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@ -2356,335 +2356,529 @@
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<h2 id="1314">13.1.4. 框架代码<a class="headerlink" href="#1314" title="Permanent link">¶</a></h2>
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<p>回溯算法可用于解决许多搜索问题、约束满足问题和组合优化问题。为提升代码通用性，我们希望将回溯算法的“尝试、回退、剪枝”的主体框架提炼出来。</p>
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<p>设 <code>state</code> 为问题的当前状态，<code>choices</code> 表示当前状态下可以做出的选择，则可得到以下回溯算法的框架代码。</p>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="k">def</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">):</span>
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<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w"> </span><span class="sd">"""回溯算法框架"""</span>
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<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a> <span class="c1"># 判断是否为解</span>
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<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a> <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
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<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a> <span class="c1"># 记录解</span>
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<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a> <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a> <span class="k">return</span>
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<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a> <span class="c1"># 遍历所有选择</span>
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<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a> <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
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<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a> <span class="c1"># 剪枝：判断选择是否合法</span>
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<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a> <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
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<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a> <span class="c1"># 尝试：做出选择，更新状态</span>
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<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a> <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a> <span class="c1"># 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a> <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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</code></pre></div>
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<p>下面，我们尝试基于此框架来解决例题三。在例题三中，状态 <code>state</code> 是节点遍历路径，选择 <code>choices</code> 是当前节点的左子节点和右子节点，结果 <code>res</code> 是路径列表，实现代码如下所示。</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="5:10"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Java</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Python</label><label for="__tabbed_5_4">Go</label><label for="__tabbed_5_5">JavaScript</label><label for="__tabbed_5_6">TypeScript</label><label for="__tabbed_5_7">C</label><label for="__tabbed_5_8">C#</label><label for="__tabbed_5_9">Swift</label><label for="__tabbed_5_10">Zig</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.java</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
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<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kt">boolean</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">).</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
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<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="p">}</span>
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<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a>
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<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="cm">/* 记录解 */</span>
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<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
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<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="p">}</span>
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<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a>
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<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
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<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="kt">boolean</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
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<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="p">}</span>
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<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a>
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<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="cm">/* 更新状态 */</span>
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<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="p">}</span>
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<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a>
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<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="cm">/* 恢复状态 */</span>
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<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a><span class="p">}</span>
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<a id="__codelineno-31-25" name="__codelineno-31-25" href="#__codelineno-31-25"></a>
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<a id="__codelineno-31-26" name="__codelineno-31-26" href="#__codelineno-31-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
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<a id="__codelineno-31-27" name="__codelineno-31-27" href="#__codelineno-31-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-28" name="__codelineno-31-28" href="#__codelineno-31-28"></a><span class="w"> </span><span class="c1">// 检查是否为解</span>
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<a id="__codelineno-31-29" name="__codelineno-31-29" href="#__codelineno-31-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-30" name="__codelineno-31-30" href="#__codelineno-31-30"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-31-31" name="__codelineno-31-31" href="#__codelineno-31-31"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-31-32" name="__codelineno-31-32" href="#__codelineno-31-32"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-31-33" name="__codelineno-31-33" href="#__codelineno-31-33"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-31-34" name="__codelineno-31-34" href="#__codelineno-31-34"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-31-35" name="__codelineno-31-35" href="#__codelineno-31-35"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-36" name="__codelineno-31-36" href="#__codelineno-31-36"></a><span class="w"> </span><span class="c1">// 剪枝：检查选择是否合法</span>
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<a id="__codelineno-31-37" name="__codelineno-31-37" href="#__codelineno-31-37"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-38" name="__codelineno-31-38" href="#__codelineno-31-38"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-31-39" name="__codelineno-31-39" href="#__codelineno-31-39"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-31-40" name="__codelineno-31-40" href="#__codelineno-31-40"></a><span class="w"> </span><span class="c1">// 进行下一轮选择</span>
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<a id="__codelineno-31-41" name="__codelineno-31-41" href="#__codelineno-31-41"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">choice</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">right</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-31-42" name="__codelineno-31-42" href="#__codelineno-31-42"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-31-43" name="__codelineno-31-43" href="#__codelineno-31-43"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-31-44" name="__codelineno-31-44" href="#__codelineno-31-44"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-31-45" name="__codelineno-31-45" href="#__codelineno-31-45"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-31-46" name="__codelineno-31-46" href="#__codelineno-31-46"></a><span class="p">}</span>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 回溯算法框架 */</span>
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<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Choice</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">State</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="c1">// 判断是否为解</span>
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<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w"> </span><span class="c1">// 剪枝：判断选择是否合法</span>
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<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 回溯算法框架 */</span>
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<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Choice</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">State</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="c1">// 判断是否为解</span>
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<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w"> </span><span class="c1">// 剪枝：判断选择是否合法</span>
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<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.cpp</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
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<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">empty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">back</span><span class="p">()</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
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<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="p">}</span>
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<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a>
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<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="cm">/* 记录解 */</span>
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<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*>></span><span class="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
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<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="p">}</span>
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<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a>
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<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
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<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
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<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="p">}</span>
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<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a>
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<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a><span class="cm">/* 更新状态 */</span>
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<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a><span class="p">}</span>
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<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a>
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<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a><span class="cm">/* 恢复状态 */</span>
