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-      <a href="../../chapter_dynamic_programming/dp_solution_pipeline.md" class="md-nav__link">
-        13.3. &nbsp; DP 解题步骤（New）
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        13.3. &nbsp; DP 解题思路（New）
       </a>
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-      <a href="../chapter_dynamic_programming/dp_solution_pipeline.md" class="md-nav__link">
-        13.3. &nbsp; DP 解题步骤（New）
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        13.3. &nbsp; DP 解题思路（New）
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-      <a href="../../chapter_dynamic_programming/dp_solution_pipeline.md" class="md-nav__link">
-        13.3. &nbsp; DP 解题步骤（New）
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        13.3. &nbsp; DP 解题思路（New）
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chapter_backtracking/permutations_problem/index.html

@@ -2017,8 +2017,8 @@
   
   
     <li class="md-nav__item">
-      <a href="../../chapter_dynamic_programming/dp_solution_pipeline.md" class="md-nav__link">
-        13.3. &nbsp; DP 解题步骤（New）
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        13.3. &nbsp; DP 解题思路（New）
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chapter_backtracking/subset_sum_problem/index.html

@@ -2017,8 +2017,8 @@
   
   
     <li class="md-nav__item">
-      <a href="../../chapter_dynamic_programming/dp_solution_pipeline.md" class="md-nav__link">
-        13.3. &nbsp; DP 解题步骤（New）
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        13.3. &nbsp; DP 解题思路（New）
       </a>
     </li>
   
