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@@ -62,17 +62,15 @@
     
     
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-<div class="highlight"><span class="filename">fractional_knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">Item</span><span class="p">:</span>
+<div class="highlight"><span class="filename">fractional_knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">Item</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;物品&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">w</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">w</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
 <a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">w</span> <span class="o">=</span> <span class="n">w</span>  <span class="c1"># 物品重量</span>
 <a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">=</span> <span class="n">v</span>  <span class="c1"># 物品价值</span>
 <a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="k">def</span> <span class="nf">fractional_knapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">fractional_knapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;分数背包：贪心&quot;&quot;&quot;</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 创建物品列表，包含两个属性：重量、价值</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="n">items</span> <span class="o">=</span> <span class="p">[</span><span class="n">Item</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span> <span class="k">for</span> <span class="n">w</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">)]</span>
@@ -3814,13 +3812,13 @@
 <a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="kt">double</span><span class="w"> </span><span class="nf">FractionalKnapsack</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="c1">// 创建物品列表，包含两个属性：重量、价值</span>
 <a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="n">Item</span><span class="p">[]</span><span class="w"> </span><span class="n">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Item</span><span class="p">[</span><span class="n">wgt</span><span class="p">.</span><span class="n">Length</span><span class="p">];</span>
-<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Item</span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
 <a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="c1">// 按照单位价值 item.v / item.w 从高到低进行排序</span>
 <a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="n">Array</span><span class="p">.</span><span class="n">Sort</span><span class="p">(</span><span class="n">items</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">y</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">y</span><span class="p">.</span><span class="n">w</span><span class="p">).</span><span class="n">CompareTo</span><span class="p">(</span><span class="n">x</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">x</span><span class="p">.</span><span class="n">w</span><span class="p">));</span>
 <a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="c1">// 循环贪心选择</span>
-<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Item</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">            </span><span class="c1">// 若剩余容量充足，则将当前物品整个装进背包</span>
@@ -3875,38 +3873,38 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">fractional_knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 物品 */</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span> <span class="nc">Item</span> <span class="p">{</span>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>    <span class="kd">var</span> <span class="nv">w</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 物品重量</span>
-<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>    <span class="kd">var</span> <span class="nv">v</span><span class="p">:</span> <span class="nb">Int</span> <span class="c1">// 物品价值</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">w</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 物品重量</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">v</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// 物品价值</span>
 <a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
-<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="kd">init</span><span class="p">(</span><span class="n">w</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
-<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>        <span class="kc">self</span><span class="p">.</span><span class="n">w</span> <span class="p">=</span> <span class="n">w</span>
-<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>        <span class="kc">self</span><span class="p">.</span><span class="n">v</span> <span class="p">=</span> <span class="n">v</span>
-<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a>    <span class="p">}</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">w</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="kc">self</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">w</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="kc">self</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="p">}</span>
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
 <a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 分数背包：贪心 */</span>
-<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">func</span> <span class="nf">fractionalKnapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Double</span> <span class="p">{</span>
-<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>    <span class="c1">// 创建物品列表，包含两个属性：重量、价值</span>
-<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>    <span class="kd">var</span> <span class="nv">items</span> <span class="p">=</span> <span class="n">zip</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">).</span><span class="bp">map</span> <span class="p">{</span> <span class="n">Item</span><span class="p">(</span><span class="n">w</span><span class="p">:</span> <span class="nv">$0</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="nv">$1</span><span class="p">)</span> <span class="p">}</span>
-<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>    <span class="c1">// 按照单位价值 item.v / item.w 从高到低进行排序</span>
-<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>    <span class="n">items</span><span class="p">.</span><span class="bp">sort</span> <span class="p">{</span> <span class="o">-</span><span class="p">(</span><span class="nb">Double</span><span class="p">(</span><span class="nv">$0</span><span class="p">.</span><span class="n">v</span><span class="p">)</span> <span class="o">/</span> <span class="nb">Double</span><span class="p">(</span><span class="nv">$0</span><span class="p">.</span><span class="n">w</span><span class="p">))</span> <span class="o">&lt;</span> <span class="o">-</span><span class="p">(</span><span class="nb">Double</span><span class="p">(</span><span class="nv">$1</span><span class="p">.</span><span class="n">v</span><span class="p">)</span> <span class="o">/</span> <span class="nb">Double</span><span class="p">(</span><span class="nv">$1</span><span class="p">.</span><span class="n">w</span><span class="p">))</span> <span class="p">}</span>
-<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>    <span class="c1">// 循环贪心选择</span>
-<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a>    <span class="kd">var</span> <span class="nv">res</span> <span class="p">=</span> <span class="mf">0.0</span>
-<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a>    <span class="kd">var</span> <span class="nv">cap</span> <span class="p">=</span> <span class="n">cap</span>
-<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a>    <span class="k">for</span> <span class="n">item</span> <span class="k">in</span> <span class="n">items</span> <span class="p">{</span>
-<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a>        <span class="k">if</span> <span class="n">item</span><span class="p">.</span><span class="n">w</span> <span class="o">&lt;=</span> <span class="n">cap</span> <span class="p">{</span>
-<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a>            <span class="c1">// 若剩余容量充足，则将当前物品整个装进背包</span>
-<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a>            <span class="n">res</span> <span class="o">+=</span> <span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">)</span>
-<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a>            <span class="n">cap</span> <span class="o">-=</span> <span class="n">item</span><span class="p">.</span><span class="n">w</span>
