deploy

2026-11-01 13:13:59 +08:00 · 2026-10-29 03:49:36 +08:00
parent 2e4fec7765
commit b67d4c595d
1348 changed files with 670900 additions and 9591 deletions
--- a/chapter_backtracking/backtracking_algorithm/index.html
+++ b/chapter_backtracking/backtracking_algorithm/index.html
@@ -32,6 +32,8 @@

          <link rel="alternate" href="/ru/chapter_backtracking/backtracking_algorithm/" hreflang="ru">

+          <link rel="alternate" href="/ko/chapter_backtracking/backtracking_algorithm/" 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/backtracking_algorithm/" hreflang="ko" class="md-select__link">
+              한국어
+            </a>
+          </li>
+
      </ul>
    </div>
  </div>
@@ -4823,7 +4831,7 @@
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_i_compact.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">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前序遍历：例题一&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">"""前序遍历：例题一"""</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="k">return</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
@@ -4886,7 +4894,7 @@
 <a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </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="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="p">).(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </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="c1">// 记录解</span>
-<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></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">root</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="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">root</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="p">}</span>
 <a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="nx">preOrderI</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</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="nx">preOrderI</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
@@ -4987,7 +4995,7 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_i_compact.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 前序遍历：例题一 */</span>
-<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">        </span><span class="k">return</span>
 <a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="p">}</span>
@@ -5017,7 +5025,7 @@
 </div>
 <details class="pythontutor">
 <summary>可视化运行</summary>
-<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D,%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E9%80%92%E5%BD%92%22%22%22%0A%20%20%20%20%23%20%E5%A6%82%E6%9E%9C%E7%B4%A2%E5%BC%95%E8%B6%85%E5%87%BA%E6%95%B0%E7%BB%84%E9%95%BF%E5%BA%A6%EF%BC%8C%E6%88%96%E8%80%85%E5%AF%B9%E5%BA%94%E7%9A%84%E5%85%83%E7%B4%A0%E4%B8%BA%20None%20%EF%BC%8C%E5%88%99%E8%BF%94%E5%9B%9E%20None%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E5%BD%93%E5%89%8D%E8%8A%82%E7%82%B9%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E9%80%92%E5%BD%92%E6%9E%84%E5%BB%BA%E5%B7%A6%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr,%202%20*%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr,%202%20*%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr,%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%EF%BC%9A%E4%BE%8B%E9%A2%98%E4%B8%80%22%22%22%0A%20%20%20%20if%20root%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%AE%B0%E5%BD%95%E8%A7%A3%0A%20%20%20%20%20%20%20%20res.append%28root%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1,%207,%203,%204,%205,%206,%207%5D%29%0A%0A%20%20%20%20%23%20%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%0A%20%20%20%20res%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E8%BE%93%E5%87%BA%E6%89%80%E6%9C%89%E5%80%BC%E4%B8%BA%207%20%E7%9A%84%E8%8A%82%E7%82%B9%22%29%0A%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20res%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" title="可视化运行" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D,%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E9%80%92%E5%BD%92%22%22%22%0A%20%20%20%20%23%20%E5%A6%82%E6%9E%9C%E7%B4%A2%E5%BC%95%E8%B6%85%E5%87%BA%E6%95%B0%E7%BB%84%E9%95%BF%E5%BA%A6%EF%BC%8C%E6%88%96%E8%80%85%E5%AF%B9%E5%BA%94%E7%9A%84%E5%85%83%E7%B4%A0%E4%B8%BA%20None%20%EF%BC%8C%E5%88%99%E8%BF%94%E5%9B%9E%20None%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E5%BD%93%E5%89%8D%E8%8A%82%E7%82%B9%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E9%80%92%E5%BD%92%E6%9E%84%E5%BB%BA%E5%B7%A6%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr,%202%20*%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr,%202%20*%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr,%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%EF%BC%9A%E4%BE%8B%E9%A2%98%E4%B8%80%22%22%22%0A%20%20%20%20if%20root%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%AE%B0%E5%BD%95%E8%A7%A3%0A%20%20%20%20%20%20%20%20res.append%28root%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1,%207,%203,%204,%205,%206,%207%5D%29%0A%0A%20%20%20%20%23%20%