">/* 获取索引为 i 节点的父节点的索引 */</span>
<a id="__codelineno-19-35" name="__codelineno-19-35" href="#__codelineno-19-35"></a> <span class="kd">func</span> <span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-19-36" name="__codelineno-19-36" href="#__codelineno-19-36"></a> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<a id="__codelineno-19-37" name="__codelineno-19-37" href="#__codelineno-19-37"></a> <span class="p">}</span>
<a id="__codelineno-19-38" name="__codelineno-19-38" href="#__codelineno-19-38"></a>
<a id="__codelineno-19-39" name="__codelineno-19-39" href="#__codelineno-19-39"></a> <span class="cm">/* 层序遍历 */</span>
<a id="__codelineno-19-40" name="__codelineno-19-40" href="#__codelineno-19-40"></a> <span class="kd">func</span> <span class="nf">levelOrder</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">{</span>
<a id="__codelineno-19-41" name="__codelineno-19-41" href="#__codelineno-19-41"></a> <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
<a id="__codelineno-19-42" name="__codelineno-19-42" href="#__codelineno-19-42"></a> <span class="c1">// 直接遍历数组</span>
<a id="__codelineno-19-43" name="__codelineno-19-43" href="#__codelineno-19-43"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">size</span><span class="p">(),</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-19-44" name="__codelineno-19-44" href="#__codelineno-19-44"></a> <span class="k">if</span> <span class="kd">let</span> <span class="nv">val</span> <span class="p">=</span> <span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-19-45" name="__codelineno-19-45" href="#__codelineno-19-45"></a> <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-19-46" name="__codelineno-19-46" href="#__codelineno-19-46"></a> <span class="p">}</span>
<a id="__codelineno-19-47" name="__codelineno-19-47" href="#__codelineno-19-47"></a> <span class="p">}</span>
<a id="__codelineno-19-48" name="__codelineno-19-48" href="#__codelineno-19-48"></a> <span class="k">return</span> <span class="n">res</span>
<a id="__codelineno-19-49" name="__codelineno-19-49" href="#__codelineno-19-49"></a> <span class="p">}</span>
<a id="__codelineno-19-50" name="__codelineno-19-50" href="#__codelineno-19-50"></a>
<a id="__codelineno-19-51" name="__codelineno-19-51" href="#__codelineno-19-51"></a> <span class="cm">/* 深度优先遍历 */</span>
<a id="__codelineno-19-52" name="__codelineno-19-52" href="#__codelineno-19-52"></a> <span class="kd">private</span> <span class="kd">func</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">order</span><span class="p">:</span> <span class="nb">String</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">{</span>
<a id="__codelineno-19-53" name="__codelineno-19-53" href="#__codelineno-19-53"></a> <span class="c1">// 若为空位，则返回</span>
<a id="__codelineno-19-54" name="__codelineno-19-54" href="#__codelineno-19-54"></a> <span class="k">guard</span> <span class="kd">let</span> <span class="nv">val</span> <span class="p">=</span> <span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-19-55" name="__codelineno-19-55" href="#__codelineno-19-55"></a> <span class="k">return</span>
<a id="__codelineno-19-56" name="__codelineno-19-56" href="#__codelineno-19-56"></a> <span class="p">}</span>
<a id="__codelineno-19-57" name="__codelineno-19-57" href="#__codelineno-19-57"></a> <span class="c1">// 前序遍历</span>
<a id="__codelineno-19-58" name="__codelineno-19-58" href="#__codelineno-19-58"></a> <span class="k">if</span> <span class="n">order</span> <span class="p">==</span> <span class="s">&quot;pre&quot;</span> <span class="p">{</span>
<a id="__codelineno-19-59" name="__codelineno-19-59" href="#__codelineno-19-59"></a> <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-19-60" name="__codelineno-19-60" href="#__codelineno-19-60"></a> <span class="p">}</span>
<a id="__codelineno-19-61" name="__codelineno-19-61" href="#__codelineno-19-61"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="kr">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">),</span> <span class="n">order</span><span class="p">:</span> <span class="n">order</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
<a id="__codelineno-19-62" name="__codelineno-19-62" href="#__codelineno-19-62"></a> <span class="c1">// 中序遍历</span>
<a id="__codelineno-19-63" name="__codelineno-19-63" href="#__codelineno-19-63"></a> <span class="k">if</span> <span class="n">order</span> <span class="p">==</span> <span class="s">&quot;in&quot;</span> <span class="p">{</span>
<a id="__codelineno-19-64" name="__codelineno-19-64" href="#__codelineno-19-64"></a> <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-19-65" name="__codelineno-19-65" href="#__codelineno-19-65"></a> <span class="p">}</span>