@@ -2426,9 +2426,36 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i_naive.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
-<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i_naive.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 回溯算法：子集和 I */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">total</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="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span> <span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a>    <span class="c1">// 子集和等于 target 时，记录解</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>    <span class="k">if</span> <span class="n">total</span> <span class="p">==</span> <span class="n">target</span> <span class="p">{</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a>        <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a>        <span class="k">return</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a>    <span class="p">}</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a>    <span class="c1">// 遍历所有选择</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">choices</span><span class="p">.</span><span class="bp">count</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a>        <span class="c1">// 剪枝：若子集和超过 target ，则跳过该选择</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>        <span class="k">if</span> <span class="n">total</span> <span class="o">+</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span> <span class="p">{</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a>            <span class="k">continue</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a>        <span class="p">}</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a>        <span class="c1">// 尝试：做出选择，更新元素和 total</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a>        <span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a>        <span class="c1">// 进行下一轮选择</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">:</span> <span class="n">target</span><span class="p">,</span> <span class="n">total</span><span class="p">:</span> <span class="n">total</span> <span class="o">+</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a>        <span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a>        <span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>    <span class="p">}</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="p">}</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="cm">/* 求解子集和 I（包含重复子集） */</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="kd">func</span> <span class="nf">subsetSumINaive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span> <span class="p">{</span>
+<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a>    <span class="kd">var</span> <span class="nv">state</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span> <span class="c1">// 状态（子集）</span>
+<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a>    <span class="kd">let</span> <span class="nv">total</span> <span class="p">=</span> <span class="mi">0</span> <span class="c1">// 子集和</span>
+<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a>    <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span> <span class="p">=</span> <span class="p">[]</span> <span class="c1">// 结果列表（子集列表）</span>
+<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">:</span> <span class="n">target</span><span class="p">,</span> <span class="n">total</span><span class="p">:</span> <span class="n">total</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="n">nums</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a>    <span class="k">return</span> <span class="n">res</span>
+<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@@ -2666,9 +2693,39 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_i.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
-<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">subsetSumI</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_i.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 回溯算法：子集和 I */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">target</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="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">start</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span> <span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a>    <span class="c1">// 子集和等于 target 时，记录解</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a>    <span class="k">if</span> <span class="n">target</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a>        <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a>        <span class="k">return</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a>    <span class="p">}</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a>    <span class="c1">// 遍历所有选择</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a>    <span class="c1">// 剪枝二：从 start 开始遍历，避免生成重复子集</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="n">start</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">choices</span><span class="p">.</span><span class="bp">count</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a>        <span class="c1">// 剪枝一：若子集和超过 target ，则直接结束循环</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a>        <span class="c1">// 这是因为数组已排序，后边元素更大，子集和一定超过 target</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a>        <span class="k">if</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="p">{</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a>            <span class="k">break</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a>        <span class="p">}</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a>        <span class="c1">// 尝试：做出选择，更新 target, start</span>
+<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a>        <span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></a>        <span class="c1">// 进行下一轮选择</span>
+<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">:</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="n">choices</span><span class="p">,</span> <span class="n">start</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a>        <span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
+<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a>        <span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a>    <span class="p">}</span>
+<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="p">}</span>
+<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a>
+<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="cm">/* 求解子集和 I */</span>
+<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="kd">func</span> <span class="nf">subsetSumI</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span> <span class="p">{</span>
+<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a>    <span class="kd">var</span> <span class="nv">state</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span> <span class="c1">// 状态（子集）</span>
+<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a>    <span class="kd">let</span> <span class="nv">nums</span> <span class="p">=</span> <span class="n">nums</span><span class="p">.</span><span class="bp">sorted</span><span class="p">()</span> <span class="c1">// 对 nums 进行排序</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a>    <span class="kd">let</span> <span class="nv">start</span> <span class="p">=</span> <span class="mi">0</span> <span class="c1">// 遍历起始点</span>
+<a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a>    <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span> <span class="p">=</span> <span class="p">[]</span> <span class="c1">// 结果列表（子集列表）</span>
+<a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">:</span> <span class="n">target</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="n">nums</span><span class="p">,</span> <span class="n">start</span><span class="p">:</span> <span class="n">start</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a>    <span class="k">return</span> <span class="n">res</span>
+<a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@@ -2923,9 +2980,44 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">subset_sum_ii.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
-<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a>
-<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">subsetSumII</span><span class="p">}</span>
+<div class="highlight"><span class="filename">subset_sum_ii.swift</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 回溯算法：子集和 II */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kd">func</span> <span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">target</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="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">start</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span> <span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a>    <span class="c1">// 子集和等于 target 时，记录解</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a>    <span class="k">if</span> <span class="n">target</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">{</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a>        <span class="n">res</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a>        <span class="k">return</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a>    <span class="p">}</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a>    <span class="c1">// 遍历所有选择</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a>    <span class="c1">// 剪枝二：从 start 开始遍历，避免生成重复子集</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a>    <span class="c1">// 剪枝三：从 start 开始遍历，避免重复选择同一元素</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="n">start</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">choices</span><span class="p">.</span><span class="bp">count</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a>        <span class="c1">// 剪枝一：若子集和超过 target ，则直接结束循环</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a>        <span class="c1">// 这是因为数组已排序，后边元素更大，子集和一定超过 target</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a>        <span class="k">if</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="p">{</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a>            <span class="k">break</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a>        <span class="p">}</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a>        <span class="c1">// 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="n">start</span><span class="p">,</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">==</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="p">{</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a>            <span class="k">continue</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a>        <span class="p">}</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a>        <span class="c1">// 尝试：做出选择，更新 target, start</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a>        <span class="n">state</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a>        <span class="c1">// 进行下一轮选择</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">:</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="n">choices</span><span class="p">,</span> <span class="n">start</span><span class="p">:</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a>        <span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a>        <span class="n">state</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a>    <span class="p">}</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="p">}</span>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="cm">/* 求解子集和 II */</span>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="kd">func</span> <span class="nf">subsetSumII</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span> <span class="p">{</span>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a>    <span class="kd">var</span> <span class="nv">state</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span> <span class="c1">// 状态（子集）</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a>    <span class="kd">let</span> <span class="nv">nums</span> <span class="p">=</span> <span class="n">nums</span><span class="p">.</span><span class="bp">sorted</span><span class="p">()</span> <span class="c1">// 对 nums 进行排序</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a>    <span class="kd">let</span> <span class="nv">start</span> <span class="p">=</span> <span class="mi">0</span> <span class="c1">// 遍历起始点</span>
+<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a>    <span class="kd">var</span> <span class="nv">res</span><span class="p">:</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span> <span class="p">=</span> <span class="p">[]</span> <span class="c1">// 结果列表（子集列表）</span>
+<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">:</span> <span class="n">target</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="n">nums</span><span class="p">,</span> <span class="n">start</span><span class="p">:</span> <span class="n">start</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a>    <span class="k">return</span> <span class="n">res</span>
+<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">

chapter_backtracking/summary/index.html

@@ -1972,8 +1972,8 @@
   
   
     <li class="md-nav__item">
-      <a href="../../chapter_dynamic_programming/dp_solution_pipeline.md" class="md-nav__link">
-        13.3. &nbsp; DP 解题步骤（New）
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        13.3. &nbsp; DP 解题思路（New）
       </a>
     </li>