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%0A%20%20%20%20res%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E8%BE%93%E5%87%BA%E6%89%80%E6%9C%89%E5%80%BC%E4%B8%BA%207%20%E7%9A%84%E8%8A%82%E7%82%B9%22%29%0A%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20res%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D,%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E9%80%92%E5%BD%92%22%22%22%0A%20%20%20%20%23%20%E5%A6%82%E6%9E%9C%E7%B4%A2%E5%BC%95%E8%B6%85%E5%87%BA%E6%95%B0%E7%BB%84%E9%95%BF%E5%BA%A6%EF%BC%8C%E6%88%96%E8%80%85%E5%AF%B9%E5%BA%94%E7%9A%84%E5%85%83%E7%B4%A0%E4%B8%BA%20None%20%EF%BC%8C%E5%88%99%E8%BF%94%E5%9B%9E%20None%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E5%BD%93%E5%89%8D%E8%8A%82%E7%82%B9%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E9%80%92%E5%BD%92%E6%9E%84%E5%BB%BA%E5%B7%A6%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr,%202%20*%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr,%202%20*%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr,%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%EF%BC%9A%E4%BE%8B%E9%A2%98%E4%B8%80%22%22%22%0A%20%20%20%20if%20root%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%AE%B0%E5%BD%95%E8%A7%A3%0A%20%20%20%20%20%20%20%20res.append%28root%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1,%207,%203,%204,%205,%206,%207%5D%29%0A%0A%20%20%20%20%23%20%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%0A%20%20%20%20res%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E8%BE%93%E5%87%BA%E6%89%80%E6%9C%89%E5%80%BC%E4%B8%BA%207%20%E7%9A%84%E8%8A%82%E7%82%B9%22%29%0A%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20res%5D%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 &gt;</a></div></p>
 </details>
 <p><img alt="在前序遍历中搜索节点" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_nodes.png" /></p>
@@ -5036,7 +5044,7 @@
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_ii_compact.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">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前序遍历：例题二&quot;&quot;&quot;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">"""前序遍历：例题二"""</span>
 <a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
 <a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>        <span class="k">return</span>
 <a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># 尝试</span>
@@ -5114,15 +5122,15 @@
 <a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">        </span><span class="k">return</span>
 <a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </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="c1">// 尝试</span>
-<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</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">path</span><span class="p">,</span><span class="w"> </span><span class="nx">root</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="o">*</span><span class="nx">path</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">path</span><span class="p">,</span><span class="w"> </span><span class="nx">root</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="k">if</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</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="c1">// 记录解</span>
-<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></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="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="o">...</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="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="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">path</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="p">}</span>
 <a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="nx">preOrderII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</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="nx">preOrderII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</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">// 回退</span>
-<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -5260,7 +5268,7 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_ii_compact.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 前序遍历：例题二 */</span>
-<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w">        </span><span class="k">return</span>
 <a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w">    </span><span class="p">}</span>
@@ -5300,7 +5308,7 @@
 </div>
 <details class="pythontutor">
 <summary>可视化运行</summary>
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 </details>
 <p>在每次“尝试”中，我们通过将当前节点添加进 <code>path</code> 来记录路径；而在“回退”前，我们需要将该节点从 <code>path</code> 中弹出，<strong>以恢复本次尝试之前的状态</strong>。</p>
@@ -5355,7 +5363,7 @@
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_iii_compact.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
-<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前序遍历：例题三&quot;&quot;&quot;</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">"""前序遍历：例题三"""</span>
 <a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="c1"># 剪枝</span>