<a id="__codelineno-19-66" name="__codelineno-19-66" href="#__codelineno-19-66"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="kr">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">),</span> <span class="n">order</span><span class="p">:</span> <span class="n">order</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
<a id="__codelineno-19-67" name="__codelineno-19-67" href="#__codelineno-19-67"></a> <span class="c1">// 后序遍历</span>
<a id="__codelineno-19-68" name="__codelineno-19-68" href="#__codelineno-19-68"></a> <span class="k">if</span> <span class="n">order</span> <span class="p">==</span> <span class="s">&quot;post&quot;</span> <span class="p">{</span>
<a id="__codelineno-19-69" name="__codelineno-19-69" href="#__codelineno-19-69"></a> <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-19-70" name="__codelineno-19-70" href="#__codelineno-19-70"></a> <span class="p">}</span>
<a id="__codelineno-19-71" name="__codelineno-19-71" href="#__codelineno-19-71"></a> <span class="p">}</span>
<a id="__codelineno-19-72" name="__codelineno-19-72" href="#__codelineno-19-72"></a>
<a id="__codelineno-19-73" name="__codelineno-19-73" href="#__codelineno-19-73"></a> <span class="cm">/* 前序遍历 */</span>
<a id="__codelineno-19-74" name="__codelineno-19-74" href="#__codelineno-19-74"></a> <span class="kd">func</span> <span class="nf">preOrder</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">{</span>
<a id="__codelineno-19-75" name="__codelineno-19-75" href="#__codelineno-19-75"></a> <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
<a id="__codelineno-19-76" name="__codelineno-19-76" href="#__codelineno-19-76"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="p">:</span> <span class="s">&quot;pre&quot;</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
<a id="__codelineno-19-77" name="__codelineno-19-77" href="#__codelineno-19-77"></a> <span class="k">return</span> <span class="n">res</span>
<a id="__codelineno-19-78" name="__codelineno-19-78" href="#__codelineno-19-78"></a> <span class="p">}</span>
<a id="__codelineno-19-79" name="__codelineno-19-79" href="#__codelineno-19-79"></a>
<a id="__codelineno-19-80" name="__codelineno-19-80" href="#__codelineno-19-80"></a> <span class="cm">/* 中序遍历 */</span>
<a id="__codelineno-19-81" name="__codelineno-19-81" href="#__codelineno-19-81"></a> <span class="kd">func</span> <span class="nf">inOrder</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">{</span>
<a id="__codelineno-19-82" name="__codelineno-19-82" href="#__codelineno-19-82"></a> <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
<a id="__codelineno-19-83" name="__codelineno-19-83" href="#__codelineno-19-83"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="p">:</span> <span class="s">&quot;in&quot;</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
<a id="__codelineno-19-84" name="__codelineno-19-84" href="#__codelineno-19-84"></a> <span class="k">return</span> <span class="n">res</span>
<a id="__codelineno-19-85" name="__codelineno-19-85" href="#__codelineno-19-85"></a> <span class="p">}</span>
<a id="__codelineno-19-86" name="__codelineno-19-86" href="#__codelineno-19-86"></a>
<a id="__codelineno-19-87" name="__codelineno-19-87" href="#__codelineno-19-87"></a> <span class="cm">/* 后序遍历 */</span>
<a id="__codelineno-19-88" name="__codelineno-19-88" href="#__codelineno-19-88"></a> <span class="kd">func</span> <span class="nf">postOrder</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">{</span>
<a id="__codelineno-19-89" name="__codelineno-19-89" href="#__codelineno-19-89"></a> <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
<a id="__codelineno-19-90" name="__codelineno-19-90" href="#__codelineno-19-90"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="p">:</span> <span class="s">&quot;post&quot;</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
<a id="__codelineno-19-91" name="__codelineno-19-91" href="#__codelineno-19-91"></a> <span class="k">return</span> <span class="n">res</span>
<a id="__codelineno-19-92" name="__codelineno-19-92" href="#__codelineno-19-92"></a> <span class="p">}</span>
<a id="__codelineno-19-93" name="__codelineno-19-93" href="#__codelineno-19-93"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

134
chapter_tree/avl_tree/index.html
Unescape View File

@ -5048,31 +5048,30 @@
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="p">@</span><span class="n">discardableResult</span>
<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="kd">func</span> <span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">root</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="p">}</span>
<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a>
<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="kd">func</span> <span class="nf">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
