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@@ -32,6 +32,8 @@
<link rel="alternate" href="/ru/chapter_backtracking/permutations_problem/" hreflang="ru">
<link rel="alternate" href="/ko/chapter_backtracking/permutations_problem/" hreflang="ko">
<link rel="icon" href="../../assets/images/favicon.png">
@@ -230,6 +232,12 @@
</a>
</li>
<li class="md-select__item">
<a href="/ko/chapter_backtracking/permutations_problem/" hreflang="ko" class="md-select__link">
한국어
</a>
</li>
</ul>
</div>
</div>
@@ -4844,7 +4852,7 @@
<div class="highlight"><span class="filename">permutations_i.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">selected</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="p">):</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Backtracking algorithm: Permutations I&quot;&quot;&quot;</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="sd">"""Backtracking algorithm: Permutations I"""</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="c1"># When the state length equals the number of elements, record the solution</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">state</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
@@ -4863,7 +4871,7 @@
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a> <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">permutations_i</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Permutations I&quot;&quot;&quot;</span>
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w"> </span><span class="sd">"""Permutations I"""</span>
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a> <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="o">=</span><span class="p">[],</span> <span class="n">choices</span><span class="o">=</span><span class="n">nums</span><span class="p">,</span> <span class="n">selected</span><span class="o">=</span><span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">),</span> <span class="n">res</span><span class="o">=</span><span class="n">res</span><span class="p">)</span>
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a> <span class="k">return</span> <span class="n">res</span>
@@ -4975,22 +4983,22 @@
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrackI</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">bool</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="c1">// When the state length equals the number of elements, record the solution</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="o">...</span><span class="p">)</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="p">...)</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">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="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">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="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="c1">// Pruning: do not allow repeated selection of elements</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">!(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="nx">backtrackI</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span>
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
@@ -5325,7 +5333,7 @@
<div class="highlight"><span class="filename">permutations_ii.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a> <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">selected</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">):</span>
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Backtracking algorithm: Permutations II&quot;&quot;&quot;</span>
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w"> </span><span class="sd">"""Backtracking algorithm: Permutations II"""</span>
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a> <span class="c1"># When the state length equals the number of elements, record the solution</span>
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">state</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a> <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
@@ -5346,7 +5354,7 @@
<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a> <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>
<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="k">def</span><span class="w"> </span><span class="nf">permutations_ii</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Permutations II&quot;&quot;&quot;</span>
<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w"> </span><span class="sd">"""Permutations II"""</span>
<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a> <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a> <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="o">=</span><span class="p">[],</span> <span class="n">choices</span><span class="o">=</span><span class="n">nums</span><span class="p">,</span> <span class="n">selected</span><span class="o">=</span><span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">),</span> <span class="n">res</span><span class="o">=</span><span class="n">res</span><span class="p">)</span>
<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a> <span class="k">return</span> <span class="n">res</span>
@@ -5464,25 +5472,25 @@
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrackII</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="kt">bool</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w"> </span><span class="c1">// When the state length equals the number of elements, record the solution</span>
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w"> </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="o">...</span><span class="p">)</span>
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w"> </span><span class="nx">newState</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="p">...)</span>
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w"> </span><span class="o">*</span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">newState</span><span class="p">)</span>
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="c1">// Traverse all choices</span>
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="nx">duplicated</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kd">struct</span><span class="p">{},</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">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="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="nx">duplicated</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kt">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kd">struct</span><span class="p">{},</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">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="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">choices</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w"> </span><span class="c1">// Pruning: do not allow repeated selection of elements and do not allow repeated selection of equal elements</span>
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">duplicated</span><span class="p">[</span><span class="nx">choice</span><span class="p">];</span><span class="w"> </span><span class="p">!</span><span class="nx">ok</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">!(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">duplicated</span><span class="p">[</span><span class="nx">choice</span><span class="p">];</span><span class="w"> </span><span class="o">!</span><span class="nx">ok</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w"> </span><span class="c1">// Attempt: make choice, update state</span>
<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w"> </span><span class="c1">// Record the selected element value</span>
<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w"> </span><span class="nx">duplicated</span><span class="p">[</span><span class="nx">choice</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w"> </span><span class="nx">duplicated</span><span class="p">[</span><span class="nx">choice</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span>
<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w"> </span><span class="c1">// Proceed to the next round of selection</span>
<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w"> </span><span class="nx">backtrackII</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w"> </span><span class="c1">// Backtrack: undo choice, restore to previous state</span>
<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span>
<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w"> </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="p">}</span>
@@ -5926,6 +5934,8 @@ aria-label="Footer"
/* Set palette on initial load */
giscus.setAttribute("data-theme", getGiscusTheme())
/* Register event handlers after documented loaded */
document.addEventListener("DOMContentLoaded", function() {
var ref = document.querySelector("[data-md-component=palette]")
@@ -6023,7 +6033,7 @@ aria-label="Footer"
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