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krahets 1 year ago
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commit da4a01aa93
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chapter_array_and_linkedlist/list/index.html
Unescape View File

@ -2813,7 +2813,7 @@
<a id="__codelineno-66-78" name="__codelineno-66-78" href="#__codelineno-66-78"></a>
<a id="__codelineno-66-79" name="__codelineno-66-79" href="#__codelineno-66-79"></a><span class="w"> </span><span class="cm">/* 列表扩容 */</span>
<a id="__codelineno-66-80" name="__codelineno-66-80" href="#__codelineno-66-80"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-66-81" name="__codelineno-66-81" href="#__codelineno-66-81"></a><span class="w"> </span><span class="c1">// 新建一个长度为 size 的数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-66-81" name="__codelineno-66-81" href="#__codelineno-66-81"></a><span class="w"> </span><span class="c1">// 新建一个长度为原数组 extendRatio 倍的新数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-66-82" name="__codelineno-66-82" href="#__codelineno-66-82"></a><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">copyOf</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">);</span>
<a id="__codelineno-66-83" name="__codelineno-66-83" href="#__codelineno-66-83"></a><span class="w"> </span><span class="c1">// 更新列表容量</span>
<a id="__codelineno-66-84" name="__codelineno-66-84" href="#__codelineno-66-84"></a><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
@ -2920,7 +2920,7 @@
<a id="__codelineno-67-85" name="__codelineno-67-85" href="#__codelineno-67-85"></a>
<a id="__codelineno-67-86" name="__codelineno-67-86" href="#__codelineno-67-86"></a><span class="w"> </span><span class="cm">/* 列表扩容 */</span>
<a id="__codelineno-67-87" name="__codelineno-67-87" href="#__codelineno-67-87"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-67-88" name="__codelineno-67-88" href="#__codelineno-67-88"></a><span class="w"> </span><span class="c1">// 新建一个长度为 size * extendRatio 的数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-67-88" name="__codelineno-67-88" href="#__codelineno-67-88"></a><span class="w"> </span><span class="c1">// 新建一个长度为原数组 extendRatio 倍的新数组</span>
<a id="__codelineno-67-89" name="__codelineno-67-89" href="#__codelineno-67-89"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">newCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
<a id="__codelineno-67-90" name="__codelineno-67-90" href="#__codelineno-67-90"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
<a id="__codelineno-67-91" name="__codelineno-67-91" href="#__codelineno-67-91"></a><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">newCapacity</span><span class="p">];</span>
@ -3014,7 +3014,7 @@
<a id="__codelineno-68-66" name="__codelineno-68-66" href="#__codelineno-68-66"></a>
<a id="__codelineno-68-67" name="__codelineno-68-67" href="#__codelineno-68-67"></a> <span class="k">def</span> <span class="nf">extend_capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-68-68" name="__codelineno-68-68" href="#__codelineno-68-68"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;列表扩容&quot;&quot;&quot;</span>
<a id="__codelineno-68-69" name="__codelineno-68-69" href="#__codelineno-68-69"></a> <span class="c1"># 新建一个长度为 self.__size 的数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-68-69" name="__codelineno-68-69" href="#__codelineno-68-69"></a> <span class="c1"># 新建一个长度为原数组 __extend_ratio 倍的新数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-68-70" name="__codelineno-68-70" href="#__codelineno-68-70"></a> <span class="bp">self</span><span class="o">.</span><span class="n">__nums</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__nums</span> <span class="o">+</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__extend_ratio</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-68-71" name="__codelineno-68-71" href="#__codelineno-68-71"></a> <span class="c1"># 更新列表容量</span>
<a id="__codelineno-68-72" name="__codelineno-68-72" href="#__codelineno-68-72"></a> <span class="bp">self</span><span class="o">.</span><span class="n">__capacity</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__nums</span><span class="p">)</span>
@ -3117,7 +3117,7 @@
<a id="__codelineno-69-90" name="__codelineno-69-90" href="#__codelineno-69-90"></a>
<a id="__codelineno-69-91" name="__codelineno-69-91" href="#__codelineno-69-91"></a><span class="cm">/* 列表扩容 */</span>