<a id="__codelineno-74-10" name="__codelineno-74-10" href="#__codelineno-74-10"></a> <span class="k">if</span> <span class="n">node</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-74-11" name="__codelineno-74-11" href="#__codelineno-74-11"></a> <span class="k">return</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-74-12" name="__codelineno-74-12" href="#__codelineno-74-12"></a> <span class="p">}</span>
<a id="__codelineno-74-13" name="__codelineno-74-13" href="#__codelineno-74-13"></a> <span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
<a id="__codelineno-74-14" name="__codelineno-74-14" href="#__codelineno-74-14"></a> <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
<a id="__codelineno-74-15" name="__codelineno-74-15" href="#__codelineno-74-15"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-74-16" name="__codelineno-74-16" href="#__codelineno-74-16"></a> <span class="p">}</span> <span class="k">else</span> <span class="k">if</span> <span class="n">val</span> <span class="o">&gt;</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
<a id="__codelineno-74-17" name="__codelineno-74-17" href="#__codelineno-74-17"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-74-18" name="__codelineno-74-18" href="#__codelineno-74-18"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-74-19" name="__codelineno-74-19" href="#__codelineno-74-19"></a> <span class="k">return</span> <span class="n">node</span> <span class="c1">// 重复节点不插入，直接返回</span>
<a id="__codelineno-74-20" name="__codelineno-74-20" href="#__codelineno-74-20"></a> <span class="p">}</span>
<a id="__codelineno-74-21" name="__codelineno-74-21" href="#__codelineno-74-21"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span> <span class="c1">// 更新节点高度</span>
<a id="__codelineno-74-22" name="__codelineno-74-22" href="#__codelineno-74-22"></a> <span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
<a id="__codelineno-74-23" name="__codelineno-74-23" href="#__codelineno-74-23"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
<a id="__codelineno-74-24" name="__codelineno-74-24" href="#__codelineno-74-24"></a> <span class="c1">// 返回子树的根节点</span>
<a id="__codelineno-74-25" name="__codelineno-74-25" href="#__codelineno-74-25"></a> <span class="k">return</span> <span class="n">node</span>
<a id="__codelineno-74-26" name="__codelineno-74-26" href="#__codelineno-74-26"></a><span class="p">}</span>
<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="kd">func</span> <span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">root</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="p">}</span>
<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a>
<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="kd">func</span> <span class="nf">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a> <span class="k">if</span> <span class="n">node</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-74-10" name="__codelineno-74-10" href="#__codelineno-74-10"></a> <span class="k">return</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-74-11" name="__codelineno-74-11" href="#__codelineno-74-11"></a> <span class="p">}</span>
<a id="__codelineno-74-12" name="__codelineno-74-12" href="#__codelineno-74-12"></a> <span class="cm">/* 1. 查找插入位置，并插入节点 */</span>
<a id="__codelineno-74-13" name="__codelineno-74-13" href="#__codelineno-74-13"></a> <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
<a id="__codelineno-74-14" name="__codelineno-74-14" href="#__codelineno-74-14"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-74-15" name="__codelineno-74-15" href="#__codelineno-74-15"></a> <span class="p">}</span> <span class="k">else</span> <span class="k">if</span> <span class="n">val</span> <span class="o">&gt;</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
<a id="__codelineno-74-16" name="__codelineno-74-16" href="#__codelineno-74-16"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-74-17" name="__codelineno-74-17" href="#__codelineno-74-17"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-74-18" name="__codelineno-74-18" href="#__codelineno-74-18"></a> <span class="k">return</span> <span class="n">node</span> <span class="c1">// 重复节点不插入，直接返回</span>
<a id="__codelineno-74-19" name="__codelineno-74-19" href="#__codelineno-74-19"></a> <span class="p">}</span>
<a id="__codelineno-74-20" name="__codelineno-74-20" href="#__codelineno-74-20"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span> <span class="c1">// 更新节点高度</span>
<a id="__codelineno-74-21" name="__codelineno-74-21" href="#__codelineno-74-21"></a> <span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
<a id="__codelineno-74-22" name="__codelineno-74-22" href="#__codelineno-74-22"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