-<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a>        <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
-<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a>            <span class="c1">// 若剩余容量不足，则将当前物品的一部分装进背包</span>
-<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a>            <span class="n">res</span> <span class="o">+=</span> <span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">)</span> <span class="o">/</span> <span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="p">)</span> <span class="o">*</span> <span class="nb">Double</span><span class="p">(</span><span class="n">cap</span><span class="p">)</span>
-<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a>            <span class="c1">// 已无剩余容量，因此跳出循环</span>
-<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a>            <span class="k">break</span>
-<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a>        <span class="p">}</span>
-<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a>    <span class="p">}</span>
-<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a>    <span class="k">return</span> <span class="n">res</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">func</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Double</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="c1">// 创建物品列表，包含两个属性：重量、价值</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">items</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">zip</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="bp">map</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">Item</span><span class="p">(</span><span class="n">w</span><span class="p">:</span><span class="w"> </span><span class="nv">$0</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">:</span><span class="w"> </span><span class="nv">$1</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="c1">// 按照单位价值 item.v / item.w 从高到低进行排序</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="n">items</span><span class="p">.</span><span class="bp">sort</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">-</span><span class="p">(</span><span class="nb">Double</span><span class="p">(</span><span class="nv">$0</span><span class="p">.</span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="nv">$0</span><span class="p">.</span><span class="n">w</span><span class="p">))</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="p">(</span><span class="nb">Double</span><span class="p">(</span><span class="nv">$1</span><span class="p">.</span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="nv">$1</span><span class="p">.</span><span class="n">w</span><span class="p">))</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="c1">// 循环贪心选择</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mf">0.0</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">cap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cap</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">items</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w">            </span><span class="c1">// 若剩余容量充足，则将当前物品整个装进背包</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">)</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></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-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w">            </span><span class="c1">// 若剩余容量不足，则将当前物品的一部分装进背包</span>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Double</span><span class="p">(</span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w">            </span><span class="c1">// 已无剩余容量，因此跳出循环</span>
+<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="w">            </span><span class="k">break</span>
+<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
 <a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -4014,25 +4012,25 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">fractional_knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 物品 */</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">struct</span> <span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="n">w</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 物品重量</span>
-<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="n">v</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 物品价值</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="n">w</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 物品重量</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="n">v</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// 物品价值</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">}</span>
 <a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a>
 <a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="k">impl</span><span class="w"> </span><span class="n">Item</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="k">fn</span> <span class="nf">new</span><span class="p">(</span><span class="n">w</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">v</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">w</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="w"> </span><span class="p">}</span>
 <a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="p">}</span>
 <a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a>
 <a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="cm">/* 分数背包：贪心 */</span>
-<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="k">fn</span> <span class="nf">fractional_knapsack</span><span class="p">(</span><span class="n">wgt</span>: <span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span>: <span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cap</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">f64</span> <span class="p">{</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="k">fn</span><span class="w"> </span><span class="nf">fractional_knapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cap</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">f64</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">    </span><span class="c1">// 创建物品列表，包含两个属性：重量、价值</span>
 <a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span>
 <a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">        </span><span class="p">.</span><span class="n">iter</span><span class="p">()</span>
 <a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="p">.</span><span class="n">zip</span><span class="p">(</span><span class="n">val</span><span class="p">.</span><span class="n">iter</span><span class="p">())</span>
-<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">        </span><span class="p">.</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="p">(</span><span class="o">&amp;</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">v</span><span class="p">)</span><span class="o">|</span><span class="w"> </span><span class="n">Item</span>::<span class="n">new</span><span class="p">(</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">))</span>
-<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">        </span><span class="p">.</span><span class="n">collect</span>::<span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Item</span><span class="o">&gt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">        </span><span class="p">.</span><span class="n">map</span><span class="p">(</span><span class="o">|</span><span class="p">(</span><span class="o">&amp;</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">v</span><span class="p">)</span><span class="o">|</span><span class="w"> </span><span class="n">Item</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">))</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">        </span><span class="p">.</span><span class="n">collect</span><span class="p">::</span><span class="o">&lt;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Item</span><span class="o">&gt;&gt;</span><span class="p">();</span>
 <a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="c1">// 按照单位价值 item.v / item.w 从高到低进行排序</span>
 <a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="n">items</span><span class="p">.</span><span class="n">sort_by</span><span class="p">(</span><span class="o">|</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="w">        </span><span class="p">(</span><span class="n">b</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="p">)</span>
@@ -4436,5 +4434,7 @@ aria-label="页脚"
         <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js"></script>
       