 <a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
 <a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>        <span class="k">return</span>
@@ -5438,15 +5446,15 @@
 <a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span>
 <a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="c1">// 尝试</span>
-<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</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">path</span><span class="p">,</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</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">path</span><span class="p">,</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span>
 <a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Val</span><span class="p">.(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">        </span><span class="c1">// 记录解</span>
-<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></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="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="o">...</span><span class="p">))</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></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="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">{},</span><span class="w"> </span><span class="o">*</span><span class="nx">path</span><span class="p">...))</span>
 <a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="nx">preOrderIII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
 <a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="nx">preOrderIII</span><span class="p">(</span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">path</span><span class="p">)</span>
 <a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="c1">// 回退</span>
-<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="o">*</span><span class="nx">path</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">path</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 <a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -5589,7 +5597,7 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_iii_compact.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 前序遍历：例题三 */</span>
-<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w">    </span><span class="c1">// 剪枝</span>
 <a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w">        </span><span class="k">return</span>
@@ -5631,7 +5639,7 @@
 </div>
 <details class="pythontutor">
 <summary>可视化运行</summary>
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+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" title="可视化运行" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0Adef%20list_to_tree_dfs%28arr%3A%20list%5Bint%5D,%20i%3A%20int%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E9%80%92%E5%BD%92%22%22%22%0A%20%20%20%20%23%20%E5%A6%82%E6%9E%9C%E7%B4%A2%E5%BC%95%E8%B6%85%E5%87%BA%E6%95%B0%E7%BB%84%E9%95%BF%E5%BA%A6%EF%BC%8C%E6%88%96%E8%80%85%E5%AF%B9%E5%BA%94%E7%9A%84%E5%85%83%E7%B4%A0%E4%B8%BA%20None%20%EF%BC%8C%E5%88%99%E8%BF%94%E5%9B%9E%20None%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len%28arr%29%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E6%9E%84%E5%BB%BA%E5%BD%93%E5%89%8D%E8%8A%82%E7%82%B9%0A%20%20%20%20root%20%3D%20TreeNode%28arr%5Bi%5D%29%0A%20%20%20%20%23%20%E9%80%92%E5%BD%92%E6%9E%84%E5%BB%BA%E5%B7%A6%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs%28arr,%202%20*%20i%20%2B%201%29%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs%28arr,%202%20*%20i%20%2B%202%29%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree%28arr%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs%28arr,%200%29%0A%0A%0Adef%20pre_order%28root%3A%20TreeNode%29%3A%0A%20%20%20%20%22%22%22%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%EF%BC%9A%E4%BE%8B%E9%A2%98%E4%B8%89%22%22%22%0A%20%20%20%20%23%20%E5%89%AA%E6%9E%9D%0A%20%20%20%20if%20root%20is%20None%20or%20root.val%20%3D%3D%203%3A%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20%23%20%E5%B0%9D%E8%AF%95%0A%20%20%20%20path.append%28root%29%0A%20%20%20%20if%20root.val%20%3D%3D%207%3A%0A%20%20%20%20%20%20%20%20%23%20%E8%AE%B0%E5%BD%95%E8%A7%A3%0A%20%20%20%20%20%20%20%20res.append%28list%28path%29%29%0A%20%20%20%20pre_order%28root.left%29%0A%20%20%20%20pre_order%28root.right%29%0A%20%20%20%20%23%20%E5%9B%9E%E9%80%80%0A%20%20%20%20path.pop%28%29%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree%28%5B1,%207,%203,%204,%205,%206,%207%5D%29%0A%0A%20%20%20%20%23%20%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%0A%20%20%20%20path%20%3D%20list%5BTreeNode%5D%28%29%0A%20%20%20%20res%20%3D%20list%5Blist%5BTreeNode%5D%5D%28%29%0A%20%20%20%20pre_order%28root%29%0A%0A%20%20%20%20print%28%22%5Cn%E8%BE%93%E5%87%BA%E6%89%80%E6%9C%89%E6%A0%B9%E8%8A%82%E7%82%B9%E5%88%B0%E8%8A%82%E7%82%B9%207%20%E7%9A%84%E8%B7%AF%E5%BE%84%EF%BC%8C%E8%B7%AF%E5%BE%84%E4%B8%AD%E4%B8%8D%E5%8C%85%E5%90%AB%E5%80%BC%E4%B8%BA%203%20%E7%9A%84%E8%8A%82%E7%82%B9%22%29%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print%28%5Bnode.val%20for%20node%20in%20path%5D%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=126&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
