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                # 排序算法 快速排序 選擇一個基準元素,通常選擇第一個元素或者最后一個元素。通過一趟掃描,將待排序列分成兩部分,一部分比基準元素小,一部分大于等于基準元素。此時基準元素在其排好序后的正確位置,然后再用同樣的方法遞歸地排序劃分的兩部分。 ``` <pre class="calibre14">``` <span class="token5">function</span> <span class="token1">quicksort</span><span class="token2">(</span>$arr<span class="token2">)</span> <span class="token2">{</span> <span class="token6">//判斷參數是否是一個數組</span> <span class="token5">if</span><span class="token2">(</span><span class="token">!</span><span class="token1">is_array</span><span class="token2">(</span>$arr<span class="token2">)</span><span class="token2">)</span> <span class="token5">return</span> <span class="token3">false</span><span class="token2">;</span> <span class="token6">//遞歸出口:數組長度為1,直接返回數組</span> $length <span class="token">=</span> <span class="token1">count</span><span class="token2">(</span>$arr<span class="token2">)</span><span class="token2">;</span> <span class="token5">if</span><span class="token2">(</span>$length<span class="token"><=</span><span class="token3">1</span><span class="token2">)</span> <span class="token5">return</span> $arr<span class="token2">;</span> <span class="token6">//數組元素有多個,則定義兩個空數組</span> $left <span class="token">=</span> $right <span class="token">=</span> <span class="token1">array</span><span class="token2">(</span><span class="token2">)</span><span class="token2">;</span> <span class="token6">//使用for循環進行遍歷,把第一個元素當做比較的對象</span> <span class="token5">for</span><span class="token2">(</span>$i<span class="token">=</span><span class="token3">1</span><span class="token2">;</span> $i<span class="token"><</span>$length<span class="token2">;</span> $i<span class="token">++</span><span class="token2">)</span> <span class="token2">{</span> <span class="token6">//判斷當前元素的大小</span> <span class="token5">if</span><span class="token2">(</span>$arr<span class="token2">[</span>$i<span class="token2">]</span><span class="token"><</span>$arr<span class="token2">[</span><span class="token3">0</span><span class="token2">]</span><span class="token2">)</span><span class="token2">{</span> $left<span class="token2">[</span><span class="token2">]</span><span class="token">=</span>$arr<span class="token2">[</span>$i<span class="token2">]</span><span class="token2">;</span> <span class="token2">}</span><span class="token5">else</span><span class="token2">{</span> $right<span class="token2">[</span><span class="token2">]</span><span class="token">=</span>$arr<span class="token2">[</span>$i<span class="token2">]</span><span class="token2">;</span> <span class="token2">}</span> <span class="token2">}</span> <span class="token6">//遞歸調用</span> $left<span class="token">=</span><span class="token1">quicksort</span><span class="token2">(</span>$left<span class="token2">)</span><span class="token2">;</span> $right<span class="token">=</span><span class="token1">quicksort</span><span class="token2">(</span>$right<span class="token2">)</span><span class="token2">;</span> <span class="token6">//將所有的結果合并</span> <span class="token5">return</span> <span class="token1">array_merge</span><span class="token2">(</span>$left<span class="token2">,</span><span class="token1">array</span><span class="token2">(</span>$arr<span class="token2">[</span><span class="token3">0</span><span class="token2">]</span><span class="token2">)</span><span class="token2">,</span>$right<span class="token2">)</span><span class="token2">;</span> <span class="token2">}</span> ``` ``` 插入排序 在要排序的一組數中,假設前面的數已經是排好順序的,現在要把第n個數插到前面的有序數中,使得這n個數也是排好順序的。如此反復循環,直到全部排好順序。 ``` <pre class="calibre14">``` <span class="token5">function</span> <span class="token1">insertsort</span><span class="token2">(</span>$arr<span class="token2">)</span> <span class="token2">{</span> $len<span class="token">=</span><span class="token1">count</span><span class="token2">(</span>$arr<span class="token2">)</span><span class="token2">;</span> <span class="token5">for</span><span class="token2">(</span>$i<span class="token">=</span><span class="token3">1</span><span class="token2">;</span> $i<span class="token"><</span>$len<span class="token2">;</span> $i<span class="token">++</span><span class="token2">)</span> <span class="token2">{</span> <span class="token6">//獲得當前需要比較的元素值。</span> $tmp <span class="token">=</span> $arr<span class="token2">[</span>$i<span class="token2">]</span><span class="token2">;</span> <span class="token6">//內層循環控制 比較 并 插入</span> <span class="token5">for</span><span class="token2">(</span>$j<span class="token">=</span>$i<span class="token">-</span><span class="token3">1</span><span class="token2">;</span> $j<span class="token">>=</span><span class="token3">0</span><span class="token2">;</span> $j<span class="token">--</span><span class="token2">)</span> <span class="token2">{</span> <span class="token6">//$arr[$i];//需要插入的元素; $arr[$j];//需要比較的元素</span> <span class="token5">if</span><span class="token2">(</span>$tmp <span class="token"><</span> $arr<span class="token2">[</span>$j<span class="token2">]</span><span class="token2">)</span> <span class="token2">{</span> <span class="token6">//發現插入的元素要小,交換位置</span> <span class="token6">//將后邊的元素與前面的元素互換</span> $arr<span class="token2">[</span>$j<span class="token">+</span><span class="token3">1</span><span class="token2">]</span> <span class="token">=</span> $arr<span class="token2">[</span>$j<span class="token2">]</span><span class="token2">;</span> <span class="token6">//將前面的數設置為 當前需要交換的數</span> $arr<span class="token2">[</span>$j<span class="token2">]</span> <span class="token">=</span> $tmp<span class="token2">;</span> <span class="token2">}</span> <span class="token5">else</span> <span class="token2">{</span> <span class="token6">//如果碰到不需要移動的元素</span> <span class="token6">//由于是已經排序好是數組,則前面的就不需要再次比較了。</span> <span class="token5">break</span><span class="token2">;</span> <span class="token2">}</span> <span class="token2">}</span> <span class="token2">}</span> <span class="token6">//將這個元素 插入到已經排序好的序列內。</span> <span class="token6">//返回</span> <span class="token5">return</span> $arr<span class="token2">;</span> <span class="token2">}</span> ``` ``` 選擇排序 在要排序的一組數中,選出最小的一個數與第一個位置的數交換。然后在剩下的數當中再找最小的與第二個位置的數交換,如此循環到倒數第二個數和最后一個數比較為止。 ``` <pre class="calibre14">``` <span class="token5">function</span> <span class="token1">selectsort</span><span class="token2">(</span>$arr<span class="token2">)</span> <span class="token2">{</span> <span class="token6">//$i 當前最小值的位置, 需要參與比較的元素</span> <span class="token5">for</span><span class="token2">(</span>$i<span class="token">=</span><span class="token3">0</span><span class="token2">,</span> $len<span class="token">=</span><span class="token1">count</span><span class="token2">(</span>$arr<span class="token2">)</span><span class="token2">;</span> $i<span class="token"><</span>$len<span class="token">-</span><span class="token3">1</span><span class="token2">;</span> $i<span class="token">++</span><span class="token2">)</span> <span class="token2">{</span> <span class="token6">//先假設最小的值的位置</span> $p <span class="token">=</span> $i<span class="token2">;</span> <span class="token6">//$j 當前都需要和哪些元素比較,$i 后邊的。