<a id="__codelineno-69-92" name="__codelineno-69-92" href="#__codelineno-69-92"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o">*</span><span class="nx">myList</span><span class="p">)</span><span class="w"> </span><span class="nx">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-69-93" name="__codelineno-69-93" href="#__codelineno-69-93"></a><span class="w"> </span><span class="c1">// 新建一个长度为 self.__size 的数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-69-93" name="__codelineno-69-93" href="#__codelineno-69-93"></a><span class="w"> </span><span class="c1">// 新建一个长度为原数组 extendRatio 倍的新数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-69-94" name="__codelineno-69-94" href="#__codelineno-69-94"></a><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">l</span><span class="p">.</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">numsCapacity</span><span class="o">*</span><span class="p">(</span><span class="nx">l</span><span class="p">.</span><span class="nx">extendRatio</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">...</span><span class="p">)</span>
<a id="__codelineno-69-95" name="__codelineno-69-95" href="#__codelineno-69-95"></a><span class="w"> </span><span class="c1">// 更新列表容量</span>
<a id="__codelineno-69-96" name="__codelineno-69-96" href="#__codelineno-69-96"></a><span class="w"> </span><span class="nx">l</span><span class="p">.</span><span class="nx">numsCapacity</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">l</span><span class="p">.</span><span class="nx">nums</span><span class="p">)</span>
@ -3209,7 +3209,7 @@
<a id="__codelineno-70-76" name="__codelineno-70-76" href="#__codelineno-70-76"></a>
<a id="__codelineno-70-77" name="__codelineno-70-77" href="#__codelineno-70-77"></a><span class="w"> </span><span class="cm">/* 列表扩容 */</span>
<a id="__codelineno-70-78" name="__codelineno-70-78" href="#__codelineno-70-78"></a><span class="w"> </span><span class="nx">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-70-79" name="__codelineno-70-79" href="#__codelineno-70-79"></a><span class="w"> </span><span class="c1">// 新建一个长度为 size 的数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-70-79" name="__codelineno-70-79" href="#__codelineno-70-79"></a><span class="w"> </span><span class="c1">// 新建一个长度为原数组 extendRatio 倍的新数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-70-80" name="__codelineno-70-80" href="#__codelineno-70-80"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">nums</span><span class="p">.</span><span class="nx">concat</span><span class="p">(</span>
<a id="__codelineno-70-81" name="__codelineno-70-81" href="#__codelineno-70-81"></a><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">extendRatio</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span>
<a id="__codelineno-70-82" name="__codelineno-70-82" href="#__codelineno-70-82"></a><span class="w"> </span><span class="p">);</span>
@ -3620,7 +3620,7 @@
<a id="__codelineno-74-85" name="__codelineno-74-85" href="#__codelineno-74-85"></a>
<a id="__codelineno-74-86" name="__codelineno-74-86" href="#__codelineno-74-86"></a> <span class="cm">/* 列表扩容 */</span>
<a id="__codelineno-74-87" name="__codelineno-74-87" href="#__codelineno-74-87"></a> <span class="kd">func</span> <span class="nf">extendCapacity</span><span class="p">()</span> <span class="p">{</span>
<a id="__codelineno-74-88" name="__codelineno-74-88" href="#__codelineno-74-88"></a> <span class="c1">// 新建一个长度为 size 的数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-74-88" name="__codelineno-74-88" href="#__codelineno-74-88"></a> <span class="c1">// 新建一个长度为原数组 extendRatio 倍的新数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-74-89" name="__codelineno-74-89" href="#__codelineno-74-89"></a> <span class="n">nums</span> <span class="p">=</span> <span class="n">nums</span> <span class="o">+</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">_capacity</span> <span class="o">*</span> <span class="p">(</span><span class="n">extendRatio</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span>
<a id="__codelineno-74-90" name="__codelineno-74-90" href="#__codelineno-74-90"></a> <span class="c1">// 更新列表容量</span>
<a id="__codelineno-74-91" name="__codelineno-74-91" href="#__codelineno-74-91"></a> <span class="n">_capacity</span> <span class="p">=</span> <span class="n">nums</span><span class="p">.</span><span class="bp">count</span>
@ -3731,7 +3731,7 @@
<a id="__codelineno-75-91" name="__codelineno-75-91" href="#__codelineno-75-91"></a>
<a id="__codelineno-75-92" name="__codelineno-75-92" href="#__codelineno-75-92"></a><span class="w"> </span><span class="c1">// 列表扩容</span>
<a id="__codelineno-75-93" name="__codelineno-75-93" href="#__codelineno-75-93"></a><span class="w"> </span><span class="kr">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">extendCapacity</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-75-94" name="__codelineno-75-94" href="#__codelineno-75-94"></a><span class="w"> </span><span class="c1">// 新建一个长度为 size * extend_ratio 的数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-75-94" name="__codelineno-75-94" href="#__codelineno-75-94"></a><span class="w"> </span><span class="c1">// 新建一个长度为原数组 extendRatio 倍的新数组，并将原数组拷贝到新数组</span>