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 </details>
 <p>“剪枝”是一个非常形象的名词。如图 13-3 所示，在搜索过程中，<strong>我们“剪掉”了不满足约束条件的搜索分支</strong>，避免许多无意义的尝试，从而提高了搜索效率。</p>
@@ -5645,7 +5653,7 @@
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">State</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="n">choice</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="n">state</span><span class="p">]):</span>
-<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;回溯算法框架&quot;&quot;&quot;</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">"""回溯算法框架"""</span>
 <a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="c1"># 判断是否为解</span>
 <a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
 <a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>        <span class="c1"># 记录解</span>
@@ -5905,7 +5913,7 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 回溯算法框架 */</span>
-<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">State?,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Choice?&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State?&gt;</span><span class="o">?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </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">List</span><span class="o">&lt;</span><span class="n">Choice?</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State?</span><span class="o">&gt;?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">    </span><span class="c1">// 判断是否为解</span>
 <a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">        </span><span class="c1">// 记录解</span>
@@ -5958,29 +5966,29 @@
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_iii_template.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;判断当前状态是否为解&quot;&quot;&quot;</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">"""判断当前状态是否为解"""</span>
 <a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="k">return</span> <span class="n">state</span> <span class="ow">and</span> <span class="n">state</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span>
 <a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>
 <a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</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="n">TreeNode</span><span class="p">]]):</span>
-<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;记录解&quot;&quot;&quot;</span>
+<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w">    </span><span class="sd">"""记录解"""</span>
 <a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></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>
 <a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a>
 <a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;判断在当前状态下，该选择是否合法&quot;&quot;&quot;</span>
+<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w">    </span><span class="sd">"""判断在当前状态下，该选择是否合法"""</span>
 <a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a>    <span class="k">return</span> <span class="n">choice</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">choice</span><span class="o">.</span><span class="n">val</span> <span class="o">!=</span> <span class="mi">3</span>
 <a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a>
 <a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a><span class="k">def</span><span class="w"> </span><span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
-<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;更新状态&quot;&quot;&quot;</span>
+<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a><span class="w">    </span><span class="sd">"""更新状态"""</span>
 <a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a>    <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a>
 <a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
-<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;恢复状态&quot;&quot;&quot;</span>
+<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="w">    </span><span class="sd">"""恢复状态"""</span>
 <a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a>    <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
 <a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a>
 <a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
 <a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</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="n">TreeNode</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="n">TreeNode</span><span class="p">]]</span>
 <a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a><span class="p">):</span>
-<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;回溯算法：例题三&quot;&quot;&quot;</span>
+<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a><span class="w">    </span><span class="sd">"""回溯算法：例题三"""</span>
 <a id="__codelineno-52-25" name="__codelineno-52-25" href="#__codelineno-52-25"></a>    <span class="c1"># 检查是否为解</span>