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<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
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<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a><span class="p">}</span>
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<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a>
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<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
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<a id="__codelineno-32-27" name="__codelineno-32-27" href="#__codelineno-32-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*>></span><span class="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-28" name="__codelineno-32-28" href="#__codelineno-32-28"></a><span class="w"> </span><span class="c1">// 检查是否为解</span>
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<a id="__codelineno-32-29" name="__codelineno-32-29" href="#__codelineno-32-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-30" name="__codelineno-32-30" href="#__codelineno-32-30"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-32-31" name="__codelineno-32-31" href="#__codelineno-32-31"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-32-32" name="__codelineno-32-32" href="#__codelineno-32-32"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-32-33" name="__codelineno-32-33" href="#__codelineno-32-33"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-32-34" name="__codelineno-32-34" href="#__codelineno-32-34"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-32-35" name="__codelineno-32-35" href="#__codelineno-32-35"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-36" name="__codelineno-32-36" href="#__codelineno-32-36"></a><span class="w"> </span><span class="c1">// 剪枝：检查选择是否合法</span>
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<a id="__codelineno-32-37" name="__codelineno-32-37" href="#__codelineno-32-37"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-38" name="__codelineno-32-38" href="#__codelineno-32-38"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-32-39" name="__codelineno-32-39" href="#__codelineno-32-39"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-32-40" name="__codelineno-32-40" href="#__codelineno-32-40"></a><span class="w"> </span><span class="c1">// 进行下一轮选择</span>
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<a id="__codelineno-32-41" name="__codelineno-32-41" href="#__codelineno-32-41"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">nextChoices</span><span class="p">{</span><span class="n">choice</span><span class="o">-></span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="o">-></span><span class="n">right</span><span class="p">};</span>
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<a id="__codelineno-32-42" name="__codelineno-32-42" href="#__codelineno-32-42"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">nextChoices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-32-43" name="__codelineno-32-43" href="#__codelineno-32-43"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-32-44" name="__codelineno-32-44" href="#__codelineno-32-44"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-32-45" name="__codelineno-32-45" href="#__codelineno-32-45"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-32-46" name="__codelineno-32-46" href="#__codelineno-32-46"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-32-47" name="__codelineno-32-47" href="#__codelineno-32-47"></a><span class="p">}</span>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="k">def</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">State</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">choice</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">state</span><span class="p">])</span> <span class="o">-></span> <span class="kc">None</span><span class="p">:</span>
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<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w"> </span><span class="sd">"""回溯算法框架"""</span>
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<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a> <span class="c1"># 判断是否为解</span>
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<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a> <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
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<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a> <span class="c1"># 记录解</span>
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<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a> <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a> <span class="k">return</span>
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<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a> <span class="c1"># 遍历所有选择</span>
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<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a> <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
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<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a> <span class="c1"># 剪枝：判断选择是否合法</span>
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<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a> <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
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<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a> <span class="c1"># 尝试：做出选择，更新状态</span>
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<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a> <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a> <span class="c1"># 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a> <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.py</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="k">def</span> <span class="nf">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">])</span> <span class="o">-></span> <span class="nb">bool</span><span class="p">:</span>
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<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="w"> </span><span class="sd">"""判断当前状态是否为解"""</span>
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<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a> <span class="k">return</span> <span class="n">state</span> <span class="ow">and</span> <span class="n">state</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span>
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<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a>
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<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="k">def</span> <span class="nf">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]]):</span>
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<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w"> </span><span class="sd">"""记录解"""</span>
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<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
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<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a>
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<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="k">def</span> <span class="nf">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="o">-></span> <span class="nb">bool</span><span class="p">:</span>
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<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w"> </span><span class="sd">"""判断在当前状态下，该选择是否合法"""</span>
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<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a> <span class="k">return</span> <span class="n">choice</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">choice</span><span class="o">.</span><span class="n">val</span> <span class="o">!=</span> <span class="mi">3</span>
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<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a>
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<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="k">def</span> <span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
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<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w"> </span><span class="sd">"""更新状态"""</span>
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<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a> <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a>
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<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="k">def</span> <span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
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<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w"> </span><span class="sd">"""恢复状态"""</span>
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<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a> <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
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<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a>
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<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="k">def</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]]):</span>
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<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w"> </span><span class="sd">"""回溯算法：例题三"""</span>
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<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a> <span class="c1"># 检查是否为解</span>
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<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></a> <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
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<a id="__codelineno-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a> <span class="c1"># 记录解</span>
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<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a> <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a> <span class="k">return</span>
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<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a> <span class="c1"># 遍历所有选择</span>
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<a id="__codelineno-33-29" name="__codelineno-33-29" href="#__codelineno-33-29"></a> <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
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<a id="__codelineno-33-30" name="__codelineno-33-30" href="#__codelineno-33-30"></a> <span class="c1"># 剪枝：检查选择是否合法</span>
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<a id="__codelineno-33-31" name="__codelineno-33-31" href="#__codelineno-33-31"></a> <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
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<a id="__codelineno-33-32" name="__codelineno-33-32" href="#__codelineno-33-32"></a> <span class="c1"># 尝试：做出选择，更新状态</span>
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<a id="__codelineno-33-33" name="__codelineno-33-33" href="#__codelineno-33-33"></a> <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-33-34" name="__codelineno-33-34" href="#__codelineno-33-34"></a> <span class="c1"># 进行下一轮选择</span>