</span> <span class="token5">for</span><span class="token2">(</span>$j<span class="token">=</span>$i<span class="token">+</span><span class="token3">1</span><span class="token2">;</span> $j<span class="token"><</span>$len<span class="token2">;</span> $j<span class="token">++</span><span class="token2">)</span> <span class="token2">{</span> <span class="token6">//$arr[$p] 是 當前已知的最小值</span> <span class="token5">if</span><span class="token2">(</span>$arr<span class="token2">[</span>$p<span class="token2">]</span> <span class="token">></span> $arr<span class="token2">[</span>$j<span class="token2">]</span><span class="token2">)</span> <span class="token2">{</span> <span class="token6">//比較,發現更小的,記錄下最小值的位置;并且在下次比較時,應該采用已知的最小值進行比較。</span> $p <span class="token">=</span> $j<span class="token2">;</span> <span class="token2">}</span> <span class="token2">}</span> <span class="token6">//已經確定了當前的最小值的位置,保存到$p中。</span> <span class="token6">//如果發現 最小值的位置與當前假設的位置$i不同,則位置互換即可</span> <span class="token5">if</span><span class="token2">(</span>$p <span class="token">!=</span> $i<span class="token2">)</span> <span class="token2">{</span> $tmp <span class="token">=</span> $arr<span class="token2">[</span>$p<span class="token2">]</span><span class="token2">;</span> $arr<span class="token2">[</span>$p<span class="token2">]</span> <span class="token">=</span> $arr<span class="token2">[</span>$i<span class="token2">]</span><span class="token2">;</span> $arr<span class="token2">[</span>$i<span class="token2">]</span> <span class="token">=</span> $tmp<span class="token2">;</span> <span class="token2">}</span> <span class="token2">}</span> <span class="token6">//返回最終結果</span> <span class="token5">return</span> $arr<span class="token2">;</span> <span class="token2">}</span> ``` ``` 冒泡排序 在要排序的一組數中,對當前還未排好的序列,從前往后對相鄰的兩個數依次進行比較和調整,讓較大的數往下沉,較小的往上冒。即,每當兩相鄰的數比較后發現它們的排序與排序要求相反時,就將它們互換 ``` <pre class="calibre14">``` <span class="token5">function</span> bubbleSort <span class="token2">(</span>$arr<span class="token2">)</span> <span class="token2">{</span> $len <span class="token">=</span> <span class="token1">count</span><span class="token2">(</span>$arr<span class="token2">)</span><span class="token2">;</span> <span class="token6">//該層循環控制 需要冒泡的輪數</span> <span class="token5">for</span> <span class="token2">(</span>$i<span class="token">=</span><span class="token3">1</span><span class="token2">;</span> $i<span class="token"><</span>$len<span class="token2">;</span> $i<span class="token">++</span><span class="token2">)</span> <span class="token2">{</span> <span class="token6">//該層循環用來控制每輪 冒出一個數 需要比較的次數</span> <span class="token5">for</span> <span class="token2">(</span>$k<span class="token">=</span><span class="token3">0</span><span class="token2">;</span> $k<span class="token"><</span>$len<span class="token">-</span>$i<span class="token2">;</span> $k<span class="token">++</span><span class="token2">)</span> <span class="token2">{</span> <span class="token5">if</span><span class="token2">(</span>$arr<span class="token2">[</span>$k<span class="token2">]</span> <span class="token">></span> $arr<span class="token2">[</span>$k<span class="token">+</span><span class="token3">1</span><span class="token2">]</span><span class="token2">)</span> <span class="token2">{</span> $tmp <span class="token">=</span> $arr<span class="token2">[</span>$k<span class="token">+</span><span class="token3">1</span><span class="token2">]</span><span class="token2">;</span> <span class="token6">// 聲明一個臨時變量</span> $arr<span class="token2">[</span>$k<span class="token">+</span><span class="token3">1</span><span class="token2">]</span> <span class="token">=</span> $arr<span class="token2">[</span>$k<span class="token2">]</span><span class="token2">;</span> $arr<span class="token2">[</span>$k<span class="token2">]</span> <span class="token">=</span> $tmp<span class="token2">;</span> <span class="token2">}</span> <span class="token2">}</span> <span class="token2">}</span> <span class="token5">return</span> $arr<span class="token2">;</span> <span class="token2">}</span> ``` ``` 思路分析:希爾排序是基于插入排序的,區別在于插入排序是相鄰的一個個比較(類似于希爾中h=1的情形), 而希爾排序是距離h的比較和替換。 