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<h3 id="函数式编程是什么">函数式编程是什么<a aria-hidden="true" tabindex="-1" href="#函数式编程是什么" class="internal"> §</a></h3>
<p>函数式编程（Functional Programming, FP）是一种编程范式，**主张用数学上的函数方式构建结构和元素之间的关系，而不是改变状态和数据。**在函数式编程中，函数是第一公民，这意味着函数可以被传递、返回和操作，就像其他的数据类型一样。函数在这里是「纯」的，意味着相同的输入始终产生相同的输出，并且没有副作用。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="Python" data-theme="default"><code data-language="Python" data-theme="default"><span data-line><span style="color:var(--shiki-color-text);"># 函数作为参数传递给另一个函数</span></span>
<span data-line><span style="color:var(--shiki-color-text);">def apply(func, value):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> return func(value)</span></span>
<span data-line><span style="color:var(--shiki-color-text);"></span></span>
<span data-line><span style="color:var(--shiki-color-text);">result = apply(lambda x: x*2, 5) # 输出10</span></span></code></pre></div>
<h3 id="函数式编程与其他编程范式的区别">函数式编程与其他编程范式的区别<a aria-hidden="true" tabindex="-1" href="#函数式编程与其他编程范式的区别" class="internal"> §</a></h3>
<p>函数式编程与命令式编程的区别在于，命令式编程关注如何完成任务，强调程序状态和改变状态的语句，而**函数式编程注重数据的映射和组合。**面向对象编程重视对象及其之间的交互，而函数式编程重视函数和数据处理。</p>
<h3 id="函数式编程的优势和局限性">函数式编程的优势和局限性<a aria-hidden="true" tabindex="-1" href="#函数式编程的优势和局限性" class="internal"> §</a></h3>
<p><strong>优势</strong>：</p>
<ul>
<li><strong>简洁性</strong>：函数式编程往往更简洁，可以用更少的代码做更多的事情。</li>
<li><strong>可维护性</strong>：由于函数式编程的代码没有副作用，它通常更容易维护和调试。</li>
<li><strong>可重用性</strong>：函数是高度模块化的，可以在多个地方重用。</li>
</ul>
<p><strong>局限性</strong>：</p>
<ul>
<li><strong>内存使用</strong>：由于函数式编程倾向于复制数据而不是改变它，它可能使用更多的内存。</li>
<li><strong>难度</strong>：对于不熟悉该范式的开发者来说，函数式编程可能较难学习。</li>
</ul>
<h2 id="python-中的基础函数式工具">Python 中的基础函数式工具<a aria-hidden="true" tabindex="-1" href="#python-中的基础函数式工具" class="internal"> §</a></h2>
<p>Python 提供了一些内置的函数式工具，如 <code>lambda</code>，<code>map()</code>，<code>filter()</code> 和 <code>reduce()</code>，它们可以帮助你以函数式的方式处理数据。</p>
<h3 id="lambda"><code>lambda</code><a aria-hidden="true" tabindex="-1" href="#lambda" class="internal"> §</a></h3>
<p><code>lambda</code> 允许我们定义简短的匿名函数。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-color-text);">double </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">lambda</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-parameter);">x</span><span style="color:var(--shiki-color-text);">: x </span><span style="color:var(--shiki-token-keyword);">*</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">2</span></span>
<span data-line><span style="color:var(--shiki-token-function);">print</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-function);">double</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-constant);">5</span><span style="color:var(--shiki-token-punctuation);">))</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出10</span></span></code></pre></div>
<h3 id="map"><code>map()</code><a aria-hidden="true" tabindex="-1" href="#map" class="internal"> §</a></h3>
<p><code>map()</code> 函数将指定函数应用于序列的每一个元素。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-color-text);">nums </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> [</span><span style="color:var(--shiki-token-constant);">1</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">2</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">3</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">4</span><span style="color:var(--shiki-color-text);">]</span></span>
<span data-line><span style="color:var(--shiki-color-text);">squared </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">list</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-function);">map</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-keyword);">lambda</span><span style="color:var(--shiki-token-punctuation);"> </span><span style="color:var(--shiki-token-parameter);">x</span><span style="color:var(--shiki-token-punctuation);">: x</span><span style="color:var(--shiki-token-keyword);">**</span><span style="color:var(--shiki-token-constant);">2</span><span style="color:var(--shiki-token-punctuation);">, nums))</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出[1, 4, 9, 16]</span></span></code></pre></div>
<h3 id="filter"><code>filter()</code><a aria-hidden="true" tabindex="-1" href="#filter" class="internal"> §</a></h3>
<p><code>filter()</code> 函数根据指定函数的判断结果来过滤序列。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-color-text);">nums </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> [</span><span style="color:var(--shiki-token-constant);">1</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">2</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">3</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">4</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">5</span><span style="color:var(--shiki-color-text);">]</span></span>