<a id="__codelineno-75-95" name="__codelineno-75-95" href="#__codelineno-75-95"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">newCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">extend_ratio</span><span class="p">;</span>
<a id="__codelineno-75-96" name="__codelineno-75-96" href="#__codelineno-75-96"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">extend</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">mem_allocator</span><span class="p">.</span><span class="n">alloc</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="w"> </span><span class="n">newCapacity</span><span class="p">);</span>
<a id="__codelineno-75-97" name="__codelineno-75-97" href="#__codelineno-75-97"></a><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">mem</span><span class="p">.</span><span class="n">set</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="w"> </span><span class="n">extend</span><span class="p">,</span><span class="w"> </span><span class="nb">@as</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
@ -3826,7 +3826,7 @@
<a id="__codelineno-76-67" name="__codelineno-76-67" href="#__codelineno-76-67"></a>
<a id="__codelineno-76-68" name="__codelineno-76-68" href="#__codelineno-76-68"></a><span class="w"> </span><span class="cm">/* 列表扩容 */</span>
<a id="__codelineno-76-69" name="__codelineno-76-69" href="#__codelineno-76-69"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-76-70" name="__codelineno-76-70" href="#__codelineno-76-70"></a><span class="w"> </span><span class="c1">// 新建一个长度为 _capacity * _extendRatio 的数组</span>
<a id="__codelineno-76-70" name="__codelineno-76-70" href="#__codelineno-76-70"></a><span class="w"> </span><span class="c1">// 新建一个长度为原数组 _extendRatio 倍的新数组</span>
<a id="__codelineno-76-71" name="__codelineno-76-71" href="#__codelineno-76-71"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="n">_newNums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">_capacity</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">_extendRatio</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
<a id="__codelineno-76-72" name="__codelineno-76-72" href="#__codelineno-76-72"></a><span class="w"> </span><span class="c1">// 将原数组拷贝到新数组</span>
<a id="__codelineno-76-73" name="__codelineno-76-73" href="#__codelineno-76-73"></a><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">copyRange</span><span class="p">(</span><span class="n">_newNums</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">_nums</span><span class="p">);</span>

20
chapter_computational_complexity/time_complexity/index.html
Unescape View File

@ -582,15 +582,15 @@
<ul class="md-nav__list">
<li class="md-nav__item">
<a href="#1" class="md-nav__link">
1) 统计操作数量
<a href="#_1" class="md-nav__link">
第一步：统计操作数量
</a>
</li>
<li class="md-nav__item">
<a href="#2" class="md-nav__link">
2) 判断渐近上界
<a href="#_2" class="md-nav__link">
第二步：判断渐近上界
</a>
</li>
@ -2164,15 +2164,15 @@
<ul class="md-nav__list">
<li class="md-nav__item">
<a href="#1" class="md-nav__link">
1) 统计操作数量
<a href="#_1" class="md-nav__link">
第一步：统计操作数量
</a>
</li>
<li class="md-nav__item">
<a href="#2" class="md-nav__link">
2) 判断渐近上界
<a href="#_2" class="md-nav__link">
第二步：判断渐近上界
</a>
</li>
@ -2794,7 +2794,7 @@ $$</p>
<h2 id="224">2.2.4. &nbsp; 推算方法<a class="headerlink" href="#224" title="Permanent link">&para;</a></h2>
<p>渐近上界的数学味儿有点重，如果你感觉没有完全理解，也无需担心。因为在实际使用中，我们只需要掌握推算方法，数学意义可以逐渐领悟。</p>
<p>根据定义，确定 <span class="arithmatex">\(f(n)\)</span> 之后，我们便可得到时间复杂度 <span class="arithmatex">\(O(f(n))\)</span> 。那么如何确定渐近上界 <span class="arithmatex">\(f(n)\)</span> 呢？总体分为两步：首先统计操作数量，然后判断渐近上界。</p>
<h3 id="1">1) 统计操作数量<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<h3 id="_1">第一步：统计操作数量<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
<p>针对代码，逐行从上到下计算即可。然而，由于上述 <span class="arithmatex">\(c \cdot f(n)\)</span> 中的常数项 <span class="arithmatex">\(c\)</span> 可以取任意大小，<strong>因此操作数量 <span class="arithmatex">\(T(n)\)</span> 中的各种系数、常数项都可以被忽略</strong>。根据此原则，可以总结出以下计数简化技巧：</p>
<ol>
<li><strong>忽略与 <span class="arithmatex">\(n\)</span> 无关的操作</strong>。因为它们都是 <span class="arithmatex">\(T(n)\)</span> 中的常数项，对时间复杂度不产生影响。</li>
@ -2988,7 +2988,7 @@ T(n) &amp; = n^2 + n &amp; \text{偷懒统计 (o.O)}
</div>
</div>
</div>
<h3 id="2">2) 判断渐近上界<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<h3 id="_2">第二步：判断渐近上界<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h3>
<p><strong>时间复杂度由多项式 <span class="arithmatex">\(T(n)\)</span> 中最高阶的项来决定</strong>。这是因为在 <span class="arithmatex">\(n\)</span> 趋于无穷大时，最高阶的项将发挥主导作用，其他项的影响都可以被忽略。</p>
<p>以下表格展示了一些例子，其中一些夸张的值是为了强调“系数无法撼动阶数”这一结论。当 <span class="arithmatex">\(n\)</span> 趋于无穷大时，这些常数变得无足轻重。</p>
<div class="center-table">

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