 <a id="__codelineno-52-26" name="__codelineno-52-26" href="#__codelineno-52-26"></a>    <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
 <a id="__codelineno-52-27" name="__codelineno-52-27" href="#__codelineno-52-27"></a>        <span class="c1"># 记录解</span>
@@ -6150,7 +6158,7 @@
 <a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a>
 <a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="cm">/* 记录解 */</span>
 <a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</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="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></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="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</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-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></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="nb">append</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</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-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="p">}</span>
 <a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a>
 <a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
@@ -6160,12 +6168,12 @@
 <a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a>
 <a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="cm">/* 更新状态 */</span>
 <a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a><span class="kd">func</span><span class="w"> </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></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-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></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-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a><span class="p">}</span>
 <a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a>
 <a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a><span class="cm">/* 恢复状态 */</span>
 <a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a><span class="kd">func</span><span class="w"> </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></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-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></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-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></a><span class="p">}</span>
 <a id="__codelineno-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a>
 <a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
@@ -6183,7 +6191,7 @@
 <a id="__codelineno-56-38" name="__codelineno-56-38" href="#__codelineno-56-38"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</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-56-39" name="__codelineno-56-39" href="#__codelineno-56-39"></a><span class="w">            </span><span class="c1">// 进行下一轮选择</span>
 <a id="__codelineno-56-40" name="__codelineno-56-40" href="#__codelineno-56-40"></a><span class="w">            </span><span class="nx">temp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
-<a id="__codelineno-56-41" name="__codelineno-56-41" href="#__codelineno-56-41"></a><span class="w">            </span><span class="nx">temp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">temp</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
+<a id="__codelineno-56-41" name="__codelineno-56-41" href="#__codelineno-56-41"></a><span class="w">            </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">temp</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Left</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">.</span><span class="nx">Right</span><span class="p">)</span>
 <a id="__codelineno-56-42" name="__codelineno-56-42" href="#__codelineno-56-42"></a><span class="w">            </span><span class="nx">backtrackIII</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">temp</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
 <a id="__codelineno-56-43" name="__codelineno-56-43" href="#__codelineno-56-43"></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-56-44" name="__codelineno-56-44" href="#__codelineno-56-44"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
@@ -6508,35 +6516,35 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">preorder_traversal_iii_template.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 判断当前状态是否为解 */</span>
-<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">):</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?</span><span class="o">&gt;</span><span class="p">):</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">isNotEmpty</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">state</span><span class="o">[</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]?.</span><span class="na">_val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">7</span>
 <a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="p">}</span>
 <a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a>
 <a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="cm">/* 记录解 */</span>