     
-  <script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
+  <script id="init-glightbox">const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});
+document$.subscribe(() => { lightbox.reload() });
+</script></body>
 </html>

chapter_greedy/greedy_algorithm/index.html

@@ -62,17 +62,15 @@
     
     
    <link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
-        html.glightbox-open { overflow: initial; height: 100%; }
-        .gslide-title { margin-top: 0px; user-select: text; }
-        .gslide-desc { color: #666; user-select: text; }
-        .gslide-image img { background: white; }
-        
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-            body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
-            </style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
+    html.glightbox-open { overflow: initial; height: 100%; }
+    .gslide-title { margin-top: 0px; user-select: text; }
+    .gslide-desc { color: #666; user-select: text; }
+    .gslide-image img { background: white; }
+    .gscrollbar-fixer { padding-right: 15px; }
+    .gdesc-inner { font-size: 0.75rem; }
+    body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
+    body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
+    body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
   
   
     
@@ -3704,7 +3702,7 @@
 <div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">coin_change_greedy.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="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<div class="highlight"><span class="filename">coin_change_greedy.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">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</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;零钱兑换：贪心&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 假设 coins 列表有序</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
@@ -3767,12 +3765,12 @@
 <div class="highlight"><span class="filename">coin_change_greedy.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 假设 coins 列表有序</span>
-<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
-<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
-<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
-<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">            </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
 <a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="c1">// 选择 coins[i]</span>
@@ -3780,7 +3778,7 @@
 <a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
 <a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
-<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -3810,23 +3808,23 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">coin_change_greedy.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>    <span class="c1">// 假设 coins 列表有序</span>
-<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>    <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">coins</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>    <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
-<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="kd">var</span> <span class="nv">amt</span> <span class="p">=</span> <span class="n">amt</span>
-<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>    <span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
-<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>    <span class="k">while</span> <span class="n">amt</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="p">{</span>
-<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a>        <span class="c1">// 找到小于且最接近剩余金额的硬币</span>
-<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="o">&amp;&amp;</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">amt</span> <span class="p">{</span>
-<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>            <span class="n">i</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a>        <span class="p">}</span>
-<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a>        <span class="c1">// 选择 coins[i]</span>
-<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>        <span class="n">amt</span> <span class="o">-=</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
-<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>        <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>    <span class="p">}</span>
-<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>    <span class="c1">// 若未找到可行方案，则返回 -1</span>
-<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>    <span class="k">return</span> <span class="n">amt</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">?</span> <span class="bp">count</span> <span class="p">:</span> <span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 假设 coins 列表有序</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">amt</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">amt</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// 循环进行贪心选择，直到无剩余金额</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="c1">// 找到小于且最接近剩余金额的硬币</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="c1">// 选择 coins[i]</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
 <a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -3895,7 +3893,7 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">coin_change_greedy.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span>: <span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">amt</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">i32</span> <span class="p">{</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 假设 coins 列表有序</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
@@ -4300,5 +4298,7 @@ aria-label="页脚"
         <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js"></script>
       
