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@ -4123,7 +4123,7 @@ O(1) < O(\log n) < O(n) < O(n^2) < O(2^n) \newline
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<h3 id="1-o1">1. &nbsp; 常数阶 <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">&para;</a></h3>
<p>常数阶常见于数量与输入数据大小 <span class="arithmatex">\(n\)</span> 无关的常量、变量、对象。</p>
<p>需要注意的是，在循环中初始化变量或调用函数而占用的内存，在进入下一循环后就会被释放，即不会累积占用空间，空间复杂度仍为 <span class="arithmatex">\(O(1)\)</span> ：</p>
<p>需要注意的是，在循环中初始化变量或调用函数而占用的内存，在进入下一循环后就会被释放，因此不会累积占用空间，空间复杂度仍为 <span class="arithmatex">\(O(1)\)</span> ：</p>
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@ -4675,7 +4675,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
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<p>以下函数的递归深度为 <span class="arithmatex">\(n\)</span> ，即同时存在 <span class="arithmatex">\(n\)</span> 个未返回的 <code>linear_recur()</code> 函数，使用 <span class="arithmatex">\(O(n)\)</span> 大小的栈帧空间：</p>
<p>如下图所示，此函数的递归深度为 <span class="arithmatex">\(n\)</span> ，即同时存在 <span class="arithmatex">\(n\)</span> 个未返回的 <code>linear_recur()</code> 函数，使用 <span class="arithmatex">\(O(n)\)</span> 大小的栈帧空间：</p>
<div class="tabbed-set tabbed-alternate" data-tabs="6:12"><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" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" 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">JS</label><label for="__tabbed_6_6">TS</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><label for="__tabbed_6_11">Dart</label><label for="__tabbed_6_12">Rust</label></div>
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@ -4992,7 +4992,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
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<p>以下函数的递归深度为 <span class="arithmatex">\(n\)</span> ，在每个递归函数中都初始化了一个数组，长度分别为 <span class="arithmatex">\(n, n-1, n-2, ..., 2, 1\)</span> ，平均长度为 <span class="arithmatex">\(n / 2\)</span> ，因此总体占用 <span class="arithmatex">\(O(n^2)\)</span> 空间。</p>
<p>如下图所示，该函数的递归深度为 <span class="arithmatex">\(n\)</span> ，在每个递归函数中都初始化了一个数组，长度分别为 <span class="arithmatex">\(n, n-1, n-2, ..., 2, 1\)</span> ，平均长度为 <span class="arithmatex">\(n / 2\)</span> ，因此总体占用 <span class="arithmatex">\(O(n^2)\)</span> 空间：</p>
<div class="tabbed-set tabbed-alternate" data-tabs="8:12"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Java</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Python</label><label for="__tabbed_8_4">Go</label><label for="__tabbed_8_5">JS</label><label for="__tabbed_8_6">TS</label><label for="__tabbed_8_7">C</label><label for="__tabbed_8_8">C#</label><label for="__tabbed_8_9">Swift</label><label for="__tabbed_8_10">Zig</label><label for="__tabbed_8_11">Dart</label><label for="__tabbed_8_12">Rust</label></div>
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@ -5134,7 +5134,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<p align="center"> 图：递归函数产生的平方阶空间复杂度 </p>
<h3 id="4-o2n">4. &nbsp; 指数阶 <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
<p>指数阶常见于二叉树。高度为 <span class="arithmatex">\(n\)</span> 的“满二叉树”的节点数量为 <span class="arithmatex">\(2^n - 1\)</span> ，占用 <span class="arithmatex">\(O(2^n)\)</span> 空间：</p>
<p>指数阶常见于二叉树。观察下图，高度为 <span class="arithmatex">\(n\)</span> 的“满二叉树”的节点数量为 <span class="arithmatex">\(2^n - 1\)</span> ，占用 <span class="arithmatex">\(O(2^n)\)</span> 空间：</p>
<div class="tabbed-set tabbed-alternate" data-tabs="9:12"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Java</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Python</label><label for="__tabbed_9_4">Go</label><label for="__tabbed_9_5">JS</label><label for="__tabbed_9_6">TS</label><label for="__tabbed_9_7">C</label><label for="__tabbed_9_8">C#</label><label for="__tabbed_9_9">Swift</label><label for="__tabbed_9_10">Zig</label><label for="__tabbed_9_11">Dart</label><label for="__tabbed_9_12">Rust</label></div>
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