-<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="o">?</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="o">?&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?</span><span class="o">&gt;?</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?</span><span class="o">&gt;?&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">state</span><span class="o">!!</span><span class="p">.</span><span class="na">toMutableList</span><span class="p">())</span>
 <a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="p">}</span>
 <a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a>
 <a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="cm">/* 判断在当前状态下，该选择是否合法 */</span>
-<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="o">?</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="p">:</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?</span><span class="o">&gt;?</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?</span><span class="p">):</span><span class="w"> </span><span class="kt">Boolean</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">_val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="m">3</span>
 <a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a><span class="p">}</span>
 <a id="__codelineno-63-15" name="__codelineno-63-15" href="#__codelineno-63-15"></a>
 <a id="__codelineno-63-16" name="__codelineno-63-16" href="#__codelineno-63-16"></a><span class="cm">/* 更新状态 */</span>
-<a id="__codelineno-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-63-18" name="__codelineno-63-18" href="#__codelineno-63-18"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
 <a id="__codelineno-63-19" name="__codelineno-63-19" href="#__codelineno-63-19"></a><span class="p">}</span>
 <a id="__codelineno-63-20" name="__codelineno-63-20" href="#__codelineno-63-20"></a>
 <a id="__codelineno-63-21" name="__codelineno-63-21" href="#__codelineno-63-21"></a><span class="cm">/* 恢复状态 */</span>
-<a id="__codelineno-63-22" name="__codelineno-63-22" href="#__codelineno-63-22"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-63-22" name="__codelineno-63-22" href="#__codelineno-63-22"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-63-23" name="__codelineno-63-23" href="#__codelineno-63-23"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="na">removeLast</span><span class="p">()</span>
 <a id="__codelineno-63-24" name="__codelineno-63-24" href="#__codelineno-63-24"></a><span class="p">}</span>
 <a id="__codelineno-63-25" name="__codelineno-63-25" href="#__codelineno-63-25"></a>
 <a id="__codelineno-63-26" name="__codelineno-63-26" href="#__codelineno-63-26"></a><span class="cm">/* 回溯算法：例题三 */</span>
 <a id="__codelineno-63-27" name="__codelineno-63-27" href="#__codelineno-63-27"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
-<a id="__codelineno-63-28" name="__codelineno-63-28" href="#__codelineno-63-28"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">,</span>
-<a id="__codelineno-63-29" name="__codelineno-63-29" href="#__codelineno-63-29"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="p">,</span>
-<a id="__codelineno-63-30" name="__codelineno-63-30" href="#__codelineno-63-30"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?&gt;</span><span class="o">?&gt;</span>
+<a id="__codelineno-63-28" name="__codelineno-63-28" href="#__codelineno-63-28"></a><span class="w">    </span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-63-29" name="__codelineno-63-29" href="#__codelineno-63-29"></a><span class="w">    </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?</span><span class="o">&gt;</span><span class="p">,</span>
+<a id="__codelineno-63-30" name="__codelineno-63-30" href="#__codelineno-63-30"></a><span class="w">    </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">MutableList</span><span class="o">&lt;</span><span class="n">TreeNode?</span><span class="o">&gt;?&gt;</span>
 <a id="__codelineno-63-31" name="__codelineno-63-31" href="#__codelineno-63-31"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-63-32" name="__codelineno-63-32" href="#__codelineno-63-32"></a><span class="w">    </span><span class="c1">// 检查是否为解</span>
 <a id="__codelineno-63-33" name="__codelineno-63-33" href="#__codelineno-63-33"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
@@ -6608,7 +6616,7 @@
 </div>
 <details class="pythontutor">
 <summary>可视化运行</summary>
