归并排序（递归与非递归写法）

本文同步发布在CSDN：https://blog.csdn.net/weixin_44385565/article/details/94588321

归并排序的基本操作是将两个有序数组合并成一个有序数组，原理是运用分治思想，递归地将一个数组的左右两部分有序数列进行归并。

C/C++的递归实现：

// mergeSort.cpp : 递归写法
//

#include <stdio.h>
#include <stdlib.h>
#define elementType int//自定义数据类型
using namespace std;

void mergeSort(elementType A[], int N);//N为数组大小，统一函数接口
void mSort(elementType A[], elementType tmpA[], int L, int rightEnd);//传入左右边界
void merge(elementType A[], elementType tmpA[], int L, int R, int rightEnd);//将有序的两个部分进行归并


int main()
{
    int N;//数组大小
    scanf("%d", &N);
    elementType* A = (elementType*)malloc(N * sizeof(elementType));
    for (int i = 0; i < N; i++)
        cin >> A[i];
    mergeSort(A, N);
    for (int i = 0; i < N; i++)
        cout << A[i] << " ";
    return 0;
}

void mergeSort(elementType A[], int N) {
    elementType* tmpA = (elementType*)malloc(N * sizeof(elementType));//申请内存建立临时数组
    if (tmpA != NULL) {
        mSort(A, tmpA, 0, N - 1);
        free(tmpA);
    }
    else
        printf("Error!
");//内存申请失败
}

void mSort(elementType A[], elementType tmpA[], int L, int rightEnd) {
    if (L < rightEnd) {
        int center = (L + rightEnd) / 2;
        mSort(A, tmpA, L, center);
        mSort(A, tmpA, center + 1, rightEnd);
        merge(A, tmpA, L, center + 1, rightEnd);
    }
}

void merge(elementType A[], elementType tmpA[], int L, int R, int rightEnd) {
    int tmpL = L,
        leftEnd = R - 1,
        elementNum = rightEnd - L + 1;
    while (L <= leftEnd && R <= rightEnd) {
        if (A[L] < A[R])
            tmpA[tmpL++] = A[L++];
        else 
            tmpA[tmpL++] = A[R++];
    }
    while (L <= leftEnd)
        tmpA[tmpL++] = A[L++];
    while (R <= rightEnd)
        tmpA[tmpL++] = A[R++];
    for (int i = 0; i < elementNum; i++, rightEnd--)
        A[rightEnd] = tmpA[rightEnd];
}

 C/C++的非递归写法：

// mergeSort_without_recursion.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。
//归并排序的非递归写法

#include <iostream>
#define elementType int
using namespace std;

void mergeSort(elementType A[], int N);
void mSort(elementType A[], elementType tmpA[], int length, int N);
void merge(elementType A[], elementType tmpA[], int L, int R, int rightEnd);

int main()
{
    int N;
    scanf("%d", &N);
    elementType* A = (elementType*)malloc(N * sizeof(elementType));
    for (int i = 0; i < N; i++)
        cin >> A[i];
    mergeSort(A, N);
    for (int i = 0; i < N; i++)
        cout << A[i] << " ";
    return 0;
}

void mergeSort(elementType A[], int N) {
    elementType* tmpA = (elementType*)malloc(N * sizeof(elementType));
    if (tmpA != NULL) {
        int length = 1;
        while (length < N) {
            mSort(A, tmpA, length, N);
            length *= 2;
            mSort(tmpA, A, length, N);
            length *= 2;
        }
        free(tmpA);
    }
    else
        printf("Error!
");//内存申请失败
}

void mSort(elementType A[], elementType tmpA[], int length, int N) {
    int i;
    for (i = 0; i <= N - length * 2; i += length * 2)
        merge(A, tmpA, i, i + length, i + length * 2 - 1);
    if (i < N - length)//还剩两个子列，将它们归并到tmpA
        merge(A, tmpA, i, i + length, N - 1);
    else//剩下最后一个子列，直接复制到tmpA
        for (int j = i; j < N; j++)
            tmpA[j] = A[j];
}

void merge(elementType A[], elementType tmpA[], int L, int R, int rightEnd) {
    int tmpL = L,
        leftEnd = R - 1;
    while (L <= leftEnd && R <= rightEnd) {
        if (A[L] < A[R])
            tmpA[tmpL++] = A[L++];
        else
            tmpA[tmpL++] = A[R++];
    }
    while (L <= leftEnd)
        tmpA[tmpL++] = A[L++];
    while (R <= rightEnd)
        tmpA[tmpL++] = A[R++];
}