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Python 哪些可以代替递归的算法？

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Jun 06, 2016 pm 04:22 PM

回复内容：

所有的递归调用，都可以做CPS变换改写成尾递归形式，然后尾递归可以改写成循环：

<span class="k">def</span> <span class="nf">fact</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
        <span class="k">return</span> <span class="mi">1</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="k">return</span> <span class="n">n</span> <span class="o">*</span> <span class="n">fact</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>


<span class="nb">id</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span>


<span class="k">def</span> <span class="nf">factCPS</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
        <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">k</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">f</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">k</span><span class="p">(</span><span class="n">n</span> <span class="o">*</span> <span class="n">x</span><span class="p">))</span>

    <span class="k">return</span> <span class="n">f</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="nb">id</span><span class="p">)</span>


<span class="k">def</span> <span class="nf">factNoRec</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
    <span class="k">def</span> <span class="nf">factory</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
        <span class="k">return</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">k</span><span class="p">(</span><span class="n">n</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span>

    <span class="n">k</span> <span class="o">=</span> <span class="nb">id</span>
    <span class="k">while</span> <span class="bp">True</span><span class="p">:</span>
        <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="k">return</span> <span class="n">k</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="n">k</span> <span class="o">=</span> <span class="n">factory</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
            <span class="n">n</span> <span class="o">-=</span> <span class="mi">1</span>


<span class="k">def</span> <span class="nf">factHolyCrap</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
    <span class="n">k</span> <span class="o">=</span> <span class="p">()</span>
    <span class="k">while</span> <span class="bp">True</span><span class="p">:</span>
        <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
            <span class="n">x</span> <span class="o">=</span> <span class="mi">1</span>
            <span class="k">while</span> <span class="n">k</span><span class="p">:</span>
                <span class="n">x</span> <span class="o">=</span> <span class="n">k</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span>
                <span class="n">k</span> <span class="o">=</span> <span class="n">k</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
            <span class="k">return</span> <span class="nb">id</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="n">k</span> <span class="o">=</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
            <span class="n">n</span> <span class="o">-=</span> <span class="mi">1</span>

<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">'__main__'</span><span class="p">:</span>
    <span class="k">print</span><span class="p">([</span><span class="n">f</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="p">[</span><span class="n">fact</span><span class="p">,</span> <span class="n">factCPS</span><span class="p">,</span> <span class="n">factNoRec</span><span class="p">,</span> <span class="n">factHolyCrap</span><span class="p">]])</span>

递归过程中需要维护一个调用栈

如果不想递归，硬是要循环，那么可以自己手动来维护这个调用栈

这样唯一的好处或许就是解除了最大递归深度的限制吧。。。给邵大神补一个java sample

<span class="kd">public</span> <span class="kd">class</span> <span class="nc">RecursionEliminationSample</span> <span class="o">{</span>
    <span class="kt">int</span> <span class="nf">factorRec</span><span class="o">(</span><span class="kt">int</span> <span class="n">n</span><span class="o">)</span> <span class="o">{</span>
        <span class="k">if</span> <span class="o">(</span><span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="o">)</span>
            <span class="k">return</span> <span class="mi">1</span><span class="o">;</span>
        <span class="k">else</span>
            <span class="k">return</span> <span class="n">n</span> <span class="o">*</span> <span class="n">factorRec</span><span class="o">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="o">);</span>
    <span class="o">}</span>

    <span class="kt">int</span> <span class="nf">factor</span><span class="o">(</span><span class="kt">int</span> <span class="n">n</span><span class="o">)</span> <span class="o">{</span>
        <span class="n">Function</span><span class="o"><</span><span class="n">Integer</span><span class="o">,</span> <span class="n">Integer</span><span class="o">></span> <span class="n">k</span> <span class="o">=</span> <span class="o">(</span><span class="n">x</span><span class="o">)</span> <span class="o">-></span> <span class="n">x</span><span class="o">;</span>
        <span class="k">while</span><span class="o">(</span><span class="kc">true</span><span class="o">)</span> <span class="o">{</span>
            <span class="k">if</span> <span class="o">(</span><span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="o">)</span>
                <span class="k">return</span> <span class="n">k</span><span class="o">.</span><span class="na">apply</span><span class="o">(</span><span class="mi">1</span><span class="o">);</span>
            <span class="k">else</span> <span class="o">{</span>
                <span class="kd">final</span> <span class="n">Function</span><span class="o"><</span><span class="n">Integer</span><span class="o">,</span> <span class="n">Integer</span><span class="o">></span> <span class="n">k0</span> <span class="o">=</span> <span class="n">k</span><span class="o">;</span>
                <span class="kd">final</span> <span class="kt">int</span> <span class="n">n0</span> <span class="o">=</span> <span class="n">n</span><span class="o">;</span>

                <span class="n">k</span> <span class="o">=</span> <span class="o">(</span><span class="n">x</span><span class="o">)</span> <span class="o">-></span> <span class="n">k0</span><span class="o">.</span><span class="na">apply</span><span class="o">(</span><span class="n">n0</span> <span class="o">*</span> <span class="n">x</span><span class="o">);</span>
                <span class="n">n</span> <span class="o">-=</span> <span class="mi">1</span><span class="o">;</span>
            <span class="o">}</span>
        <span class="o">}</span>
    <span class="o">}</span>
<span class="o">}</span>

用循环实现？可以自己建个栈来保存状态。你只需要搞明白在递归的时候程序往栈上面放了些什么，然后用自己的栈模拟即可。
技巧上倒是可以参照从fortran时代积累的递归转迭代的技术。不是完全没有解决方案：
Does Python optimize tail recursion? 时代积累的递归转迭代的技术。然后用自己的栈模拟即可。，话j

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