deploy

chapter_greedy/fractional_knapsack_problem/index.html

@@ -3425,7 +3425,7 @@
 
 <h3 id="_2">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>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:11"><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" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label><label for="__tabbed_1_11">Dart</label></div>
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 <div class="tabbed-content">
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 <div class="highlight"><span class="filename">fractional_knapsack.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 物品 */</span>
@@ -3644,6 +3644,51 @@
 <a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></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 class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.rs</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="k">struct</span> <span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="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-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></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-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="k">impl</span><span class="w"> </span><span class="n">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></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-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></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-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="p">}</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="cm">/* 分数背包：贪心 */</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></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-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></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-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></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-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">        </span><span class="p">.</span><span class="n">iter</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><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-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></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-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></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-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></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-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></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-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></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>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">            </span><span class="p">.</span><span class="n">partial_cmp</span><span class="p">(</span><span class="o">&amp;</span><span class="p">(</span><span class="n">a</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">a</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>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">            </span><span class="p">.</span><span class="n">unwrap</span><span class="p">()</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </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="c1">// 循环贪心选择</span>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></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">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0</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="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="o">&amp;</span><span class="n">items</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></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-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></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-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></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="n">v</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="p">;</span>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></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><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><span class="w"> </span><span class="k">else</span><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="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-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></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="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">item</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="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">f64</span><span class="p">;</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a><span class="w">            </span><span class="c1">// 已无剩余容量，因此跳出循环</span>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w">        </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="p">}</span>
+<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a><span class="p">}</span>
+</code></pre></div>
+</div>
 </div>
 </div>
 <p>最差情况下，需要遍历整个物品列表，<strong>因此时间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> ，其中 <span class="arithmatex">\(n\)</span> 为物品数量。</p>

chapter_greedy/greedy_algorithm/index.html

@@ -3426,7 +3426,7 @@
 <p align="center"> Fig. 零钱兑换的贪心策略 </p>
 
 <p>实现代码如下所示。你可能会不由地发出感叹：So Clean ！贪心算法仅用十行代码就解决了零钱兑换问题。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:11"><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" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label><label for="__tabbed_1_11">Dart</label></div>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><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" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label><label for="__tabbed_1_11">Dart</label><label for="__tabbed_1_12">Rust</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">coin_change_greedy.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
@@ -3557,6 +3557,31 @@
 <div class="highlight"><span class="filename">coin_change_greedy.dart</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></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">coinChangeGreedy</span><span class="p">}</span>
 </code></pre></div>
 </div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.rs</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 零钱兑换：贪心 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></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-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// 假设 coins 列表有序</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></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-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></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>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></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-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></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-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></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-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">        </span><span class="k">while</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-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></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>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="c1">// 选择 coins[i]</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></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-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="n">count</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-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="c1">// 若未找到可行方案，则返回 -1</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">    </span><span class="k">if</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="p">{</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="n">count</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></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-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">        </span><span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
 </div>
 </div>
 <h2 id="1511">15.1.1. &nbsp; 贪心优点与局限性<a class="headerlink" href="#1511" title="Permanent link">&para;</a></h2>

chapter_greedy/max_capacity_problem/index.html

@@ -3469,7 +3469,7 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 <h3 id="_2">代码实现<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h3>
 <p>代码循环最多 <span class="arithmatex">\(n\)</span> 轮，<strong>因此时间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
 <p>变量 <span class="arithmatex">\(i\)</span> , <span class="arithmatex">\(j\)</span> , <span class="arithmatex">\(res\)</span> 使用常数大小额外空间，<strong>因此空间复杂度为 <span class="arithmatex">\(O(1)\)</span></strong> 。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="2:11"><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" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label><label for="__tabbed_2_9">Swift</label><label for="__tabbed_2_10">Zig</label><label for="__tabbed_2_11">Dart</label></div>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><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" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label><label for="__tabbed_2_9">Swift</label><label for="__tabbed_2_10">Zig</label><label for="__tabbed_2_11">Dart</label><label for="__tabbed_2_12">Rust</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">max_capacity.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 最大容量：贪心 */</span>
@@ -3607,6 +3607,30 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
 <div class="highlight"><span class="filename">max_capacity.dart</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></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">maxCapacity</span><span class="p">}</span>
 </code></pre></div>
 </div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.rs</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 最大容量：贪心 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></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-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="c1">// 初始化 i, j 分列数组两端</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></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-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></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>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="c1">// 初始最大容量为 0</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></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">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-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="c1">// 循环贪心选择，直至两板相遇</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></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-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">        </span><span class="c1">// 更新最大容量</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></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-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></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-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="c1">// 向内移动短板</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></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-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></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>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></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><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="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w">    </span><span class="n">res</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
 </div>
 </div>
 <h3 id="_3">正确性证明<a class="headerlink" href="#_3" title="Permanent link">&para;</a></h3>

chapter_greedy/max_product_cutting_problem/index.html

@@ -3445,7 +3445,7 @@ n & \geq 4
 n = 3 a + b
 \]</div>
 <p>请注意，对于 <span class="arithmatex">\(n \leq 3\)</span> 的边界情况，必须拆分出一个 <span class="arithmatex">\(1\)</span> ，乘积为 <span class="arithmatex">\(1 \times (n - 1)\)</span> 。</p>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:11"><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" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label><label for="__tabbed_1_11">Dart</label></div>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><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" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label><label for="__tabbed_1_11">Dart</label><label for="__tabbed_1_12">Rust</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">max_product_cutting.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 最大切分乘积：贪心 */</span>
@@ -3581,6 +3581,29 @@ n = 3 a + b
 <div class="highlight"><span class="filename">max_product_cutting.dart</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></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">maxProductCutting</span><span class="p">}</span>
 </code></pre></div>
 </div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.rs</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 最大切分乘积：贪心 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></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-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></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-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></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-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></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-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></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-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="kd">let</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-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w">    </span><span class="kd">let</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-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></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="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </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="c1">// 当余数为 1 时，将一对 1 * 3 转化为 2 * 2</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="mi">3_</span><span class="k">i32</span><span class="p">.</span><span class="n">pow</span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">u32</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-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </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="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="c1">// 当余数为 2 时，不做处理</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="mi">3_</span><span class="k">i32</span><span class="p">.</span><span class="n">pow</span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">u32</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-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">        </span><span class="c1">// 当余数为 0 时，不做处理</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="mi">3_</span><span class="k">i32</span><span class="p">.</span><span class="n">pow</span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">u32</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="p">}</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
 </div>
 </div>
 <p><img alt="最大切分乘积的计算方法" src="../max_product_cutting_problem.assets/max_product_cutting_greedy_calculation.png" /></p>