     
-  <script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
+  <script id="init-glightbox">const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});
+document$.subscribe(() => { lightbox.reload() });
+</script></body>
 </html>

chapter_greedy/index.html

@@ -62,17 +62,15 @@
     
     
    <link href="../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
-        html.glightbox-open { overflow: initial; height: 100%; }
-        .gslide-title { margin-top: 0px; user-select: text; }
-        .gslide-desc { color: #666; user-select: text; }
-        .gslide-image img { background: white; }
-        
-            .gscrollbar-fixer { padding-right: 15px; }
-            .gdesc-inner { font-size: 0.75rem; }
-            body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
-            body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
-            body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
-            </style> <script src="../assets/javascripts/glightbox.min.js"></script></head>
+    html.glightbox-open { overflow: initial; height: 100%; }
+    .gslide-title { margin-top: 0px; user-select: text; }
+    .gslide-desc { color: #666; user-select: text; }
+    .gslide-image img { background: white; }
+    .gscrollbar-fixer { padding-right: 15px; }
+    .gdesc-inner { font-size: 0.75rem; }
+    body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
+    body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
+    body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../assets/javascripts/glightbox.min.js"></script></head>
   
   
     
@@ -3846,5 +3844,7 @@ aria-label="页脚"
         <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js"></script>
       
     
-  <script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
+  <script id="init-glightbox">const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});
+document$.subscribe(() => { lightbox.reload() });
+</script></body>
 </html>

chapter_greedy/max_capacity_problem/index.html

@@ -62,17 +62,15 @@
     
     
    <link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
-        html.glightbox-open { overflow: initial; height: 100%; }
-        .gslide-title { margin-top: 0px; user-select: text; }
-        .gslide-desc { color: #666; user-select: text; }
-        .gslide-image img { background: white; }
-        
-            .gscrollbar-fixer { padding-right: 15px; }
-            .gdesc-inner { font-size: 0.75rem; }
-            body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
-            body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
-            body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
-            </style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
+    html.glightbox-open { overflow: initial; height: 100%; }
+    .gslide-title { margin-top: 0px; user-select: text; }
+    .gslide-desc { color: #666; user-select: text; }
+    .gslide-image img { background: white; }
+    .gscrollbar-fixer { padding-right: 15px; }
+    .gdesc-inner { font-size: 0.75rem; }
+    body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
+    body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
+    body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
   
   
     
@@ -3743,7 +3741,7 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 <div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_capacity.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="nf">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<div class="highlight"><span class="filename">max_capacity.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">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</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;最大容量：贪心&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 初始化 i, j，使其分列数组两端</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">ht</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
@@ -3812,9 +3810,9 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 <div class="highlight"><span class="filename">max_capacity.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最大容量：贪心 */</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MaxCapacity</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 初始化 i, j，使其分列数组两端</span>
-<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="c1">// 初始最大容量为 0</span>
-<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="c1">// 循环贪心选择，直至两板相遇</span>
 <a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">        </span><span class="c1">// 更新最大容量</span>
@@ -3856,24 +3854,24 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">max_capacity.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 最大容量：贪心 */</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">maxCapacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>    <span class="c1">// 初始化 i, j，使其分列数组两端</span>
-<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>    <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">ht</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span> <span class="n">j</span> <span class="p">=</span> <span class="n">ht</span><span class="p">.</span><span class="n">endIndex</span> <span class="o">-</span> <span class="mi">1</span>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>    <span class="c1">// 初始最大容量为 0</span>
-<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="kd">var</span> <span class="nv">res</span> <span class="p">=</span> <span class="mi">0</span>
-<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>    <span class="c1">// 循环贪心选择，直至两板相遇</span>
-<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="p">{</span>
-<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a>        <span class="c1">// 更新最大容量</span>
-<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>        <span class="kd">let</span> <span class="nv">cap</span> <span class="p">=</span> <span class="bp">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span>
-<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>        <span class="n">res</span> <span class="p">=</span> <span class="bp">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">cap</span><span class="p">)</span>
-<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a>        <span class="c1">// 向内移动短板</span>
-<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a>        <span class="k">if</span> <span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="p">{</span>
-<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
-<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>        <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
-<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
-<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>        <span class="p">}</span>
-<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>    <span class="p">}</span>
-<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a>    <span class="k">return</span> <span class="n">res</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 初始化 i, j，使其分列数组两端</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">endIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="c1">// 初始最大容量为 0</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// 循环贪心选择，直至两板相遇</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="c1">// 更新最大容量</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">cap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="c1">// 向内移动短板</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></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-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
 <a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -3950,7 +3948,7 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">max_capacity.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 最大容量：贪心 */</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">max_capacity</span><span class="p">(</span><span class="n">ht</span>: <span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span>-&gt; <span class="kt">i32</span> <span class="p">{</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 初始化 i, j，使其分列数组两端</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
@@ -3959,8 +3957,8 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 <a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="c1">// 循环贪心选择，直至两板相遇</span>
 <a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">        </span><span class="c1">// 更新最大容量</span>
-<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
-<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
 <a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="c1">// 向内移动短板</span>
 <a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
@@ -4317,5 +4315,7 @@ aria-label="页脚"
         <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js"></script>
       