<a id="__codelineno-74-23" name="__codelineno-74-23" href="#__codelineno-74-23"></a> <span class="c1">// 返回子树的根节点</span>
<a id="__codelineno-74-24" name="__codelineno-74-24" href="#__codelineno-74-24"></a> <span class="k">return</span> <span class="n">node</span>
<a id="__codelineno-74-25" name="__codelineno-74-25" href="#__codelineno-74-25"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -5482,49 +5481,48 @@
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="p">@</span><span class="n">discardableResult</span>
<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="kd">func</span> <span class="nf">remove</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">root</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="p">}</span>
<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a>
<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="kd">func</span> <span class="nf">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a> <span class="k">if</span> <span class="n">node</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a> <span class="k">return</span> <span class="kc">nil</span>
<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a> <span class="p">}</span>
<a id="__codelineno-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></a> <span class="cm">/* 1. 查找节点，并删除之 */</span>
<a id="__codelineno-85-14" name="__codelineno-85-14" href="#__codelineno-85-14"></a> <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
<a id="__codelineno-85-15" name="__codelineno-85-15" href="#__codelineno-85-15"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-85-16" name="__codelineno-85-16" href="#__codelineno-85-16"></a> <span class="p">}</span> <span class="k">else</span> <span class="k">if</span> <span class="n">val</span> <span class="o">&gt;</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
<a id="__codelineno-85-17" name="__codelineno-85-17" href="#__codelineno-85-17"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-85-18" name="__codelineno-85-18" href="#__codelineno-85-18"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-85-19" name="__codelineno-85-19" href="#__codelineno-85-19"></a> <span class="k">if</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-85-20" name="__codelineno-85-20" href="#__codelineno-85-20"></a> <span class="kd">let</span> <span class="nv">child</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">?</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-85-21" name="__codelineno-85-21" href="#__codelineno-85-21"></a> <span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
<a id="__codelineno-85-22" name="__codelineno-85-22" href="#__codelineno-85-22"></a> <span class="k">if</span> <span class="n">child</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-85-23" name="__codelineno-85-23" href="#__codelineno-85-23"></a> <span class="k">return</span> <span class="kc">nil</span>
<a id="__codelineno-85-24" name="__codelineno-85-24" href="#__codelineno-85-24"></a> <span class="p">}</span>
<a id="__codelineno-85-25" name="__codelineno-85-25" href="#__codelineno-85-25"></a> <span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
<a id="__codelineno-85-26" name="__codelineno-85-26" href="#__codelineno-85-26"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-85-27" name="__codelineno-85-27" href="#__codelineno-85-27"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-85-28" name="__codelineno-85-28" href="#__codelineno-85-28"></a> <span class="p">}</span>
<a id="__codelineno-85-29" name="__codelineno-85-29" href="#__codelineno-85-29"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-85-30" name="__codelineno-85-30" href="#__codelineno-85-30"></a> <span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
<a id="__codelineno-85-31" name="__codelineno-85-31" href="#__codelineno-85-31"></a> <span class="kd">var</span> <span class="nv">temp</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-85-32" name="__codelineno-85-32" href="#__codelineno-85-32"></a> <span class="k">while</span> <span class="n">temp</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-85-33" name="__codelineno-85-33" href="#__codelineno-85-33"></a> <span class="n">temp</span> <span class="p">=</span> <span class="n">temp</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-85-34" name="__codelineno-85-34" href="#__codelineno-85-34"></a> <span class="p">}</span>
<a id="__codelineno-85-35" name="__codelineno-85-35" href="#__codelineno-85-35"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">temp</span><span class="p">!.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-85-36" name="__codelineno-85-36" href="#__codelineno-85-36"></a> <span class="n">node</span><span class="p">?.</span><span class="n">val</span> <span class="p">=</span> <span class="n">temp</span><span class="p">!.</span><span class="n">val</span>
