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@ -1883,11 +1883,65 @@
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">bucket_sort.js</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bucketSort</span><span class="p">}</span>
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<div class="highlight"><span class="filename">bucket_sort.js</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 桶排序 */</span>
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<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bucketSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="c1">// 初始化 k = n/2 个桶，预期向每个桶分配 2 个元素</span>
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<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
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<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
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<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="nx">buckets</span><span class="p">.</span><span class="nx">push</span><span class="p">([]);</span>
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<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="c1">// 1. 将数组元素分配到各个桶中</span>
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<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="c1">// 输入数据范围 [0, 1)，使用 num * k 映射到索引范围 [0, k-1]</span>
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<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k</span><span class="p">);</span>
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<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// 将 num 添加进桶 i</span>
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<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
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<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="c1">// 2. 对各个桶执行排序</span>
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<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="c1">// 使用内置排序函数，也可以替换成其它排序算法</span>
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<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span>
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<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="c1">// 3. 遍历桶合并结果</span>
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<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
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<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
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<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">bucket_sort.ts</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bucketSort</span><span class="p">}</span>
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<div class="highlight"><span class="filename">bucket_sort.ts</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 桶排序 */</span>
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<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bucketSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="c1">// 初始化 k = n/2 个桶，预期向每个桶分配 2 个元素</span>
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<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
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<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">buckets</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
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<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="nx">buckets</span><span class="p">.</span><span class="nx">push</span><span class="p">([]);</span>
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<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="c1">// 1. 将数组元素分配到各个桶中</span>
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<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="c1">// 输入数据范围 [0, 1)，使用 num * k 映射到索引范围 [0, k-1]</span>
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<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k</span><span class="p">);</span>
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<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="c1">// 将 num 添加进桶 i</span>
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<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="nx">buckets</span><span class="p">[</span><span class="nx">i</span><span class="p">].</span><span class="nx">push</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
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<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="c1">// 2. 对各个桶执行排序</span>
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<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w"> </span><span class="c1">// 使用内置排序函数，也可以替换成其它排序算法</span>
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<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w"> </span><span class="nx">bucket</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span>
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<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w"> </span><span class="c1">// 3. 遍历桶合并结果</span>
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<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
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<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
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<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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@ -1944,7 +1998,7 @@
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<p>桶排序是否稳定取决于排序桶内元素的算法是否稳定。</p>
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<h2 id="1163">11.6.3. 如何实现平均分配<a class="headerlink" href="#1163" title="Permanent link">¶</a></h2>
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<p>桶排序的时间复杂度理论上可以达到 <span class="arithmatex">\(O(n)\)</span> ，<strong>难点是需要将元素均匀分配到各个桶中</strong>，因为现实中的数据往往都不是均匀分布的。举个例子，假设我们想要把淘宝的所有商品根据价格范围平均分配到 10 个桶中，然而商品价格不是均匀分布的，100 元以下非常多、1000 元以上非常少；如果我们将价格区间平均划为 10 份，那么各个桶内的商品数量差距会非常大。</p>
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<p>为了实现平均分配，我们可以先大致设置一个分界线，将数据粗略分到 3 个桶，分配完后，<strong>再把商品较多的桶继续划分为 3 个桶，直至所有桶内元素数量大致平均为止</strong>。此方法本质上是生成一个递归树，让叶结点的值尽量平均。当然，不一定非要划分为 3 个桶，可以根据数据特点灵活选取。</p>
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<p>为了实现平均分配，我们可以先大致设置一个分界线，将数据粗略分到 3 个桶，分配完后，<strong>再把商品较多的桶继续划分为 3 个桶，直至所有桶内元素数量大致平均为止</strong>。此方法本质上是生成一个递归树，让叶节点的值尽量平均。当然，不一定非要划分为 3 个桶，可以根据数据特点灵活选取。</p>
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<p><img alt="递归划分桶" src="../bucket_sort.assets/scatter_in_buckets_recursively.png" /></p>
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<p align="center"> Fig. 递归划分桶 </p>
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