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<a id="__codelineno-33-35" name="__codelineno-33-35" href="#__codelineno-33-35"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="p">[</span><span class="n">choice</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">choice</span><span class="o">.</span><span class="n">right</span><span class="p">],</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-33-36" name="__codelineno-33-36" href="#__codelineno-33-36"></a> <span class="c1"># 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-33-37" name="__codelineno-33-37" href="#__codelineno-33-37"></a> <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 回溯算法框架 */</span>
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<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="nx">State</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="p">[]</span><span class="nx">Choice</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="nx">State</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="c1">// 判断是否为解</span>
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<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
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<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w"> </span><span class="k">return</span>
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<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></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>
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<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w"> </span><span class="c1">// 剪枝：判断选择是否合法</span>
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<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
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<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
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<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
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<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.go</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></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">isSolution</span><span class="p">}</span>
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<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
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<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></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">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a>
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<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></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">isValid</span><span class="p">}</span>
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<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a>
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<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></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">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a>
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<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></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">undoChoice</span><span class="p">}</span>
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<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a>
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<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></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>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 回溯算法框架 */</span>
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<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="c1">// 判断是否为解</span>
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<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
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<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w"> </span><span class="c1">// 剪枝：判断选择是否合法</span>
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<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
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<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
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<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
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<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-34-20" name="__codelineno-34-20" href="#__codelineno-34-20"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.js</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
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<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
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<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a>
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<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
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<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a>
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<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a>
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<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
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<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a>
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<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 回溯算法框架 */</span>
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<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">State</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">Choice</span><span class="p">[],</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">State</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="c1">// 判断是否为解</span>
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<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
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<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w"> </span><span class="c1">// 剪枝：判断选择是否合法</span>
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<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
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<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
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<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
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<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.ts</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="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
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<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
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<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a>
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<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
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<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a>
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<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a>
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<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
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<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a>
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<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 回溯算法框架 */</span>
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<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">Choice</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numChoices</span><span class="p">,</span><span class="w"> </span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numRes</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="c1">// 判断是否为解</span>
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<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">numRes</span><span class="p">);</span>
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<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">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="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">numChoices</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="w"> </span><span class="c1">// 剪枝：判断选择是否合法</span>
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<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
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<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">numChoices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">numRes</span><span class="p">);</span>
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<a id="__codelineno-36-16" name="__codelineno-36-16" href="#__codelineno-36-16"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-36-17" name="__codelineno-36-17" href="#__codelineno-36-17"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
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<a id="__codelineno-36-18" name="__codelineno-36-18" href="#__codelineno-36-18"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-36-19" name="__codelineno-36-19" href="#__codelineno-36-19"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-36-20" name="__codelineno-36-20" href="#__codelineno-36-20"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.c</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></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">isSolution</span><span class="p">}</span>
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<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
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<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></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">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a>
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<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></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">isValid</span><span class="p">}</span>
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<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a>
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<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></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">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a>
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<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></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">undoChoice</span><span class="p">}</span>
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<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a>
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<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></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">backtrack</span><span class="p">}</span>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 回溯算法框架 */</span>
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<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Choice</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">State</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="c1">// 判断是否为解</span>
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<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w"> </span><span class="c1">// 剪枝：判断选择是否合法</span>
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<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.cs</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
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<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="o">^</span><span class="m">1</span><span class="p">].</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">;</span>