<a id="__codelineno-85-37" name="__codelineno-85-37" href="#__codelineno-85-37"></a> <span class="p">}</span>
<a id="__codelineno-85-38" name="__codelineno-85-38" href="#__codelineno-85-38"></a> <span class="p">}</span>
<a id="__codelineno-85-39" name="__codelineno-85-39" href="#__codelineno-85-39"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span> <span class="c1">// 更新节点高度</span>
<a id="__codelineno-85-40" name="__codelineno-85-40" href="#__codelineno-85-40"></a> <span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
<a id="__codelineno-85-41" name="__codelineno-85-41" href="#__codelineno-85-41"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
<a id="__codelineno-85-42" name="__codelineno-85-42" href="#__codelineno-85-42"></a> <span class="c1">// 返回子树的根节点</span>
<a id="__codelineno-85-43" name="__codelineno-85-43" href="#__codelineno-85-43"></a> <span class="k">return</span> <span class="n">node</span>
<a id="__codelineno-85-44" name="__codelineno-85-44" href="#__codelineno-85-44"></a><span class="p">}</span>
<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kd">func</span> <span class="nf">remove</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">root</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="p">}</span>
<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a>
<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="kd">func</span> <span class="nf">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a> <span class="kd">var</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">node</span>
<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a> <span class="k">if</span> <span class="n">node</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a> <span class="k">return</span> <span class="kc">nil</span>
<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a> <span class="p">}</span>
<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a> <span class="cm">/* 1. 查找节点，并删除之 */</span>
<a id="__codelineno-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></a> <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
<a id="__codelineno-85-14" name="__codelineno-85-14" href="#__codelineno-85-14"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-85-15" name="__codelineno-85-15" href="#__codelineno-85-15"></a> <span class="p">}</span> <span class="k">else</span> <span class="k">if</span> <span class="n">val</span> <span class="o">&gt;</span> <span class="n">node</span><span class="p">!.</span><span class="n">val</span> <span class="p">{</span>
<a id="__codelineno-85-16" name="__codelineno-85-16" href="#__codelineno-85-16"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-85-17" name="__codelineno-85-17" href="#__codelineno-85-17"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-85-18" name="__codelineno-85-18" href="#__codelineno-85-18"></a> <span class="k">if</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-85-19" name="__codelineno-85-19" href="#__codelineno-85-19"></a> <span class="kd">let</span> <span class="nv">child</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">?</span> <span class="n">node</span><span class="p">?.</span><span class="kr">left</span> <span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-85-20" name="__codelineno-85-20" href="#__codelineno-85-20"></a> <span class="c1">// 子节点数量 = 0 ，直接删除 node 并返回</span>
<a id="__codelineno-85-21" name="__codelineno-85-21" href="#__codelineno-85-21"></a> <span class="k">if</span> <span class="n">child</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-85-22" name="__codelineno-85-22" href="#__codelineno-85-22"></a> <span class="k">return</span> <span class="kc">nil</span>
<a id="__codelineno-85-23" name="__codelineno-85-23" href="#__codelineno-85-23"></a> <span class="p">}</span>
<a id="__codelineno-85-24" name="__codelineno-85-24" href="#__codelineno-85-24"></a> <span class="c1">// 子节点数量 = 1 ，直接删除 node</span>
<a id="__codelineno-85-25" name="__codelineno-85-25" href="#__codelineno-85-25"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-85-26" name="__codelineno-85-26" href="#__codelineno-85-26"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-85-27" name="__codelineno-85-27" href="#__codelineno-85-27"></a> <span class="p">}</span>
<a id="__codelineno-85-28" name="__codelineno-85-28" href="#__codelineno-85-28"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-85-29" name="__codelineno-85-29" href="#__codelineno-85-29"></a> <span class="c1">// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