<span data-line><span style="color:var(--shiki-color-text);">evens </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">list</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-function);">filter</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-keyword);">lambda</span><span style="color:var(--shiki-token-punctuation);"> </span><span style="color:var(--shiki-token-parameter);">x</span><span style="color:var(--shiki-token-punctuation);">: x </span><span style="color:var(--shiki-token-keyword);">%</span><span style="color:var(--shiki-token-punctuation);"> </span><span style="color:var(--shiki-token-constant);">2</span><span style="color:var(--shiki-token-punctuation);"> </span><span style="color:var(--shiki-token-keyword);">==</span><span style="color:var(--shiki-token-punctuation);"> </span><span style="color:var(--shiki-token-constant);">0</span><span style="color:var(--shiki-token-punctuation);">, nums))</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出[2, 4]</span></span></code></pre></div>
<h3 id="reduce"><code>reduce()</code><a aria-hidden="true" tabindex="-1" href="#reduce" class="internal"> §</a></h3>
<p><code>reduce()</code> 函数对序列中的元素进行连续、累计地应用指定函数。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-keyword);">from</span><span style="color:var(--shiki-color-text);"> functools </span><span style="color:var(--shiki-token-keyword);">import</span><span style="color:var(--shiki-color-text);"> reduce</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-color-text);">nums </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> [</span><span style="color:var(--shiki-token-constant);">1</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">2</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">3</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">4</span><span style="color:var(--shiki-color-text);">]</span></span>
<span data-line><span style="color:var(--shiki-color-text);">product </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">reduce</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-keyword);">lambda</span><span style="color:var(--shiki-token-punctuation);"> </span><span style="color:var(--shiki-token-parameter);">x</span><span style="color:var(--shiki-token-punctuation);">, </span><span style="color:var(--shiki-token-parameter);">y</span><span style="color:var(--shiki-token-punctuation);">: x</span><span style="color:var(--shiki-token-keyword);">*</span><span style="color:var(--shiki-token-punctuation);">y, nums)</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出24</span></span></code></pre></div>
<h3 id="functools-模块"><code>functools</code> 模块<a aria-hidden="true" tabindex="-1" href="#functools-模块" class="internal"> §</a></h3>
<p><code>functools</code> 模块提供了一些用于函数式编程的实用工具，如偏函数等。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-keyword);">from</span><span style="color:var(--shiki-color-text);"> functools </span><span style="color:var(--shiki-token-keyword);">import</span><span style="color:var(--shiki-color-text);"> partial</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">multiply</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">x</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-parameter);">y</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> x </span><span style="color:var(--shiki-token-keyword);">*</span><span style="color:var(--shiki-color-text);"> y</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-color-text);">double </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">partial</span><span style="color:var(--shiki-token-punctuation);">(multiply, </span><span style="color:var(--shiki-token-constant);">2</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line><span style="color:var(--shiki-token-function);">print</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-function);">double</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-constant);">4</span><span style="color:var(--shiki-token-punctuation);">))</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出8</span></span></code></pre></div>
<h2 id="高阶函数">高阶函数<a aria-hidden="true" tabindex="-1" href="#高阶函数" class="internal"> §</a></h2>
<h3 id="高阶函是数什么">高阶函是数什么<a aria-hidden="true" tabindex="-1" href="#高阶函是数什么" class="internal"> §</a></h3>
<p>高阶函数接受一个或多个函数作为参数，或者返回一个函数。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">greet</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">type_</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">if</span><span style="color:var(--shiki-color-text);"> type_ </span><span style="color:var(--shiki-token-keyword);">==</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-string-expression);">'hello'</span><span style="color:var(--shiki-token-punctuation);">:</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">lambda</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-parameter);">name</span><span style="color:var(--shiki-color-text);">: </span><span style="color:var(--shiki-token-string-expression);">&quot;Hello, &quot;</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">+</span><span style="color:var(--shiki-color-text);"> name</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">else</span><span style="color:var(--shiki-token-punctuation);">:</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">lambda</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-parameter);">name</span><span style="color:var(--shiki-color-text);">: </span><span style="color:var(--shiki-token-string-expression);">&quot;Hi, &quot;</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">+</span><span style="color:var(--shiki-color-text);"> name</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-color-text);">greeting </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">greet</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-string-expression);">'hello'</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line><span style="color:var(--shiki-token-function);">print</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-function);">greeting</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-string-expression);">'Alice'</span><span style="color:var(--shiki-token-punctuation);">))</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出'Hello, Alice'</span></span></code></pre></div>
