【Data Structure】nlogn-SortMethods(Quick/Heap/Shell/Merge)

排序算法有很多,主要有： 

一、插入排序（包括ShellSort希尔排序）

二、选择排序（包括HeapSort堆排序）

三、快速（Quick）排序

四、归并（Merge）排序

五、基数排序 等

每个人排序的分类也不同。

这里针对一些先进的算法（时间复杂度nlogn）进行一些总结（Given in the form of C language）。

QuickSort/HeapSort/ShellSort/MergeSort

1.QuickSort

#pragma once#include "Swap.h"typedef int ElemType;int Partition(ElemType arr[], int low, int high) {int pivotkey = arr[low];while (low < high) {while (low < high && arr[high] >= pivotkey)--high;Swap(arr[low], arr[high]);while (low < high && arr[low] <= pivotkey)++low;Swap(arr[high],arr[low]);}return low;}void QSort(ElemType arr[], int low, int high) {int pivotloc = 0;if (low < high) {pivotloc = Partition(arr, low, high);QSort(arr, low, pivotloc - 1);QSort(arr, pivotloc + 1, high);}}void QuickSort(ElemType arr[], int length) {QSort(arr, 0, length - 1);}

2.HeapSort

#pragma once#include "Swap.h"#include "LT.h"typedef int HeapType;void HeapAdjust(HeapType arr[], int s, int m) {int rc = arr[s];for (int j = 2 * s ; j <= m; j *= 2) {if (j < m && LT(arr[j], arr[j + 1]))++j;if (!LT(rc, arr[j]))break;arr[s] = arr[j];s = j;}arr[s] = rc;}void HeapSort(HeapType arr[], int length) {for (int i = length / 2 - 1; i >= 0; --i)HeapAdjust(arr, i, length);for (int i = length - 1; i > 0; --i) {Swap(arr[0],arr[i]);HeapAdjust(arr, 0, i - 1);}}

3.ShellSort

#pragma once#include "LT.h"typedef int Elemtype;void ShellInsert(Elemtype arr[], int dk,int length) {int i, j, temp;for (i = dk; i < length; ++i)if ( LT(arr[i], arr[i - dk]) ) {temp = arr[i];for (j = i - dk; j > 0 && LT(temp, arr[j]); j -= dk)arr[j + dk] = arr[j];arr[j + dk] = temp;}}void ShellSort(Elemtype arr[], int dlta[], int t,int length) {for (int k = 0; k < t; ++k)ShellInsert(arr, dlta[k],length);}

4.MergeSort

#pragma oncetypedef int RcdType;void Merge(int arr[], int tarr[], int start, int mid, int end) {int i = start, j = mid + 1, k = 0, m = mid, n = end;while (i <= m && j <= n){if (arr[i] <= arr[j])tarr[k++] = arr[i++];elsetarr[k++] = arr[j++];}while (i <= m)tarr[k++] = arr[i++];while (j <= n)tarr[k++] = arr[j++];for (i = 0; i < k; i++)arr[start + i] = tarr[i];}void MSort(RcdType arr[], RcdType tarr[], int start, int end) {if (start < end) {int mid = (start + end) / 2;MSort(arr, tarr, start, mid);MSort(arr, tarr, mid + 1, end);Merge(arr, tarr, start, mid, end);}}void MergeSort(int arr[],int n) {int tarr[10];MSort(arr, tarr, 0, n - 1);}

LT.h 比较a和b的大小

#pragma oncebool LT(int a, int b) {if (a < b)return true;return false;}

Swap.h 交换a和b的值

#pragma oncevoid Swap(int &a, int &b) {int t = a;a = b;b = t;}

以上代码用Main.cpp验证

#include <stdio.h>#include "QuickSort.h"#include "HeapSort.h"#include "ShellSort.h"#include "MergeSort.h"#define SIZE 10#define DSIZE 3int main() {int a[SIZE] = { 3,5,8,2,7,4,9,6,1,10 }; // An Examplefor (int i = 0;i < SIZE; ++i)printf("%d ", a[i]);printf("\n");QuickSort(a, SIZE); // QuickSortHeapSort(a,SIZE); //HeapSortint dlta[DSIZE] = { 5,3,1 }; //假定设此组步长ShellSort(a, dlta, DSIZE, SIZE); //ShellSortMergeSort(a, SIZE); //MergeSortfor (int i = 0;i < SIZE; ++i)printf("%d ", a[i]);printf("\n");return 0;}

以上所列算法的O(n) = nlogn，但该MergeSort（又称二路归并）以递归形式调用，实用性较差。

实际中多采用QuickSort