<a id="__codelineno-85-30" name="__codelineno-85-30" href="#__codelineno-85-30"></a> <span class="kd">var</span> <span class="nv">temp</span> <span class="p">=</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-85-31" name="__codelineno-85-31" href="#__codelineno-85-31"></a> <span class="k">while</span> <span class="n">temp</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-85-32" name="__codelineno-85-32" href="#__codelineno-85-32"></a> <span class="n">temp</span> <span class="p">=</span> <span class="n">temp</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-85-33" name="__codelineno-85-33" href="#__codelineno-85-33"></a> <span class="p">}</span>
<a id="__codelineno-85-34" name="__codelineno-85-34" href="#__codelineno-85-34"></a> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">?.</span><span class="kr">right</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="n">temp</span><span class="p">!.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-85-35" name="__codelineno-85-35" href="#__codelineno-85-35"></a> <span class="n">node</span><span class="p">?.</span><span class="n">val</span> <span class="p">=</span> <span class="n">temp</span><span class="p">!.</span><span class="n">val</span>
<a id="__codelineno-85-36" name="__codelineno-85-36" href="#__codelineno-85-36"></a> <span class="p">}</span>
<a id="__codelineno-85-37" name="__codelineno-85-37" href="#__codelineno-85-37"></a> <span class="p">}</span>
<a id="__codelineno-85-38" name="__codelineno-85-38" href="#__codelineno-85-38"></a> <span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span> <span class="c1">// 更新节点高度</span>
<a id="__codelineno-85-39" name="__codelineno-85-39" href="#__codelineno-85-39"></a> <span class="cm">/* 2. 执行旋转操作，使该子树重新恢复平衡 */</span>
<a id="__codelineno-85-40" name="__codelineno-85-40" href="#__codelineno-85-40"></a> <span class="n">node</span> <span class="p">=</span> <span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">:</span> <span class="n">node</span><span class="p">)</span>
<a id="__codelineno-85-41" name="__codelineno-85-41" href="#__codelineno-85-41"></a> <span class="c1">// 返回子树的根节点</span>
<a id="__codelineno-85-42" name="__codelineno-85-42" href="#__codelineno-85-42"></a> <span class="k">return</span> <span class="n">node</span>
<a id="__codelineno-85-43" name="__codelineno-85-43" href="#__codelineno-85-43"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

113
chapter_tree/binary_search_tree/index.html
Unescape View File

@ -4495,63 +4495,62 @@
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="p">@</span><span class="n">discardableResult</span>
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="kd">func</span> <span class="nf">remove</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a> <span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a> <span class="k">if</span> <span class="n">root</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a> <span class="k">return</span>
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a> <span class="p">}</span>
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a> <span class="kd">var</span> <span class="nv">cur</span> <span class="p">=</span> <span class="n">root</span>
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a> <span class="kd">var</span> <span class="nv">pre</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?</span>
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a> <span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a> <span class="k">while</span> <span class="n">cur</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a> <span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="p">==</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a> <span class="k">break</span>
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a> <span class="p">}</span>
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a> <span class="n">pre</span> <span class="p">=</span> <span class="n">cur</span>
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a> <span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a> <span class="p">}</span>
<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a> <span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a> <span class="p">}</span>
<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a> <span class="p">}</span>
<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a> <span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a> <span class="k">if</span> <span class="n">cur</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a> <span class="k">return</span>
<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a> <span class="p">}</span>
<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a> <span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a> <span class="c1">// 当子节点数量 = 0 / 1 时， child = null / 该子节点</span>