<h3 id="在-python-中创建和使用高阶函数">在 Python 中创建和使用高阶函数<a aria-hidden="true" tabindex="-1" href="#在-python-中创建和使用高阶函数" class="internal"> §</a></h3>
<p>除了 Python 内置的如 map、filter 和 reduce 这样的高阶函数外，我们也可以创建自己的高阶函数。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">apply</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">func</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-parameter);">data</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> [</span><span style="color:var(--shiki-token-function);">func</span><span style="color:var(--shiki-token-punctuation);">(item)</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">for</span><span style="color:var(--shiki-color-text);"> item </span><span style="color:var(--shiki-token-keyword);">in</span><span style="color:var(--shiki-color-text);"> data]</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-color-text);">nums </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> [</span><span style="color:var(--shiki-token-constant);">1</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">2</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">3</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">4</span><span style="color:var(--shiki-color-text);">]</span></span>
<span data-line><span style="color:var(--shiki-color-text);">result </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">apply</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-keyword);">lambda</span><span style="color:var(--shiki-token-punctuation);"> </span><span style="color:var(--shiki-token-parameter);">x</span><span style="color:var(--shiki-token-punctuation);">: x</span><span style="color:var(--shiki-token-keyword);">*</span><span style="color:var(--shiki-token-constant);">2</span><span style="color:var(--shiki-token-punctuation);">, nums)</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出[2, 4, 6, 8]</span></span></code></pre></div>
<h2 id="纯函数和不变性">纯函数和不变性<a aria-hidden="true" tabindex="-1" href="#纯函数和不变性" class="internal"> §</a></h2>
<h3 id="纯函数是什么">纯函数是什么<a aria-hidden="true" tabindex="-1" href="#纯函数是什么" class="internal"> §</a></h3>
<p>纯函数是函数式编程的核心概念之一。一个函数被认为是纯的，当它满足以下条件时：</p>
<ul>
<li><strong>给定相同的输入，总是返回相同的输出。</strong></li>
<li><strong>没有任何副作用（例如修改全局状态、修改传入的参数、进行 I/O 操作等）。</strong></li>
</ul>
<p>这些特性使纯函数变得可预测且容易测试。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-comment);"># 纯函数示例</span></span>
<span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">add</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">x</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-parameter);">y</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> x </span><span style="color:var(--shiki-token-keyword);">+</span><span style="color:var(--shiki-color-text);"> y</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-token-comment);"># 不纯的函数示例，因为它改变了外部状态</span></span>
<span data-line><span style="color:var(--shiki-color-text);">counter </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">0</span></span>
<span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">increment</span><span style="color:var(--shiki-color-text);">():</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">global</span><span style="color:var(--shiki-color-text);"> counter</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> counter </span><span style="color:var(--shiki-token-keyword);">+=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">1</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> counter</span></span></code></pre></div>
<h3 id="数据的不变性">数据的不变性<a aria-hidden="true" tabindex="-1" href="#数据的不变性" class="internal"> §</a></h3>
<p>在函数式编程中，数据是不可变的。这意味着一旦一个数据结构被创建，就不能再改变它。而是每次需要修改数据时，都会返回一个新的数据副本。</p>
<p>这一特性增加了代码的可读性和可预测性，因为你不必担心数据在不知情的情况下被修改。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-comment);"># 使用列表作为示例</span></span>
<span data-line><span style="color:var(--shiki-color-text);">lst </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> [</span><span style="color:var(--shiki-token-constant);">1</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">2</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">3</span><span style="color:var(--shiki-color-text);">]</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-token-comment);"># 错误的做法：修改原始列表</span></span>