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<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="p">}</span>
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<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
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<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="cm">/* 记录解 */</span>
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<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="k">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
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<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="p">}</span>
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<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a>
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<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
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<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
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<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="p">}</span>
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<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a>
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<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a><span class="cm">/* 更新状态 */</span>
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<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a><span class="k">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 回溯算法框架 */</span>
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<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kd">func</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="n">State</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="p">[</span><span class="n">Choice</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="n">State</span><span class="p">])</span> <span class="p">{</span>
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<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a> <span class="c1">// 判断是否为解</span>
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<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a> <span class="k">if</span> <span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a> <span class="c1">// 记录解</span>
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<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a> <span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a> <span class="k">return</span>
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<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a> <span class="p">}</span>
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<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a> <span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a> <span class="k">for</span> <span class="n">choice</span> <span class="k">in</span> <span class="n">choices</span> <span class="p">{</span>
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<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a> <span class="c1">// 剪枝：判断选择是否合法</span>
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<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a> <span class="k">if</span> <span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">choice</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a> <span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a> <span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a> <span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a> <span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a> <span class="p">}</span>
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<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a> <span class="p">}</span>
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<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a>
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<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a><span class="cm">/* 恢复状态 */</span>
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<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a><span class="k">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-23" name="__codelineno-38-23" href="#__codelineno-38-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
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<a id="__codelineno-38-24" name="__codelineno-38-24" href="#__codelineno-38-24"></a><span class="p">}</span>
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<a id="__codelineno-38-25" name="__codelineno-38-25" href="#__codelineno-38-25"></a>
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<a id="__codelineno-38-26" name="__codelineno-38-26" href="#__codelineno-38-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
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<a id="__codelineno-38-27" name="__codelineno-38-27" href="#__codelineno-38-27"></a><span class="k">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-28" name="__codelineno-38-28" href="#__codelineno-38-28"></a><span class="w"> </span><span class="c1">// 检查是否为解</span>
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<a id="__codelineno-38-29" name="__codelineno-38-29" href="#__codelineno-38-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-30" name="__codelineno-38-30" href="#__codelineno-38-30"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-38-31" name="__codelineno-38-31" href="#__codelineno-38-31"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-38-32" name="__codelineno-38-32" href="#__codelineno-38-32"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-38-33" name="__codelineno-38-33" href="#__codelineno-38-33"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-38-34" name="__codelineno-38-34" href="#__codelineno-38-34"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-38-35" name="__codelineno-38-35" href="#__codelineno-38-35"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-36" name="__codelineno-38-36" href="#__codelineno-38-36"></a><span class="w"> </span><span class="c1">// 剪枝：检查选择是否合法</span>
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<a id="__codelineno-38-37" name="__codelineno-38-37" href="#__codelineno-38-37"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-38" name="__codelineno-38-38" href="#__codelineno-38-38"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-38-39" name="__codelineno-38-39" href="#__codelineno-38-39"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-38-40" name="__codelineno-38-40" href="#__codelineno-38-40"></a><span class="w"> </span><span class="c1">// 进行下一轮选择</span>
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<a id="__codelineno-38-41" name="__codelineno-38-41" href="#__codelineno-38-41"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-38-42" name="__codelineno-38-42" href="#__codelineno-38-42"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-38-43" name="__codelineno-38-43" href="#__codelineno-38-43"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-38-44" name="__codelineno-38-44" href="#__codelineno-38-44"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-38-45" name="__codelineno-38-45" href="#__codelineno-38-45"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-38-46" name="__codelineno-38-46" href="#__codelineno-38-46"></a><span class="p">}</span>
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<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.swift</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
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<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="kd">func</span> <span class="nf">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">])</span> <span class="p">-></span> <span class="nb">Bool</span> <span class="p">{</span>
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<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a> <span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="bp">isEmpty</span> <span class="o">&&</span> <span class="n">state</span><span class="p">.</span><span class="bp">last</span><span class="p">!.</span><span class="n">val</span> <span class="p">==</span> <span class="mi">7</span>
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<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="p">}</span>
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<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>
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<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="cm">/* 记录解 */</span>
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<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="kd">func</span> <span class="nf">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">[</span><span class="n">TreeNode</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="n">TreeNode</span><span class="p">]])</span> <span class="p">{</span>
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<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a> <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
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<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="p">}</span>
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<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>
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<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
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<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a><span class="kd">func</span> <span class="nf">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?)</span> <span class="p">-></span> <span class="nb">Bool</span> <span class="p">{</span>
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<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a> <span class="n">choice</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="o">&&</span> <span class="n">choice</span><span class="p">!.</span><span class="n">val</span> <span class="o">!=</span> <span class="mi">3</span>
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<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a><span class="p">}</span>
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<a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a>
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<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a><span class="cm">/* 更新状态 */</span>
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<a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a><span class="kd">func</span> <span class="nf">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a> <span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-39-19" name="__codelineno-39-19" href="#__codelineno-39-19"></a><span class="p">}</span>
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<a id="__codelineno-39-20" name="__codelineno-39-20" href="#__codelineno-39-20"></a>
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<a id="__codelineno-39-21" name="__codelineno-39-21" href="#__codelineno-39-21"></a><span class="cm">/* 恢复状态 */</span>
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<a id="__codelineno-39-22" name="__codelineno-39-22" href="#__codelineno-39-22"></a><span class="kd">func</span> <span class="nf">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-39-23" name="__codelineno-39-23" href="#__codelineno-39-23"></a> <span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
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<a id="__codelineno-39-24" name="__codelineno-39-24" href="#__codelineno-39-24"></a><span class="p">}</span>
