deploy

chapter_dynamic_programming/knapsack_problem/index.html

@@ -3956,7 +3956,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 0-1 背包：暴力搜索 */</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">knapsackDFS</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="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</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="n">value</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</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="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
 <a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
 <a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
 <a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
@@ -3966,11 +3966,11 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="c1">// 若超过背包容量，则只能选择不放入背包</span>
 <a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
 <a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="c1">// 计算不放入和放入物品 i 的最大价值</span>
-<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
-<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">value</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
 <a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">    </span><span class="c1">// 返回两种方案中价值更大的那一个</span>
 <a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">)</span>
 <a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="p">}</span>
@@ -4296,7 +4296,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 0-1 背包：记忆化搜索 */</span>
 <a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">knapsackDFSMem</span><span class="p">(</span>
 <a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">    </span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
-<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">    </span><span class="n">value</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">    </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
 <a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w">    </span><span class="n">mem</span><span class="p">:</span><span class="w"> </span><span class="n">Array</span><span class="o">&lt;</span><span class="n">IntArray</span><span class="o">&gt;</span><span class="p">,</span>
 <a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
 <a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w">    </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
@@ -4311,11 +4311,11 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">    </span><span class="c1">// 若超过背包容量，则只能选择不放入背包</span>
 <a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
 <a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w">    </span><span class="c1">// 计算不放入和放入物品 i 的最大价值</span>
-<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
-<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">value</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
+<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">_val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
 <a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w">    </span><span class="c1">// 记录并返回两种方案中价值更大的那一个</span>
 <a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">)</span>
 <a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
@@ -4635,7 +4635,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* 0-1 背包：动态规划 */</span>
 <a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">knapsackDP</span><span class="p">(</span>
 <a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w">    </span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
-<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w">    </span><span class="n">value</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w">    </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
 <a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w">    </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
 <a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">size</span>
@@ -4649,7 +4649,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span>
 <a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a><span class="w">                </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
-<a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">value</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span>
 <a id="__codelineno-39-19" name="__codelineno-39-19" href="#__codelineno-39-19"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-39-20" name="__codelineno-39-20" href="#__codelineno-39-20"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-39-21" name="__codelineno-39-21" href="#__codelineno-39-21"></a><span class="w">    </span><span class="p">}</span>
@@ -5007,7 +5007,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 0-1 背包：空间优化后的动态规划 */</span>
 <a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">knapsackDPComp</span><span class="p">(</span>
 <a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
-<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="n">value</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
 <a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">    </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
 <a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">size</span>
@@ -5020,7 +5020,7 @@ dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
 <a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="w">                </span><span class="c1">// 不选和选物品 i 这两种方案的较大值</span>
 <a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span>
-<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="w">                    </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">value</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="w">                    </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">_val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span>
 <a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a><span class="w">    </span><span class="p">}</span>