JAVA 九種排序算法詳解（下）

{"type":"doc","content":[{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"八、快速排序：","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"1.基本思想：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"選擇一個基準元素,通常選擇第一個元素或者最後一個元素,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,一部分大於等於基準元素,此時基準元素在其排好序後的正確位置,然後再用同樣的方法遞歸地排序劃分的兩部分。","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"2.實現過程：","attrs":{}}]},{"type":"bulletedlist","content":[{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"原數組值：","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":"none"},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"32 , 43, 23, 13, 5","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"第一輪比較：選擇第一個數爲p，小於p的數放在左邊，大於p的數放在右邊，結果如下：","attrs":{}}]}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"​\t\t32 , 13, 5, ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"32,","attrs":{}},{"type":"text","text":" 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, 5, ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"23,","attrs":{}},{"type":"text","text":" 32, 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, ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"13,","attrs":{}},{"type":"text","text":" 23, 32, 43","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":"none"},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如圖所示：","attrs":{}}]}]}],"attrs":{}},{"type":"listitem","attrs":{"listStyle":"none"},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/09/092cf1c2afbe6611fbf9abf22a44c282.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"3.實現代碼：","attrs":{}}]},{"type":"codeblock","attrs":{"lang":"java"},"content":[{"type":"text","text":"package cn.hz.demo2;\n\n/**\n * @author hz\n * @version 1.0\n *\n * 快速排序\n * 需求分析：\n * 選擇第一個數爲p，小於p的數放在左邊，大於p的數放在右邊。\n * 遞歸的將p左邊和右邊的數都按照第一步進行，直到不能遞歸。\n *\n */\npublic class Demo8 {\n public static void main(String[] args) {\n int[] a={49,38,65,97,76,13,27,49,78,34,12,64,1}; //定義需要排序數組\n System.out.println(\"快速排序前\");\n for (int ia:a){\n System.out.print(ia+\"t\");\n }\n //快速排序\n quickSort(a,0,a.length-1);\n System.out.println(\"n快速排序後\");\n for (int ia:a){\n System.out.print(ia+\"t\");\n }\n\n }\n public static void quickSort(int[] numbers, int start, int end) {\n if (start < end) {\n int base = numbers[start]; // 選定的基準值（第一個數值作爲基準值）\n int temp; // 記錄臨時中間值\n int i = start, j = end;\n do {\n while ((numbers[i] < base) && (i < end))\n i++;\n while ((numbers[j] > base) && (j > start))\n j--;\n if (i <= j) {\n temp = numbers[i];\n numbers[i] = numbers[j];\n numbers[j] = temp;\n i++;\n j--;\n }\n } while (i <= j);\n if (start < j)\n quickSort(numbers, start, j);\n if (end > i)\n quickSort(numbers, i, end);\n }\n }\n}\n","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"實現效果：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/7b/7bd3b5e622aae338c8095ffe6fc04dff.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"4.分析：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"快速排序是不穩定的排序。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"快速排序的時間複雜度爲O(nlogn)。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"當n較大時使用快排比較好，當序列基本有序時用快排反而不好。","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"5.穩定性總結：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"快速排序有兩個方向，左邊的i下標一直往右走（當條件a[i] <= a[center_index]時），其中center_index是中樞元素的數組下標，一般取爲數組第0個元素。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"而右邊的j下標一直往左走（當a[j] > a[center_index]時）。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如果i和j都走不動了，i <= j, 交換a[i]和a[j],重複上面的過程，直到i>j。交換a[j]和a[center_index]，完成一趟快速排序。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"在中樞元素和a[j]交換的時候，很有可能把前面的元素的穩定性打亂，比如序列爲 5 3 3 4 3 8 9 10 11","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"現在中樞元素5和3(第5個元素，下標從1開始計)交換就會把元素3的穩定性打亂。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所以快速排序是一個不穩定的排序算法，不穩定發生在中樞元素和a[j]交換的時刻。","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","text":"九、歸併排序：","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"1.基本思想：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"歸併（Merge）排序法是將兩個（或兩個以上）有序表合併成一個新的有序表，即把待排序序列分爲若干個子序列，每個子序列是有序的。然後再把有序子序列合併爲整體有序序列。","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"2.實現過程：","attrs":{}}]},{"type":"bulletedlist","content":[{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"原數組值：","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":"none"},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"32 , 43, 23, 13, 5","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"第一輪比較：選擇相鄰兩個數組成一個有序序列，結果如下：","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":"none"},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"32 , 43, 13, 23, 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23, 32, 43, 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5， 13, 23, 32, 43,","attrs":{}}]}]},{"type":"listitem","attrs":{"listStyle":"none"},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"如圖所示：","attrs":{}}]}]}],"attrs":{}},{"type":"listitem","attrs":{"listStyle":"none"},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}}]},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f6/f6e70fb7cbee966d9d8791f862b99ae2.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"heading","attrs":{"align":null,"level":3},"content":[{"type":"text","text":"3.實現代碼：","attrs":{}}]},{"type":"codeblock","attrs":{"lang":"java"},"content":[{"type":"text","text":"package cn.hz.demo2;\n\n/**\n * @author hz\n * @version 1.0\n *\n * 歸併排序\n * 需求分析:\n * 選擇相鄰兩個數組成一個有序序列。\n * 選擇相鄰的兩個有序序列組成一個有序序列。\n * 重複第二步，直到全部組成一個有序序列。\n */\npublic class Demo9 {\n public static void main(String[] args) {\n int[] a={49,38,65,97,76,13,27,49,78,34,12,64,1,8};\n System.out.println(\"歸併排序之前：\");\n for (int i = 0; i < a.length; i++) {\n System.out.print(a[i]+\" \");\n }\n //歸併排序\n mergeSort(a,0,a.length-1);\n System.out.println();\n System.out.println(\"排序之後：\");\n for (int i = 0; i < a.length; i++) {\n System.out.print(a[i]+\" \");\n }\n }\n private static void mergeSort(int[] a, int left, int right) {\n if(left max) {\n max = array[i];\n }\n }\n int time = 0;\n //判斷位數;\n while (max > 0) {\n max /= 10;\n time++;\n }\n //建立10個隊列;\n List queue = new ArrayList();\n for (int i = 0; i < 10; i++) {\n ArrayList queue1 = new ArrayList();\n queue.add(queue1);\n }\n //進行time次分配和收集;\n for (int i = 0; i < time; i++) {\n //分配數組元素;\n for (int j = 0; j < array.length; j++) {\n //得到數字的第time+1位數;\n int x = array[j] % (int) Math.pow(10, i + 1) / (int) Math.pow(10, i);\n ArrayList queue2 = queue.get(x);\n queue2.add(array[j]);\n queue.set(x, queue2);\n }\n int count = 0;//元素計數器;\n //收集隊列元素;\n for (int k = 0; k < 10; k++) {\n while (queue.get(k).size() > 0) {\n ArrayList queue3 = queue.get(k);\n array[count] = queue3.get(0);\n queue3.remove(0);\n count++;\n }\n }\n }\n\n System.out.println(\"n基數排序之後：\");\n for (int i = 0; i < array.length; i++) {\n System.out.print(array[i]+\" \");\n }\n\n\n 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