<span data-line><span style="color:var(--shiki-color-text);">lst</span><span style="color:var(--shiki-token-punctuation);">.</span><span style="color:var(--shiki-token-function);">append</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-constant);">4</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-token-comment);"># 正确的做法：创建新的列表</span></span>
<span data-line><span style="color:var(--shiki-color-text);">new_lst </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> lst </span><span style="color:var(--shiki-token-keyword);">+</span><span style="color:var(--shiki-color-text);"> [</span><span style="color:var(--shiki-token-constant);">4</span><span style="color:var(--shiki-color-text);">]</span></span></code></pre></div>
<h2 id="装饰器">装饰器<a aria-hidden="true" tabindex="-1" href="#装饰器" class="internal"> §</a></h2>
<h3 id="python-中的装饰器">Python 中的装饰器<a aria-hidden="true" tabindex="-1" href="#python-中的装饰器" class="internal"> §</a></h3>
<p>装饰器是 Python 中的一个强大工具，它允许开发者**在不修改原始函数代码的情况下，给函数增加新的功能。**它们通常用于日志、权限检查、统计或其他跨越多个函数或方法的通用任务。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">my_decorator</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">func</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">wrapper</span><span style="color:var(--shiki-color-text);">():</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">print</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-string-expression);">&quot;Something is happening before the function is called.&quot;</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">func</span><span style="color:var(--shiki-token-punctuation);">()</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">print</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-string-expression);">&quot;Something is happening after the function is called.&quot;</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> wrapper</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-token-function);">@my_decorator</span></span>
<span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">say_hello</span><span style="color:var(--shiki-color-text);">():</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">print</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-string-expression);">&quot;Hello!&quot;</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-token-function);">say_hello</span><span style="color:var(--shiki-token-punctuation);">()</span></span></code></pre></div>
<h3 id="如何利用装饰器优化代码">如何利用装饰器优化代码<a aria-hidden="true" tabindex="-1" href="#如何利用装饰器优化代码" class="internal"> §</a></h3>
<p>如上所示，装饰器是一个返回另一个函数的函数。要使用装饰器，只需在你想要装饰的函数上方加上 <code>@decorator_name</code>。</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">repeat</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">num</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">decorator_repeat</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">func</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">wrapper</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-keyword);">*</span><span style="color:var(--shiki-token-parameter);">args</span><span style="color:var(--shiki-token-punctuation);">,</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">**</span><span style="color:var(--shiki-token-parameter);">kwargs</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">for</span><span style="color:var(--shiki-color-text);"> _ </span><span style="color:var(--shiki-token-keyword);">in</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">range</span><span style="color:var(--shiki-token-punctuation);">(num):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> result </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">func</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-keyword);">*</span><span style="color:var(--shiki-token-punctuation);">args, </span><span style="color:var(--shiki-token-keyword);">**</span><span style="color:var(--shiki-token-punctuation);">kwargs)</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> result</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> wrapper</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> decorator_repeat</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-token-function);">@repeat</span><span style="color:var(--shiki-token-punctuation);">(num</span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-token-constant);">4</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">greet</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">name</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">print</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-keyword);">f</span><span style="color:var(--shiki-token-string-expression);">&quot;Hello, </span><span style="color:var(--shiki-token-constant);">{</span><span style="color:var(--shiki-token-punctuation);">name</span><span style="color:var(--shiki-token-constant);">}</span><span style="color:var(--shiki-token-string-expression);">&quot;</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-token-function);">greet</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-string-expression);">&quot;Alice&quot;</span><span style="color:var(--shiki-token-punctuation);">)</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出四次 &quot;Hello, Alice&quot;</span></span></code></pre></div>
<h2 id="闭包和自由变量">闭包和自由变量<a aria-hidden="true" tabindex="-1" href="#闭包和自由变量" class="internal"> §</a></h2>