     
-  <script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
+  <script id="init-glightbox">const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});
+document$.subscribe(() => { lightbox.reload() });
+</script></body>
 </html>

chapter_greedy/max_product_cutting_problem/index.html

@@ -62,17 +62,15 @@
     
     
    <link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
-        html.glightbox-open { overflow: initial; height: 100%; }
-        .gslide-title { margin-top: 0px; user-select: text; }
-        .gslide-desc { color: #666; user-select: text; }
-        .gslide-image img { background: white; }
-        
-            .gscrollbar-fixer { padding-right: 15px; }
-            .gdesc-inner { font-size: 0.75rem; }
-            body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
-            body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
-            body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
-            </style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
+    html.glightbox-open { overflow: initial; height: 100%; }
+    .gslide-title { margin-top: 0px; user-select: text; }
+    .gslide-desc { color: #666; user-select: text; }
+    .gslide-image img { background: white; }
+    .gscrollbar-fixer { padding-right: 15px; }
+    .gdesc-inner { font-size: 0.75rem; }
+    body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
+    body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
+    body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
   
   
     
@@ -3719,7 +3717,7 @@ n = 3 a + b
 <div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">max_product_cutting.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="nf">max_product_cutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<div class="highlight"><span class="filename">max_product_cutting.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">max_product_cutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</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;最大切分乘积：贪心&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 当 n &lt;= 3 时，必须切分出一个 1</span>
 <a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">3</span><span class="p">:</span>
@@ -3786,22 +3784,22 @@ n = 3 a + b
 <div class="highlight"><span class="filename">max_product_cutting.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最大切分乘积：贪心 */</span>
 <a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MaxProductCutting</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 当 n &lt;= 3 时，必须切分出一个 1</span>
-<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</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-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
 <a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="c1">// 贪心地切分出 3 ，a 为 3 的个数，b 为余数</span>
-<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
-<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
-<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</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="p">{</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="c1">// 当余数为 1 时，将一对 1 * 3 转化为 2 * 2</span>
-<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">Math</span><span class="p">.</span><span class="n">Pow</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</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="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">Math</span><span class="p">.</span><span class="n">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="c1">// 当余数为 2 时，不做处理</span>
-<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">Math</span><span class="p">.</span><span class="n">Pow</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">Math</span><span class="p">.</span><span class="n">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
 <a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="c1">// 当余数为 0 时，不做处理</span>
-<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">Math</span><span class="p">.</span><span class="n">Pow</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">Math</span><span class="p">.</span><span class="n">Pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
 <a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -3830,24 +3828,24 @@ n = 3 a + b
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">max_product_cutting.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 最大切分乘积：贪心 */</span>
-<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">maxProductCutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
-<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>    <span class="c1">// 当 n &lt;= 3 时，必须切分出一个 1</span>
-<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">3</span> <span class="p">{</span>
-<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>        <span class="k">return</span> <span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="p">}</span>
-<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>    <span class="c1">// 贪心地切分出 3 ，a 为 3 的个数，b 为余数</span>
-<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>    <span class="kd">let</span> <span class="nv">a</span> <span class="p">=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">3</span>
-<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a>    <span class="kd">let</span> <span class="nv">b</span> <span class="p">=</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">3</span>
-<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>    <span class="k">if</span> <span class="n">b</span> <span class="p">==</span> <span class="mi">1</span> <span class="p">{</span>