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<a id="__codelineno-39-25" name="__codelineno-39-25" href="#__codelineno-39-25"></a>
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<a id="__codelineno-39-26" name="__codelineno-39-26" href="#__codelineno-39-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
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<a id="__codelineno-39-27" name="__codelineno-39-27" href="#__codelineno-39-27"></a><span class="kd">func</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="p">[</span><span class="n">TreeNode</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="n">TreeNode</span><span class="p">]])</span> <span class="p">{</span>
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<a id="__codelineno-39-28" name="__codelineno-39-28" href="#__codelineno-39-28"></a> <span class="c1">// 检查是否为解</span>
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<a id="__codelineno-39-29" name="__codelineno-39-29" href="#__codelineno-39-29"></a> <span class="k">if</span> <span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-39-30" name="__codelineno-39-30" href="#__codelineno-39-30"></a> <span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-39-31" name="__codelineno-39-31" href="#__codelineno-39-31"></a> <span class="k">return</span>
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<a id="__codelineno-39-32" name="__codelineno-39-32" href="#__codelineno-39-32"></a> <span class="p">}</span>
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<a id="__codelineno-39-33" name="__codelineno-39-33" href="#__codelineno-39-33"></a> <span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-39-34" name="__codelineno-39-34" href="#__codelineno-39-34"></a> <span class="k">for</span> <span class="n">choice</span> <span class="k">in</span> <span class="n">choices</span> <span class="p">{</span>
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<a id="__codelineno-39-35" name="__codelineno-39-35" href="#__codelineno-39-35"></a> <span class="c1">// 剪枝：检查选择是否合法</span>
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<a id="__codelineno-39-36" name="__codelineno-39-36" href="#__codelineno-39-36"></a> <span class="k">if</span> <span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">choice</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-39-37" name="__codelineno-39-37" href="#__codelineno-39-37"></a> <span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-39-38" name="__codelineno-39-38" href="#__codelineno-39-38"></a> <span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-39-39" name="__codelineno-39-39" href="#__codelineno-39-39"></a> <span class="c1">// 进行下一轮选择</span>
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<a id="__codelineno-39-40" name="__codelineno-39-40" href="#__codelineno-39-40"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="p">[</span><span class="n">choice</span><span class="p">.</span><span class="kr">left</span><span class="p">,</span> <span class="n">choice</span><span class="p">.</span><span class="kr">right</span><span class="p">].</span><span class="n">compactMap</span> <span class="p">{</span> <span class="nv">$0</span> <span class="p">},</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-39-41" name="__codelineno-39-41" href="#__codelineno-39-41"></a> <span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-39-42" name="__codelineno-39-42" href="#__codelineno-39-42"></a> <span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-39-43" name="__codelineno-39-43" href="#__codelineno-39-43"></a> <span class="p">}</span>
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<a id="__codelineno-39-44" name="__codelineno-39-44" href="#__codelineno-39-44"></a> <span class="p">}</span>
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<a id="__codelineno-39-45" name="__codelineno-39-45" href="#__codelineno-39-45"></a><span class="p">}</span>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a>
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</code></pre></div>
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</div>
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</div>
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</div>
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<p>下面，我们尝试基于此框架来解决例题三。在例题三中，状态 <code>state</code> 是节点遍历路径，选择 <code>choices</code> 是当前节点的左子节点和右子节点，结果 <code>res</code> 是路径列表，实现代码如下所示。</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="6:10"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Java</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Python</label><label for="__tabbed_6_4">Go</label><label for="__tabbed_6_5">JavaScript</label><label for="__tabbed_6_6">TypeScript</label><label for="__tabbed_6_7">C</label><label for="__tabbed_6_8">C#</label><label for="__tabbed_6_9">Swift</label><label for="__tabbed_6_10">Zig</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.zig</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></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">isSolution</span><span class="p">}</span>
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<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a>
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<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></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">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a>
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<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></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">isValid</span><span class="p">}</span>
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<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a>
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<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></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">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a>
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<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></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">undoChoice</span><span class="p">}</span>
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.java</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
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<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">boolean</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">).</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
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<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="p">}</span>
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<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a>
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<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="cm">/* 记录解 */</span>
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<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
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<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="p">}</span>
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<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a>
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<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></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">backtrack</span><span class="p">}</span>
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<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
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<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="kt">boolean</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
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<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="p">}</span>
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<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a>
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<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="cm">/* 更新状态 */</span>
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<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="p">}</span>
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<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a>
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<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="cm">/* 恢复状态 */</span>
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<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-23" name="__codelineno-40-23" href="#__codelineno-40-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-40-24" name="__codelineno-40-24" href="#__codelineno-40-24"></a><span class="p">}</span>
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<a id="__codelineno-40-25" name="__codelineno-40-25" href="#__codelineno-40-25"></a>
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<a id="__codelineno-40-26" name="__codelineno-40-26" href="#__codelineno-40-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
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<a id="__codelineno-40-27" name="__codelineno-40-27" href="#__codelineno-40-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-28" name="__codelineno-40-28" href="#__codelineno-40-28"></a><span class="w"> </span><span class="c1">// 检查是否为解</span>
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<a id="__codelineno-40-29" name="__codelineno-40-29" href="#__codelineno-40-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-30" name="__codelineno-40-30" href="#__codelineno-40-30"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-40-31" name="__codelineno-40-31" href="#__codelineno-40-31"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-40-32" name="__codelineno-40-32" href="#__codelineno-40-32"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-40-33" name="__codelineno-40-33" href="#__codelineno-40-33"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-40-34" name="__codelineno-40-34" href="#__codelineno-40-34"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-40-35" name="__codelineno-40-35" href="#__codelineno-40-35"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-36" name="__codelineno-40-36" href="#__codelineno-40-36"></a><span class="w"> </span><span class="c1">// 剪枝：检查选择是否合法</span>
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<a id="__codelineno-40-37" name="__codelineno-40-37" href="#__codelineno-40-37"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-40-38" name="__codelineno-40-38" href="#__codelineno-40-38"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-40-39" name="__codelineno-40-39" href="#__codelineno-40-39"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-40-40" name="__codelineno-40-40" href="#__codelineno-40-40"></a><span class="w"> </span><span class="c1">// 进行下一轮选择</span>
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<a id="__codelineno-40-41" name="__codelineno-40-41" href="#__codelineno-40-41"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">choice</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">right</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-40-42" name="__codelineno-40-42" href="#__codelineno-40-42"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-40-43" name="__codelineno-40-43" href="#__codelineno-40-43"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-40-44" name="__codelineno-40-44" href="#__codelineno-40-44"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-40-45" name="__codelineno-40-45" href="#__codelineno-40-45"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-40-46" name="__codelineno-40-46" href="#__codelineno-40-46"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.cpp</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