-<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%0A%20%20%20%20def%20__init__(self%2C%20val%3A%20int%20%3D%200)%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%0Adef%20list_to_tree_dfs(arr%3A%20list%5Bint%5D%2C%20i%3A%20int)%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E9%80%92%E5%BD%92%22%22%22%0A%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len(arr)%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%0A%20%20%20%20root%20%3D%20TreeNode(arr%5Bi%5D)%0A%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs(arr%2C%202%20*%20i%20%2B%201)%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs(arr%2C%202%20*%20i%20%2B%202)%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree(arr%3A%20list%5Bint%5D)%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs(arr%2C%200)%0A%0A%0Adef%20is_solution(state%3A%20list%5BTreeNode%5D)%20-%3E%20bool%3A%0A%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%BD%93%E5%89%8D%E7%8A%B6%E6%80%81%E6%98%AF%E5%90%A6%E4%B8%BA%E8%A7%A3%22%22%22%0A%20%20%20%20return%20state%20and%20state%5B-1%5D.val%20%3D%3D%207%0A%0Adef%20record_solution(state%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D)%3A%0A%20%20%20%20%22%22%22%E8%AE%B0%E5%BD%95%E8%A7%A3%22%22%22%0A%20%20%20%20res.append(list(state))%0A%0Adef%20is_valid(state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode)%20-%3E%20bool%3A%0A%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%9C%A8%E5%BD%93%E5%89%8D%E7%8A%B6%E6%80%81%E4%B8%8B%EF%BC%8C%E8%AF%A5%E9%80%89%E6%8B%A9%E6%98%AF%E5%90%A6%E5%90%88%E6%B3%95%22%22%22%0A%20%20%20%20return%20choice%20is%20not%20None%20and%20choice.val%20!%3D%203%0A%0Adef%20make_choice(state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode)%3A%0A%20%20%20%20%22%22%22%E6%9B%B4%E6%96%B0%E7%8A%B6%E6%80%81%22%22%22%0A%20%20%20%20state.append(choice)%0A%0Adef%20undo_choice(state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode)%3A%0A%20%20%20%20%22%22%22%E6%81%A2%E5%A4%8D%E7%8A%B6%E6%80%81%22%22%22%0A%20%20%20%20state.pop()%0A%0Adef%20backtrack(%0A%20%20%20%20state%3A%20list%5BTreeNode%5D%2C%20choices%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D%0A)%3A%0A%20%20%20%20%22%22%22%E5%9B%9E%E6%BA%AF%E7%AE%97%E6%B3%95%EF%BC%9A%E4%BE%8B%E9%A2%98%E4%B8%89%22%22%22%0A%0A%20%20%20%20if%20is_solution(state)%3A%0A%0A%20%20%20%20%20%20%20%20record_solution(state%2C%20res)%0A%0A%20%20%20%20for%20choice%20in%20choices%3A%0A%0A%20%20%20%20%20%20%20%20if%20is_valid(state%2C%20choice)%3A%0A%0A%20%20%20%20%20%20%20%20%20%20%20%20make_choice(state%2C%20choice)%0A%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack(state%2C%20%5Bchoice.left%2C%20choice.right%5D%2C%20res)%0A%0A%20%20%20%20%20%20%20%20%20%20%20%20undo_choice(state%2C%20choice)%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree(%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D)%0A%0A%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack(state%3D%5B%5D%2C%20choices%3D%5Broot%5D%2C%20res%3Dres)%0A%20%20%20%20print(%22%5Cn%E8%BE%93%E5%87%BA%E6%89%80%E6%9C%89%E8%B7%AF%E5%BE%84%22)%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print(%5Bnode.val%20for%20node%20in%20path%5D)&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=138&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
+<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" title="可视化运行" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%0A%20%20%20%20def%20__init__(self%2C%20val%3A%20int%20%3D%200)%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%0Adef%20list_to_tree_dfs(arr%3A%20list%5Bint%5D%2C%20i%3A%20int)%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E9%80%92%E5%BD%92%22%22%22%0A%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len(arr)%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%0A%20%20%20%20root%20%3D%20TreeNode(arr%5Bi%5D)%0A%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs(arr%2C%202%20*%20i%20%2B%201)%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs(arr%2C%202%20*%20i%20%2B%202)%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree(arr%3A%20list%5Bint%5D)%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs(arr%2C%200)%0A%0A%0Adef%20is_solution(state%3A%20list%5BTreeNode%5D)%20-%3E%20bool%3A%0A%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%BD%93%E5%89%8D%E7%8A%B6%E6%80%81%E6%98%AF%E5%90%A6%E4%B8%BA%E8%A7%A3%22%22%22%0A%20%20%20%20return%20state%20and%20state%5B-1%5D.val%20%3D%3D%207%0A%0Adef%20record_solution(state%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D)%3A%0A%20%20%20%20%22%22%22%E8%AE%B0%E5%BD%95%E8%A7%A3%22%22%22%0A%20%20%20%20res.append(list(state))%0A%0Adef%20is_valid(state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode)%20-%3E%20bool%3A%0A%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%9C%A8%E5%BD%93%E5%89%8D%E7%8A%B6%E6%80%81%E4%B8%8B%EF%BC%8C%E8%AF%A5%E9%80%89%E6%8B%A9%E6%98%AF%E5%90%A6%E5%90%88%E6%B3%95%22%22%22%0A%20%20%20%20return%20choice%20is%20not%20None%20and%20choice.val%20!