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@ -3647,7 +3647,7 @@
<h3 id="2">2. &nbsp; 代码实现<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>我们建立了一个物品类 <code>Item</code> ，以便将物品按照单位价值进行排序。循环进行贪心选择，当背包已满时跳出并返回解：</p>
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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>
@ -4045,9 +4045,79 @@
</code></pre></div>
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<div class="highlight"><span class="filename">fractional_knapsack.zig</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
<div class="highlight"><span class="filename">fractional_knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 物品 */</span>
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Item</span><span class="p">(</span>
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">w</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="c1">// 物品</span>
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">v</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="c1">// 物品价值</span>
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="p">)</span>
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm">/* 分数背包：贪心 */</span>
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span>
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="n">value</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="p">):</span><span class="w"> </span><span class="kt">Double</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></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-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></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="o">=</span><span class="w"> </span><span class="n">c</span>
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="o">&lt;</span><span class="n">Item</span><span class="o">&gt;</span><span class="p">(</span><span class="n">wgt</span><span class="p">.</span><span class="na">size</span><span class="p">)</span>
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </span><span class="n">items</span><span class="o">[</span><span class="n">i</span><span class="o">]</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">wgt</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></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-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">items</span><span class="p">,</span><span class="w"> </span><span class="n">Comparator</span><span class="p">.</span><span class="na">comparingDouble</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">item</span><span class="p">:</span><span class="w"> </span><span class="n">Item</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="o">-</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="na">v</span><span class="p">.</span><span class="na">toDouble</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="p">)</span><span class="w"> </span><span class="p">})</span>
<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w"> </span><span class="c1">// 循环贪心选择</span>
<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></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="o">=</span><span class="w"> </span><span class="m">0.0</span>
<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</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-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></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="o">!!</span><span class="p">.</span><span class="na">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-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></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-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></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">item</span><span class="p">.</span><span class="na">v</span><span class="p">.</span><span class="na">toDouble</span><span class="p">()</span>
<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></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="na">w</span>
<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></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-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></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-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></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">item</span><span class="p">.</span><span class="na">v</span><span class="p">.</span><span class="na">toDouble</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span>
<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w"> </span><span class="c1">// 已无剩余容量，因此跳出循环</span>
<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="p">}</span>
<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a>
<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="cm">/* 分数背包：贪心 */</span>
<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span>
<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="w"> </span><span class="n">wgt</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="w"> </span><span class="n">value</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a><span class="w"> </span><span class="n">c</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
<a id="__codelineno-11-43" name="__codelineno-11-43" href="#__codelineno-11-43"></a><span class="p">):</span><span class="w"> </span><span class="kt">Double</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-44" name="__codelineno-11-44" href="#__codelineno-11-44"></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-11-45" name="__codelineno-11-45" href="#__codelineno-11-45"></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="o">=</span><span class="w"> </span><span class="n">c</span>
<a id="__codelineno-11-46" name="__codelineno-11-46" href="#__codelineno-11-46"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arrayOfNulls</span><span class="o">&lt;</span><span class="n">Item</span><span class="o">&gt;</span><span class="p">(</span><span class="n">wgt</span><span class="p">.</span><span class="na">size</span><span class="p">)</span>
<a id="__codelineno-11-47" name="__codelineno-11-47" href="#__codelineno-11-47"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-48" name="__codelineno-11-48" href="#__codelineno-11-48"></a><span class="w"> </span><span class="n">items</span><span class="o">[</span><span class="n">i</span><span class="o">]</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">wgt</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
<a id="__codelineno-11-49" name="__codelineno-11-49" href="#__codelineno-11-49"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-50" name="__codelineno-11-50" href="#__codelineno-11-50"></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-11-51" name="__codelineno-11-51" href="#__codelineno-11-51"></a><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">items</span><span class="p">,</span><span class="w"> </span><span class="n">Comparator</span><span class="p">.</span><span class="na">comparingDouble</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">item</span><span class="p">:</span><span class="w"> </span><span class="n">Item</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="o">-</span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="na">v</span><span class="p">.</span><span class="na">toDouble</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="p">)</span><span class="w"> </span><span class="p">})</span>
<a id="__codelineno-11-52" name="__codelineno-11-52" href="#__codelineno-11-52"></a><span class="w"> </span><span class="c1">// 循环贪心选择</span>
<a id="__codelineno-11-53" name="__codelineno-11-53" href="#__codelineno-11-53"></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="o">=</span><span class="w"> </span><span class="m">0.0</span>
<a id="__codelineno-11-54" name="__codelineno-11-54" href="#__codelineno-11-54"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</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-11-55" name="__codelineno-11-55" href="#__codelineno-11-55"></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="o">!!</span><span class="p">.</span><span class="na">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-11-56" name="__codelineno-11-56" href="#__codelineno-11-56"></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-11-57" name="__codelineno-11-57" href="#__codelineno-11-57"></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">item</span><span class="p">.</span><span class="na">v</span><span class="p">.</span><span class="na">toDouble</span><span class="p">()</span>
<a id="__codelineno-11-58" name="__codelineno-11-58" href="#__codelineno-11-58"></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="na">w</span>
<a id="__codelineno-11-59" name="__codelineno-11-59" href="#__codelineno-11-59"></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-11-60" name="__codelineno-11-60" href="#__codelineno-11-60"></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-11-61" name="__codelineno-11-61" href="#__codelineno-11-61"></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">item</span><span class="p">.</span><span class="na">v</span><span class="p">.</span><span class="na">toDouble</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span>
<a id="__codelineno-11-62" name="__codelineno-11-62" href="#__codelineno-11-62"></a><span class="w"> </span><span class="c1">// 已无剩余容量，因此跳出循环</span>
<a id="__codelineno-11-63" name="__codelineno-11-63" href="#__codelineno-11-63"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-11-64" name="__codelineno-11-64" href="#__codelineno-11-64"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-65" name="__codelineno-11-65" href="#__codelineno-11-65"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-66" name="__codelineno-11-66" href="#__codelineno-11-66"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-11-67" name="__codelineno-11-67" href="#__codelineno-11-67"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fractional_knapsack.zig</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
</code></pre></div>
</div>
</div>