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<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">empty</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">back</span><span class="p">()</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
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<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="p">}</span>
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<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a>
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<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="cm">/* 记录解 */</span>
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<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*>></span><span class="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
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<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="p">}</span>
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<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a>
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<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
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<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
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<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="p">}</span>
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<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a>
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<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="cm">/* 更新状态 */</span>
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<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a><span class="p">}</span>
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<a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a>
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<a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></a><span class="cm">/* 恢复状态 */</span>
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<a id="__codelineno-41-22" name="__codelineno-41-22" href="#__codelineno-41-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-23" name="__codelineno-41-23" href="#__codelineno-41-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
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<a id="__codelineno-41-24" name="__codelineno-41-24" href="#__codelineno-41-24"></a><span class="p">}</span>
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<a id="__codelineno-41-25" name="__codelineno-41-25" href="#__codelineno-41-25"></a>
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<a id="__codelineno-41-26" name="__codelineno-41-26" href="#__codelineno-41-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
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<a id="__codelineno-41-27" name="__codelineno-41-27" href="#__codelineno-41-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*>></span><span class="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-28" name="__codelineno-41-28" href="#__codelineno-41-28"></a><span class="w"> </span><span class="c1">// 检查是否为解</span>
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<a id="__codelineno-41-29" name="__codelineno-41-29" href="#__codelineno-41-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-30" name="__codelineno-41-30" href="#__codelineno-41-30"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-41-31" name="__codelineno-41-31" href="#__codelineno-41-31"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-41-32" name="__codelineno-41-32" href="#__codelineno-41-32"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-41-33" name="__codelineno-41-33" href="#__codelineno-41-33"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-41-34" name="__codelineno-41-34" href="#__codelineno-41-34"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-41-35" name="__codelineno-41-35" href="#__codelineno-41-35"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-36" name="__codelineno-41-36" href="#__codelineno-41-36"></a><span class="w"> </span><span class="c1">// 剪枝：检查选择是否合法</span>
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<a id="__codelineno-41-37" name="__codelineno-41-37" href="#__codelineno-41-37"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-38" name="__codelineno-41-38" href="#__codelineno-41-38"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-41-39" name="__codelineno-41-39" href="#__codelineno-41-39"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-41-40" name="__codelineno-41-40" href="#__codelineno-41-40"></a><span class="w"> </span><span class="c1">// 进行下一轮选择</span>
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<a id="__codelineno-41-41" name="__codelineno-41-41" href="#__codelineno-41-41"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">nextChoices</span><span class="p">{</span><span class="n">choice</span><span class="o">-></span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="o">-></span><span class="n">right</span><span class="p">};</span>
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<a id="__codelineno-41-42" name="__codelineno-41-42" href="#__codelineno-41-42"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">nextChoices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-41-43" name="__codelineno-41-43" href="#__codelineno-41-43"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-41-44" name="__codelineno-41-44" href="#__codelineno-41-44"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-41-45" name="__codelineno-41-45" href="#__codelineno-41-45"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-41-46" name="__codelineno-41-46" href="#__codelineno-41-46"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-41-47" name="__codelineno-41-47" href="#__codelineno-41-47"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span> <span class="nf">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">])</span> <span class="o">-></span> <span class="nb">bool</span><span class="p">:</span>
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<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="sd">"""判断当前状态是否为解"""</span>
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<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a> <span class="k">return</span> <span class="n">state</span> <span class="ow">and</span> <span class="n">state</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span>
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<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>
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<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="k">def</span> <span class="nf">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]]):</span>
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<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w"> </span><span class="sd">"""记录解"""</span>
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<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
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<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>
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<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="k">def</span> <span class="nf">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="o">-></span> <span class="nb">bool</span><span class="p">:</span>
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<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w"> </span><span class="sd">"""判断在当前状态下，该选择是否合法"""</span>
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<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a> <span class="k">return</span> <span class="n">choice</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">choice</span><span class="o">.</span><span class="n">val</span> <span class="o">!=</span> <span class="mi">3</span>
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<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a>
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<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="k">def</span> <span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
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<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="w"> </span><span class="sd">"""更新状态"""</span>
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<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a> <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a>
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<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a><span class="k">def</span> <span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
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<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a><span class="w"> </span><span class="sd">"""恢复状态"""</span>
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<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a> <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
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<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a>
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<a id="__codelineno-42-21" name="__codelineno-42-21" href="#__codelineno-42-21"></a><span class="k">def</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]]):</span>
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<a id="__codelineno-42-22" name="__codelineno-42-22" href="#__codelineno-42-22"></a><span class="w"> </span><span class="sd">"""回溯算法：例题三"""</span>
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<a id="__codelineno-42-23" name="__codelineno-42-23" href="#__codelineno-42-23"></a> <span class="c1"># 检查是否为解</span>
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<a id="__codelineno-42-24" name="__codelineno-42-24" href="#__codelineno-42-24"></a> <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
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<a id="__codelineno-42-25" name="__codelineno-42-25" href="#__codelineno-42-25"></a> <span class="c1"># 记录解</span>
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<a id="__codelineno-42-26" name="__codelineno-42-26" href="#__codelineno-42-26"></a> <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-42-27" name="__codelineno-42-27" href="#__codelineno-42-27"></a> <span class="k">return</span>
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<a id="__codelineno-42-28" name="__codelineno-42-28" href="#__codelineno-42-28"></a> <span class="c1"># 遍历所有选择</span>
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<a id="__codelineno-42-29" name="__codelineno-42-29" href="#__codelineno-42-29"></a> <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
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<a id="__codelineno-42-30" name="__codelineno-42-30" href="#__codelineno-42-30"></a> <span class="c1"># 剪枝：检查选择是否合法</span>
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<a id="__codelineno-42-31" name="__codelineno-42-31" href="#__codelineno-42-31"></a> <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
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<a id="__codelineno-42-32" name="__codelineno-42-32" href="#__codelineno-42-32"></a> <span class="c1"># 尝试：做出选择，更新状态</span>