<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a> <span class="kd">let</span> <span class="nv">child</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">?</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span> <span class="p">:</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a> <span class="c1">// 删除节点 cur</span>
<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a> <span class="k">if</span> <span class="n">cur</span> <span class="o">!==</span> <span class="n">root</span> <span class="p">{</span>
<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a> <span class="k">if</span> <span class="n">pre</span><span class="p">?.</span><span class="kr">left</span> <span class="p">===</span> <span class="n">cur</span> <span class="p">{</span>
<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a> <span class="n">pre</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a> <span class="n">pre</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-30-40" name="__codelineno-30-40" href="#__codelineno-30-40"></a> <span class="p">}</span>
<a id="__codelineno-30-41" name="__codelineno-30-41" href="#__codelineno-30-41"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-30-42" name="__codelineno-30-42" href="#__codelineno-30-42"></a> <span class="c1">// 若删除节点为根节点，则重新指定根节点</span>
<a id="__codelineno-30-43" name="__codelineno-30-43" href="#__codelineno-30-43"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-30-44" name="__codelineno-30-44" href="#__codelineno-30-44"></a> <span class="p">}</span>
<a id="__codelineno-30-45" name="__codelineno-30-45" href="#__codelineno-30-45"></a> <span class="p">}</span>
<a id="__codelineno-30-46" name="__codelineno-30-46" href="#__codelineno-30-46"></a> <span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-30-47" name="__codelineno-30-47" href="#__codelineno-30-47"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-30-48" name="__codelineno-30-48" href="#__codelineno-30-48"></a> <span class="c1">// 获取中序遍历中 cur 的下一个节点</span>
<a id="__codelineno-30-49" name="__codelineno-30-49" href="#__codelineno-30-49"></a> <span class="kd">var</span> <span class="nv">tmp</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-30-50" name="__codelineno-30-50" href="#__codelineno-30-50"></a> <span class="k">while</span> <span class="n">tmp</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-51" name="__codelineno-30-51" href="#__codelineno-30-51"></a> <span class="n">tmp</span> <span class="p">=</span> <span class="n">tmp</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-30-52" name="__codelineno-30-52" href="#__codelineno-30-52"></a> <span class="p">}</span>
<a id="__codelineno-30-53" name="__codelineno-30-53" href="#__codelineno-30-53"></a> <span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-30-54" name="__codelineno-30-54" href="#__codelineno-30-54"></a> <span class="n">remove</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="n">tmp</span><span class="p">!.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-30-55" name="__codelineno-30-55" href="#__codelineno-30-55"></a> <span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-30-56" name="__codelineno-30-56" href="#__codelineno-30-56"></a> <span class="n">cur</span><span class="p">?.</span><span class="n">val</span> <span class="p">=</span> <span class="n">tmp</span><span class="p">!.</span><span class="n">val</span>
<a id="__codelineno-30-57" name="__codelineno-30-57" href="#__codelineno-30-57"></a> <span class="p">}</span>
<a id="__codelineno-30-58" name="__codelineno-30-58" href="#__codelineno-30-58"></a><span class="p">}</span>
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span> <span class="nf">remove</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a> <span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a> <span class="k">if</span> <span class="n">root</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a> <span class="k">return</span>
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a> <span class="p">}</span>
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a> <span class="kd">var</span> <span class="nv">cur</span> <span class="p">=</span> <span class="n">root</span>
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a> <span class="kd">var</span> <span class="nv">pre</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?</span>
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a> <span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a> <span class="k">while</span> <span class="n">cur</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a> <span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="p">==</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a> <span class="k">break</span>
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a> <span class="p">}</span>
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a> <span class="n">pre</span> <span class="p">=</span> <span class="n">cur</span>