希爾排序中一個常數因子n,原數組被分成各個小組,每個小組由h個元素組成,很可能會有多余的元素。 當然每次循環的時候,h也是遞減的(h=h/n)。第一次循環就是從下標為h開始。 希爾排序的一個思想就是,分成小組去排序 ``` <pre class="calibre16">``` <span class="token5">function</span> <span class="token1">shellsort</span><span class="token2">(</span>array $arr<span class="token2">)</span><span class="token2">{</span> <span class="token6">// 將$arr按升序排列</span> $len <span class="token">=</span> <span class="token1">count</span><span class="token2">(</span>$arr<span class="token2">)</span><span class="token2">;</span> $f <span class="token">=</span> <span class="token3">3</span><span class="token2">;</span><span class="token6">// 定義因子</span> $h <span class="token">=</span> <span class="token3">1</span><span class="token2">;</span><span class="token6">// 最小為1</span> <span class="token5">while</span> <span class="token2">(</span>$h <span class="token"><</span> $len<span class="token">/</span>$f<span class="token2">)</span><span class="token2">{</span> $h <span class="token">=</span> $f<span class="token">*</span>$h <span class="token">+</span> <span class="token3">1</span><span class="token2">;</span> <span class="token6">// 1, 4, 13, 40, 121, 364, 1093, ...</span> <span class="token2">}</span> <span class="token5">while</span> <span class="token2">(</span>$h <span class="token">>=</span> <span class="token3">1</span><span class="token2">)</span><span class="token2">{</span> <span class="token6">// 將數組變為h有序</span> <span class="token5">for</span> <span class="token2">(</span>$i <span class="token">=</span> $h<span class="token2">;</span> $i <span class="token"><</span> $len<span class="token2">;</span> $i<span class="token">++</span><span class="token2">)</span><span class="token2">{</span> <span class="token6">// 將a[i]插入到a[i-h], a[i-2*h], a[i-3*h]... 之中 (算法的關鍵)</span> <span class="token5">for</span> <span class="token2">(</span>$j <span class="token">=</span> $i<span class="token2">;</span> $j <span class="token">>=</span> $h<span class="token2">;</span> $j <span class="token">-</span><span class="token">=</span> $h<span class="token2">)</span><span class="token2">{</span> <span class="token5">if</span> <span class="token2">(</span>$arr<span class="token2">[</span>$j<span class="token2">]</span> <span class="token"><</span> $arr<span class="token2">[</span>$j<span class="token">-</span>$h<span class="token2">]</span><span class="token2">)</span><span class="token2">{</span> $temp <span class="token">=</span> $arr<span class="token2">[</span>$j<span class="token2">]</span><span class="token2">;</span> $arr<span class="token2">[</span>$j<span class="token2">]</span> <span class="token">=</span> $arr<span class="token2">[</span>$j<span class="token">-</span>$h<span class="token2">]</span><span class="token2">;</span> $arr<span class="token2">[</span>$j<span class="token">-</span>$h<span class="token2">]</span> <span class="token">=</span> $temp<span class="token2">;</span> <span class="token2">}</span> <span class="token6">//print_r($arr);echo '<br/>'; // 打開這行注釋,可以看到每一步被替換的情形</span> <span class="token2">}</span> <span class="token2">}</span> $h <span class="token">=</span> <span class="token1">intval</span><span class="token2">(</span>$h<span class="token">/</span>$f<span class="token2">)</span><span class="token2">;</span> <span class="token2">}</span> <span class="token5">return</span> $arr<span class="token2">;</span> <span class="token2">}</span> ``` ```
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