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<a id="__codelineno-42-33" name="__codelineno-42-33" href="#__codelineno-42-33"></a> <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-42-34" name="__codelineno-42-34" href="#__codelineno-42-34"></a> <span class="c1"># 进行下一轮选择</span>
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<a id="__codelineno-42-35" name="__codelineno-42-35" href="#__codelineno-42-35"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="p">[</span><span class="n">choice</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">choice</span><span class="o">.</span><span class="n">right</span><span class="p">],</span> <span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-42-36" name="__codelineno-42-36" href="#__codelineno-42-36"></a> <span class="c1"># 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-42-37" name="__codelineno-42-37" href="#__codelineno-42-37"></a> <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></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">isSolution</span><span class="p">}</span>
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<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a>
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<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></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">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a>
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<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></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">isValid</span><span class="p">}</span>
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<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a>
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<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></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">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a>
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<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></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">undoChoice</span><span class="p">}</span>
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<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a>
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<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></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>
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</code></pre></div>
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</div>
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.js</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
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<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a>
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<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a>
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<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
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<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a>
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<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a>
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<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
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<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a>
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<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.ts</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
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<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a>
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<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a>
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<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
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<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a>
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<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a>
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<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
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<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a>
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<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
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</code></pre></div>
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.c</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></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">isSolution</span><span class="p">}</span>
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<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a>
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<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></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">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a>
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<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></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">isValid</span><span class="p">}</span>
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<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a>
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<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></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">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a>
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<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></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">undoChoice</span><span class="p">}</span>
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<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a>
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<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></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">backtrack</span><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.cs</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
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<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">state</span><span class="p">[</span><span class="o">^</span><span class="m">1</span><span class="p">].</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span><span class="p">;</span>
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<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="p">}</span>
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<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a>
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<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="cm">/* 记录解 */</span>
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<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="k">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
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<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="p">}</span>
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<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a>
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<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
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<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
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<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="p">}</span>
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<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a>
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<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="cm">/* 更新状态 */</span>
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<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="k">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="p">}</span>
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<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a>
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<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="cm">/* 恢复状态 */</span>
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<a id="__codelineno-47-22" name="__codelineno-47-22" href="#__codelineno-47-22"></a><span class="k">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-47-23" name="__codelineno-47-23" href="#__codelineno-47-23"></a><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
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<a id="__codelineno-47-24" name="__codelineno-47-24" href="#__codelineno-47-24"></a><span class="p">}</span>
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<a id="__codelineno-47-25" name="__codelineno-47-25" href="#__codelineno-47-25"></a>
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<a id="__codelineno-47-26" name="__codelineno-47-26" href="#__codelineno-47-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
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<a id="__codelineno-47-27" name="__codelineno-47-27" href="#__codelineno-47-27"></a><span class="k">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-47-28" name="__codelineno-47-28" href="#__codelineno-47-28"></a><span class="w"> </span><span class="c1">// 检查是否为解</span>
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<a id="__codelineno-47-29" name="__codelineno-47-29" href="#__codelineno-47-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-47-30" name="__codelineno-47-30" href="#__codelineno-47-30"></a><span class="w"> </span><span class="c1">// 记录解</span>
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<a id="__codelineno-47-31" name="__codelineno-47-31" href="#__codelineno-47-31"></a><span class="w"> </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-47-32" name="__codelineno-47-32" href="#__codelineno-47-32"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-47-33" name="__codelineno-47-33" href="#__codelineno-47-33"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-47-34" name="__codelineno-47-34" href="#__codelineno-47-34"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-47-35" name="__codelineno-47-35" href="#__codelineno-47-35"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-47-36" name="__codelineno-47-36" href="#__codelineno-47-36"></a><span class="w"> </span><span class="c1">// 剪枝：检查选择是否合法</span>
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<a id="__codelineno-47-37" name="__codelineno-47-37" href="#__codelineno-47-37"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-47-38" name="__codelineno-47-38" href="#__codelineno-47-38"></a><span class="w"> </span><span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-47-39" name="__codelineno-47-39" href="#__codelineno-47-39"></a><span class="w"> </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-47-40" name="__codelineno-47-40" href="#__codelineno-47-40"></a><span class="w"> </span><span class="c1">// 进行下一轮选择</span>
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<a id="__codelineno-47-41" name="__codelineno-47-41" href="#__codelineno-47-41"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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<a id="__codelineno-47-42" name="__codelineno-47-42" href="#__codelineno-47-42"></a><span class="w"> </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-47-43" name="__codelineno-47-43" href="#__codelineno-47-43"></a><span class="w"> </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