<p>闭包是一种特殊的函数，它可以记住在其所在作用域中声明的自由变量的值，即使它们在函数外部是不可用的。在更简单的语言中，闭包允许函数携带与之相关的数据。</p>
<p><strong>在 Python 中，当内部函数引用了外部函数中的变量，内部函数就被认为是闭包。</strong></p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">outer_function</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">x</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">inner_function</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">y</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> x </span><span style="color:var(--shiki-token-keyword);">+</span><span style="color:var(--shiki-color-text);"> y</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> inner_function</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-color-text);">closure </span><span style="color:var(--shiki-token-keyword);">=</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">outer_function</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-constant);">10</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line><span style="color:var(--shiki-token-function);">print</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-function);">closure</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-constant);">5</span><span style="color:var(--shiki-token-punctuation);">))</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出15</span></span></code></pre></div>
<h2 id="递归">递归<a aria-hidden="true" tabindex="-1" href="#递归" class="internal"> §</a></h2>
<p>递归是一种编程技巧，其中函数调用自身以解决较小的问题实例。递归通常与某种终止条件结合使用，以防止无限的自我调用。递归函数的经典例子是计算阶乘：</p>
<div data-rehype-pretty-code-fragment><pre style="background-color:var(--shiki-color-background);" tabindex="0" data-language="python" data-theme="default"><code data-language="python" data-theme="default"><span data-line><span style="color:var(--shiki-token-comment);"># 此函数会不断调用自己，直到n为1。</span></span>
<span data-line><span style="color:var(--shiki-token-keyword);">def</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">factorial</span><span style="color:var(--shiki-color-text);">(</span><span style="color:var(--shiki-token-parameter);">n</span><span style="color:var(--shiki-color-text);">):</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">if</span><span style="color:var(--shiki-color-text);"> n </span><span style="color:var(--shiki-token-keyword);">==</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">1</span><span style="color:var(--shiki-token-punctuation);">:</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-constant);">1</span></span>
<span data-line><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-keyword);">return</span><span style="color:var(--shiki-color-text);"> n </span><span style="color:var(--shiki-token-keyword);">*</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-function);">factorial</span><span style="color:var(--shiki-token-punctuation);">(n </span><span style="color:var(--shiki-token-keyword);">-</span><span style="color:var(--shiki-token-punctuation);"> </span><span style="color:var(--shiki-token-constant);">1</span><span style="color:var(--shiki-token-punctuation);">)</span></span>
<span data-line> </span>
<span data-line><span style="color:var(--shiki-token-function);">print</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-function);">factorial</span><span style="color:var(--shiki-token-punctuation);">(</span><span style="color:var(--shiki-token-constant);">5</span><span style="color:var(--shiki-token-punctuation);">))</span><span style="color:var(--shiki-color-text);"> </span><span style="color:var(--shiki-token-comment);"># 输出120</span></span></code></pre></div>
<h3 id="递归迭代对比">递归、迭代对比<a aria-hidden="true" tabindex="-1" href="#递归迭代对比" class="internal"> §</a></h3>
<table><thead><tr><th>对比点</th><th>递归</th><th>迭代</th></tr></thead><tbody><tr><td><strong>直观性</strong></td><td>通常更直观和更容易实现</td><td>通常需要使用循环结构，可能不如递归直观</td></tr><tr><td><strong>自然选择</strong></td><td>对于某些问题，如树的遍历，递归是自然的选择</td><td>对于基本的数据结构，如数组和链表，迭代是自然选择</td></tr><tr><td><strong>函数调用</strong></td><td>可能会导致大量的函数调用，从而可能达到调用堆栈的限制</td><td>由于是循环结构，不会导致函数调用的堆栈溢出</td></tr><tr><td><strong>效率</strong></td><td>对于大量的递归，可能不如迭代高效</td><td>对于简单的循环，迭代可能更加高效</td></tr><tr><td><strong>内存使用</strong></td><td>每次调用自己都需要额外的内存来存储变量和信息，可能会导致调用堆栈溢出</td><td>通常更为内存高效，因为它不需要为每次循环存储额外的信息</td></tr><tr><td><strong>实现方式</strong></td><td>函数调用自己，直到满足某个条件</td><td>使用循环结构，如 <code>for</code> 和 <code>while</code></td></tr></tbody></table></article></div><div class="right sidebar"><div class="graph "><h3>Graph View</h3><div class="graph-outer"><div id="graph-container" data-cfg="{&quot;drag&quot;:true,&quot;zoom&quot;:true,&quot;depth&quot;:1,&quot;scale&quot;:1.1,&quot;repelForce&quot;:0.5,&quot;centerForce&quot;:0.3,&quot;linkDistance&quot;:30,&quot;fontSize&quot;:0.6,&quot;opacityScale&quot;:1,&quot;showTags&quot;:true,&quot;removeTags&quot;:[]}"></div><svg version="1.1" id="global-graph-icon" xmlns="http://www.w3.org/2000/svg" xmlnsXlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 55 55" fill="currentColor" xmlSpace="preserve"><path d="M49,0c-3.309,0-6,2.691-6,6c0,1.035,0.263,2.009,0.726,2.86l-9.829,9.829C32.542,17.634,30.846,17,29,17
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