%3D%203%0A%0Adef%20make_choice(state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode)%3A%0A%20%20%20%20%22%22%22%E6%9B%B4%E6%96%B0%E7%8A%B6%E6%80%81%22%22%22%0A%20%20%20%20state.append(choice)%0A%0Adef%20undo_choice(state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode)%3A%0A%20%20%20%20%22%22%22%E6%81%A2%E5%A4%8D%E7%8A%B6%E6%80%81%22%22%22%0A%20%20%20%20state.pop()%0A%0Adef%20backtrack(%0A%20%20%20%20state%3A%20list%5BTreeNode%5D%2C%20choices%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D%0A)%3A%0A%20%20%20%20%22%22%22%E5%9B%9E%E6%BA%AF%E7%AE%97%E6%B3%95%EF%BC%9A%E4%BE%8B%E9%A2%98%E4%B8%89%22%22%22%0A%0A%20%20%20%20if%20is_solution(state)%3A%0A%0A%20%20%20%20%20%20%20%20record_solution(state%2C%20res)%0A%0A%20%20%20%20for%20choice%20in%20choices%3A%0A%0A%20%20%20%20%20%20%20%20if%20is_valid(state%2C%20choice)%3A%0A%0A%20%20%20%20%20%20%20%20%20%20%20%20make_choice(state%2C%20choice)%0A%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack(state%2C%20%5Bchoice.left%2C%20choice.right%5D%2C%20res)%0A%0A%20%20%20%20%20%20%20%20%20%20%20%20undo_choice(state%2C%20choice)%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree(%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D)%0A%0A%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack(state%3D%5B%5D%2C%20choices%3D%5Broot%5D%2C%20res%3Dres)%0A%20%20%20%20print(%22%5Cn%E8%BE%93%E5%87%BA%E6%89%80%E6%9C%89%E8%B7%AF%E5%BE%84%22)%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print(%5Bnode.val%20for%20node%20in%20path%5D)&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=138&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 <div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%0A%20%20%20%20def%20__init__(self%2C%20val%3A%20int%20%3D%200)%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%0A%0Adef%20list_to_tree_dfs(arr%3A%20list%5Bint%5D%2C%20i%3A%20int)%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E9%80%92%E5%BD%92%22%22%22%0A%0A%20%20%20%20if%20i%20%3C%200%20or%20i%20%3E%3D%20len(arr)%20or%20arr%5Bi%5D%20is%20None%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%0A%20%20%20%20root%20%3D%20TreeNode(arr%5Bi%5D)%0A%0A%20%20%20%20root.left%20%3D%20list_to_tree_dfs(arr%2C%202%20*%20i%20%2B%201)%0A%20%20%20%20root.right%20%3D%20list_to_tree_dfs(arr%2C%202%20*%20i%20%2B%202)%0A%20%20%20%20return%20root%0A%0Adef%20list_to_tree(arr%3A%20list%5Bint%5D)%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E5%B0%86%E5%88%97%E8%A1%A8%E5%8F%8D%E5%BA%8F%E5%88%97%E5%8C%96%E4%B8%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20return%20list_to_tree_dfs(arr%2C%200)%0A%0A%0Adef%20is_solution(state%3A%20list%5BTreeNode%5D)%20-%3E%20bool%3A%0A%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%BD%93%E5%89%8D%E7%8A%B6%E6%80%81%E6%98%AF%E5%90%A6%E4%B8%BA%E8%A7%A3%22%22%22%0A%20%20%20%20return%20state%20and%20state%5B-1%5D.val%20%3D%3D%207%0A%0Adef%20record_solution(state%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D)%3A%0A%20%20%20%20%22%22%22%E8%AE%B0%E5%BD%95%E8%A7%A3%22%22%22%0A%20%20%20%20res.append(list(state))%0A%0Adef%20is_valid(state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode)%20-%3E%20bool%3A%0A%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%9C%A8%E5%BD%93%E5%89%8D%E7%8A%B6%E6%80%81%E4%B8%8B%EF%BC%8C%E8%AF%A5%E9%80%89%E6%8B%A9%E6%98%AF%E5%90%A6%E5%90%88%E6%B3%95%22%22%22%0A%20%20%20%20return%20choice%20is%20not%20None%20and%20choice.val%20!%3D%203%0A%0Adef%20make_choice(state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode)%3A%0A%20%20%20%20%22%22%22%E6%9B%B4%E6%96%B0%E7%8A%B6%E6%80%81%22%22%22%0A%20%20%20%20state.append(choice)%0A%0Adef%20undo_choice(state%3A%20list%5BTreeNode%5D%2C%20choice%3A%20TreeNode)%3A%0A%20%20%20%20%22%22%22%E6%81%A2%E5%A4%8D%E7%8A%B6%E6%80%81%22%22%22%0A%20%20%20%20state.pop()%0A%0Adef%20backtrack(%0A%20%20%20%20state%3A%20list%5BTreeNode%5D%2C%20choices%3A%20list%5BTreeNode%5D%2C%20res%3A%20list%5Blist%5BTreeNode%5D%5D%0A)%3A%0A%20%20%20%20%22%22%22%E5%9B%9E%E6%BA%AF%E7%AE%97%E6%B3%95%EF%BC%9A%E4%BE%8B%E9%A2%98%E4%B8%89%22%22%22%0A%0A%20%20%20%20if%20is_solution(state)%3A%0A%0A%20%20%20%20%20%20%20%20record_solution(state%2C%20res)%0A%0A%20%20%20%20for%20choice%20in%20choices%3A%0A%0A%20%20%20%20%20%20%20%20if%20is_valid(state%2C%20choice)%3A%0A%0A%20%20%20%20%20%20%20%20%20%20%20%20make_choice(state%2C%20choice)%0A%0A%20%20%20%20%20%20%20%20%20%20%20%20backtrack(state%2C%20%5Bchoice.left%2C%20choice.right%5D%2C%20res)%0A%0A%20%20%20%20%20%20%20%20%20%20%20%20undo_choice(state%2C%20choice)%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20root%20%3D%20list_to_tree(%5B1%2C%207%2C%203%2C%204%2C%205%2C%206%2C%207%5D)%0A%0A%0A%20%20%20%20res%20%3D%20%5B%5D%0A%20%20%20%20backtrack(state%3D%5B%5D%2C%20choices%3D%5Broot%5D%2C%20res%3Dres)%0A%20%20%20%20print(%22%5Cn%E8%BE%93%E5%87%BA%E6%89%80%E6%9C%89%E8%B7%AF%E5%BE%84%22)%0A%20%20%20%20for%20path%20in%20res%3A%0A%20%20%20%20%20%20%20%20print(%5Bnode.val%20for%20node%20in%20path%5D)&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=138&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 &gt;</a></div></p>
 </details>
 <p>根据题意，我们在找到值为 <span class="arithmatex">\(7\)</span> 的节点后应该继续搜索，<strong>因此需要将记录解之后的 <code>return</code> 语句删除</strong>。图 13-4 对比了保留或删除 <code>return</code> 语句的搜索过程。</p>
@@ -6813,6 +6821,8 @@ aria-label="页脚"
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+
+
    /* Register event handlers after documented loaded */
    document.addEventListener("DOMContentLoaded", function() {
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@@ -6910,7 +6920,7 @@ aria-label="页脚"
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