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krahets
2023-07-31 03:27:17 +08:00
parent 5039f48f06
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13 changed files with 737 additions and 367 deletions

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@@ -3722,9 +3722,52 @@
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<div class="highlight"><span class="filename">permutations_i.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></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">backtrack</span><span class="p">}</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></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">permutationsI</span><span class="p">}</span>
<div class="highlight"><span class="filename">permutations_i.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 回溯算法:全排列 I */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></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="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="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="w"> </span><span class="o">*</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">vector</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>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="c1">// 当状态长度等于元素数量时,记录解</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="o">-&gt;</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="o">-&gt;</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="n">vector</span><span class="w"> </span><span class="o">*</span><span class="n">newState</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newVector</span><span class="p">();</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></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">&lt;</span><span class="w"> </span><span class="n">state</span><span class="o">-&gt;</span><span class="n">size</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>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="n">vectorPushback</span><span class="p">(</span><span class="n">newState</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="n">vectorPushback</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">newState</span><span class="p">);</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="c1">// 遍历所有选择</span>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></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">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="o">-&gt;</span><span class="n">size</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>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="kt">int</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">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><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="o">*</span><span class="p">((</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)(</span><span class="n">choices</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]));</span>
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w"> </span><span class="c1">// 剪枝:不允许重复选择元素 且 不允许重复选择相等元素</span>
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">select</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">*</span><span class="p">((</span><span class="kt">bool</span><span class="w"> </span><span class="o">*</span><span class="p">)(</span><span class="n">selected</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]));</span>
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">select</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w"> </span><span class="c1">// 尝试:做出选择,更新状态</span>
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w"> </span><span class="o">*</span><span class="p">((</span><span class="kt">bool</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">selected</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w"> </span><span class="n">vectorPushback</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>
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w"> </span><span class="c1">// 进行下一轮选择</span>
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></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">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w"> </span><span class="c1">// 回退:撤销选择,恢复到之前的状态</span>
<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w"> </span><span class="o">*</span><span class="p">((</span><span class="kt">bool</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">selected</span><span class="o">-&gt;</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w"> </span><span class="n">vectorPopback</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="p">}</span>
<a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a>
<a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="cm">/* 全排列 I */</span>
<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="n">vector</span><span class="w"> </span><span class="o">*</span><span class="nf">permutationsI</span><span class="p">(</span><span class="n">vector</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w"> </span><span class="n">vector</span><span class="w"> </span><span class="o">*</span><span class="n">iState</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newVector</span><span class="p">();</span>
<a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a>
<a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">select</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="nb">false</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">};</span>
<a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w"> </span><span class="n">vector</span><span class="w"> </span><span class="o">*</span><span class="n">bSelected</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newVector</span><span class="p">();</span>
<a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></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">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="o">-&gt;</span><span class="n">size</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>
<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="w"> </span><span class="n">vectorPushback</span><span class="p">(</span><span class="n">bSelected</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">select</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
<a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a>
<a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a><span class="w"> </span><span class="n">vector</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newVector</span><span class="p">();</span>
<a id="__codelineno-6-42" name="__codelineno-6-42" href="#__codelineno-6-42"></a>
<a id="__codelineno-6-43" name="__codelineno-6-43" href="#__codelineno-6-43"></a><span class="w"> </span><span class="c1">// 前序遍历</span>
<a id="__codelineno-6-44" name="__codelineno-6-44" href="#__codelineno-6-44"></a><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">iState</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">bSelected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
<a id="__codelineno-6-45" name="__codelineno-6-45" href="#__codelineno-6-45"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a id="__codelineno-6-46" name="__codelineno-6-46" href="#__codelineno-6-46"></a><span class="p">}</span>
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