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a> <span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a> <span class="p">}</span>
<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a> <span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a> <span class="p">}</span>
<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a> <span class="p">}</span>
<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a> <span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a> <span class="k">if</span> <span class="n">cur</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a> <span class="k">return</span>
<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a> <span class="p">}</span>
<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a> <span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a> <span class="c1">// 当子节点数量 = 0 / 1 时， child = null / 该子节点</span>
<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a> <span class="kd">let</span> <span class="nv">child</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">?</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span> <span class="p">:</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a> <span class="c1">// 删除节点 cur</span>
<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a> <span class="k">if</span> <span class="n">cur</span> <span class="o">!==</span> <span class="n">root</span> <span class="p">{</span>
<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a> <span class="k">if</span> <span class="n">pre</span><span class="p">?.</span><span class="kr">left</span> <span class="p">===</span> <span class="n">cur</span> <span class="p">{</span>
<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a> <span class="n">pre</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a> <span class="n">pre</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a> <span class="p">}</span>
<a id="__codelineno-30-40" name="__codelineno-30-40" href="#__codelineno-30-40"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-30-41" name="__codelineno-30-41" href="#__codelineno-30-41"></a> <span class="c1">// 若删除节点为根节点，则重新指定根节点</span>
<a id="__codelineno-30-42" name="__codelineno-30-42" href="#__codelineno-30-42"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-30-43" name="__codelineno-30-43" href="#__codelineno-30-43"></a> <span class="p">}</span>
<a id="__codelineno-30-44" name="__codelineno-30-44" href="#__codelineno-30-44"></a> <span class="p">}</span>
<a id="__codelineno-30-45" name="__codelineno-30-45" href="#__codelineno-30-45"></a> <span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-30-46" name="__codelineno-30-46" href="#__codelineno-30-46"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-30-47" name="__codelineno-30-47" href="#__codelineno-30-47"></a> <span class="c1">// 获取中序遍历中 cur 的下一个节点</span>
<a id="__codelineno-30-48" name="__codelineno-30-48" href="#__codelineno-30-48"></a> <span class="kd">var</span> <span class="nv">tmp</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-30-49" name="__codelineno-30-49" href="#__codelineno-30-49"></a> <span class="k">while</span> <span class="n">tmp</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-30-50" name="__codelineno-30-50" href="#__codelineno-30-50"></a> <span class="n">tmp</span> <span class="p">=</span> <span class="n">tmp</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-30-51" name="__codelineno-30-51" href="#__codelineno-30-51"></a> <span class="p">}</span>
<a id="__codelineno-30-52" name="__codelineno-30-52" href="#__codelineno-30-52"></a> <span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-30-53" name="__codelineno-30-53" href="#__codelineno-30-53"></a> <span class="n">remove</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="n">tmp</span><span class="p">!.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-30-54" name="__codelineno-30-54" href="#__codelineno-30-54"></a> <span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-30-55" name="__codelineno-30-55" href="#__codelineno-30-55"></a> <span class="n">cur</span><span class="p">?.</span><span class="n">val</span> <span class="p">=</span> <span class="n">tmp</span><span class="p">!.</span><span class="n">val</span>
<a id="__codelineno-30-56" name="__codelineno-30-56" href="#__codelineno-30-56"></a> <span class="p">}</span>
<a id="__codelineno-30-57" name="__codelineno-30-57" href="#__codelineno-30-57"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">

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search/search_index.json
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sitemap.xml
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@ -2,502 +2,502 @@
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