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<a id="__codelineno-47-44" name="__codelineno-47-44" href="#__codelineno-47-44"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-47-45" name="__codelineno-47-45" href="#__codelineno-47-45"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-47-46" name="__codelineno-47-46" href="#__codelineno-47-46"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.swift</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
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<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="kd">func</span> <span class="nf">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">])</span> <span class="p">-></span> <span class="nb">Bool</span> <span class="p">{</span>
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<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a> <span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="bp">isEmpty</span> <span class="o">&&</span> <span class="n">state</span><span class="p">.</span><span class="bp">last</span><span class="p">!.</span><span class="n">val</span> <span class="p">==</span> <span class="mi">7</span>
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<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="p">}</span>
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<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a>
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<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="cm">/* 记录解 */</span>
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<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="kd">func</span> <span class="nf">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">[</span><span class="n">TreeNode</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="n">TreeNode</span><span class="p">]])</span> <span class="p">{</span>
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<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a> <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
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<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="p">}</span>
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<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a>
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<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
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<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="kd">func</span> <span class="nf">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?)</span> <span class="p">-></span> <span class="nb">Bool</span> <span class="p">{</span>
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<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a> <span class="n">choice</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="o">&&</span> <span class="n">choice</span><span class="p">!.</span><span class="n">val</span> <span class="o">!=</span> <span class="mi">3</span>
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<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="p">}</span>
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<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a>
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<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="cm">/* 更新状态 */</span>
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<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="kd">func</span> <span class="nf">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a> <span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="p">}</span>
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<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a>
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<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a><span class="cm">/* 恢复状态 */</span>
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<a id="__codelineno-48-22" name="__codelineno-48-22" href="#__codelineno-48-22"></a><span class="kd">func</span> <span class="nf">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-48-23" name="__codelineno-48-23" href="#__codelineno-48-23"></a> <span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
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<a id="__codelineno-48-24" name="__codelineno-48-24" href="#__codelineno-48-24"></a><span class="p">}</span>
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<a id="__codelineno-48-25" name="__codelineno-48-25" href="#__codelineno-48-25"></a>
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<a id="__codelineno-48-26" name="__codelineno-48-26" href="#__codelineno-48-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
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<a id="__codelineno-48-27" name="__codelineno-48-27" href="#__codelineno-48-27"></a><span class="kd">func</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="p">[</span><span class="n">TreeNode</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="n">TreeNode</span><span class="p">]])</span> <span class="p">{</span>
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<a id="__codelineno-48-28" name="__codelineno-48-28" href="#__codelineno-48-28"></a> <span class="c1">// 检查是否为解</span>
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<a id="__codelineno-48-29" name="__codelineno-48-29" href="#__codelineno-48-29"></a> <span class="k">if</span> <span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-48-30" name="__codelineno-48-30" href="#__codelineno-48-30"></a> <span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-48-31" name="__codelineno-48-31" href="#__codelineno-48-31"></a> <span class="k">return</span>
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<a id="__codelineno-48-32" name="__codelineno-48-32" href="#__codelineno-48-32"></a> <span class="p">}</span>
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<a id="__codelineno-48-33" name="__codelineno-48-33" href="#__codelineno-48-33"></a> <span class="c1">// 遍历所有选择</span>
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<a id="__codelineno-48-34" name="__codelineno-48-34" href="#__codelineno-48-34"></a> <span class="k">for</span> <span class="n">choice</span> <span class="k">in</span> <span class="n">choices</span> <span class="p">{</span>
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<a id="__codelineno-48-35" name="__codelineno-48-35" href="#__codelineno-48-35"></a> <span class="c1">// 剪枝：检查选择是否合法</span>
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<a id="__codelineno-48-36" name="__codelineno-48-36" href="#__codelineno-48-36"></a> <span class="k">if</span> <span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">choice</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-48-37" name="__codelineno-48-37" href="#__codelineno-48-37"></a> <span class="c1">// 尝试：做出选择，更新状态</span>
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<a id="__codelineno-48-38" name="__codelineno-48-38" href="#__codelineno-48-38"></a> <span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-48-39" name="__codelineno-48-39" href="#__codelineno-48-39"></a> <span class="c1">// 进行下一轮选择</span>
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<a id="__codelineno-48-40" name="__codelineno-48-40" href="#__codelineno-48-40"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="p">[</span><span class="n">choice</span><span class="p">.</span><span class="kr">left</span><span class="p">,</span> <span class="n">choice</span><span class="p">.</span><span class="kr">right</span><span class="p">].</span><span class="n">compactMap</span> <span class="p">{</span> <span class="nv">$0</span> <span class="p">},</span> <span class="n">res</span><span class="p">:</span> <span class="p">&</span><span class="n">res</span><span class="p">)</span>
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<a id="__codelineno-48-41" name="__codelineno-48-41" href="#__codelineno-48-41"></a> <span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
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<a id="__codelineno-48-42" name="__codelineno-48-42" href="#__codelineno-48-42"></a> <span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">choice</span><span class="p">)</span>
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<a id="__codelineno-48-43" name="__codelineno-48-43" href="#__codelineno-48-43"></a> <span class="p">}</span>
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<a id="__codelineno-48-44" name="__codelineno-48-44" href="#__codelineno-48-44"></a> <span class="p">}</span>
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<a id="__codelineno-48-45" name="__codelineno-48-45" href="#__codelineno-48-45"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">preorder_traversal_iii_template.zig</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></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">isSolution</span><span class="p">}</span>
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<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a>
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<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></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">recordSolution</span><span class="p">}</span>
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<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a>
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<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></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">isValid</span><span class="p">}</span>
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<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a>
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<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></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">makeChoice</span><span class="p">}</span>
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<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a>
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<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></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">undoChoice</span><span class="p">}</span>
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<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a>
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<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></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">backtrack</span><span class="p">}</span>
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</code></pre></div>
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</div>
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</div>
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</div>
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<p>相较于基于前序遍历的实现代码，基于回溯算法框架的实现代码虽然显得啰嗦，但通用性更好，适用于各种不同的回溯算法问题。实际上，<strong>所有回溯问题都可以在该框架下解决</strong>。我们只需要根据问题特点来定义框架中的各个变量，实现各个方法即可。</p>
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<p>相较于基于前序遍历的实现代码，基于回溯算法框架的实现代码虽然显得啰嗦，但通用性更好。实际上，<strong>所有回溯问题都可以在该框架下解决</strong>。我们需要根据具体问题来定义 <code>state</code> 和 <code>choices</code> ，并实现框架中的各个方法。</p>
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<h2 id="1315">13.1.5. 典型例题<a class="headerlink" href="#1315" title="Permanent link">¶</a></h2>
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<p><strong>搜索问题</strong>：这类问题的目标是找到满足特定条件的解决方案。</p>
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<ul>
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krahets
2 years ago