-<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>        <span class="c1">// 当余数为 1 时，将一对 1 * 3 转化为 2 * 2</span>
-<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a>        <span class="k">return</span> <span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span>
-<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a>    <span class="p">}</span>
-<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>    <span class="k">if</span> <span class="n">b</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
-<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>        <span class="c1">// 当余数为 2 时，不做处理</span>
-<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>        <span class="k">return</span> <span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span>
-<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>    <span class="p">}</span>
-<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>    <span class="c1">// 当余数为 0 时，不做处理</span>
-<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a>    <span class="k">return</span> <span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">maxProductCutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="c1">// 当 n &lt;= 3 时，必须切分出一个 1</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="c1">// 贪心地切分出 3 ，a 为 3 的个数，b 为余数</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="c1">// 当余数为 1 时，将一对 1 * 3 转化为 2 * 2</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="c1">// 当余数为 2 时，不做处理</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="c1">// 当余数为 0 时，不做处理</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span>
 <a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="p">}</span>
 </code></pre></div>
 </div>
@@ -3922,7 +3920,7 @@ n = 3 a + b
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">max_product_cutting.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 最大切分乘积：贪心 */</span>
-<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">max_product_cutting</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">i32</span> <span class="p">{</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">max_product_cutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="c1">// 当 n &lt;= 3 时，必须切分出一个 1</span>
 <a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
@@ -4026,9 +4024,9 @@ n = 3 a + b
 </ul>
 <p>变量 <span class="arithmatex">\(a\)</span> 和 <span class="arithmatex">\(b\)</span> 使用常数大小的额外空间，<strong>因此空间复杂度为 <span class="arithmatex">\(O(1)\)</span></strong> 。</p>
 <h3 id="3">3. &nbsp; 正确性证明<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
-<p>使用反证法，只分析 <span class="arithmatex">\(n \geq 3\)</span> 的情况。</p>
+<p>使用反证法，只分析 <span class="arithmatex">\(n \geq 4\)</span> 的情况。</p>
 <ol>
-<li><strong>所有因子 <span class="arithmatex">\(\leq 3\)</span></strong> ：假设最优切分方案中存在 <span class="arithmatex">\(\geq 4\)</span> 的因子 <span class="arithmatex">\(x\)</span> ，那么一定可以将其继续划分为 <span class="arithmatex">\(2(x-2)\)</span> ，从而获得更大的乘积。这与假设矛盾。</li>
+<li><strong>所有因子 <span class="arithmatex">\(\leq 3\)</span></strong> ：假设最优切分方案中存在 <span class="arithmatex">\(\geq 4\)</span> 的因子 <span class="arithmatex">\(x\)</span> ，那么一定可以将其继续划分为 <span class="arithmatex">\(2(x-2)\)</span> ，从而获得更大（或相等）的乘积。这与假设矛盾。</li>
 <li><strong>切分方案不包含 <span class="arithmatex">\(1\)</span></strong> ：假设最优切分方案中存在一个因子 <span class="arithmatex">\(1\)</span> ，那么它一定可以合并入另外一个因子中，以获得更大的乘积。这与假设矛盾。</li>
 <li><strong>切分方案最多包含两个 <span class="arithmatex">\(2\)</span></strong> ：假设最优切分方案中包含三个 <span class="arithmatex">\(2\)</span> ，那么一定可以替换为两个 <span class="arithmatex">\(3\)</span> ，乘积更大。这与假设矛盾。</li>
 </ol>
@@ -4282,5 +4280,7 @@ aria-label="页脚"
         <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js"></script>
       
     
-  <script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
+  <script id="init-glightbox">const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});
+document$.subscribe(() => { lightbox.reload() });
+</script></body>
 </html>

chapter_greedy/summary/index.html

@@ -62,17 +62,15 @@
     
     
    <link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
-        html.glightbox-open { overflow: initial; height: 100%; }
-        .gslide-title { margin-top: 0px; user-select: text; }
-        .gslide-desc { color: #666; user-select: text; }
-        .gslide-image img { background: white; }
-        
-            .gscrollbar-fixer { padding-right: 15px; }
-            .gdesc-inner { font-size: 0.75rem; }
-            body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
-            body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
-            body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
-            </style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
+    html.glightbox-open { overflow: initial; height: 100%; }
+    .gslide-title { margin-top: 0px; user-select: text; }
+    .gslide-desc { color: #666; user-select: text; }
+    .gslide-image img { background: white; }
+    .gscrollbar-fixer { padding-right: 15px; }
+    .gdesc-inner { font-size: 0.75rem; }
+    body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
+    body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
+    body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
   
   
     
@@ -3837,5 +3835,7 @@ aria-label="页脚"
         <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js"></script>
       
     
-  <script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
+  <script id="init-glightbox">const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});
+document$.subscribe(() => { lightbox.reload() });
+</script></body>
 </html>