合并排序（分治法）

//merge_sort.h
#ifndef MERGE_SORT_H
#define MERGE_SORT_H

template <class Type>
void MergeSort(Type a[], int n);

#include "merge_sort.template"

#endif

//merge_sort.template
template <class Type>
void MergeSort(Type a[], int n)
{
    Type *b = new Type[n];
    int s = 1;
    while (s < n)
    {
        MergePass(a, b, s, n);  //合并到数组b
        s += s;
        MergePass(b, a, s, n);  //合并到数组a
        s += s;
    }
    delete b;
}

template <class Type>
void MergePass(Type x[], Type y[], int s, int n)
{
    int i = 0;
    while (i <= n - s * 2)
    {
        Merge(x, y, i, i + s - 1, i + 2 * s - 1);  //合并大小为s的相邻两段子数组
        i += s * 2;
    }
    if (i + s < n)  //剩下的元素少于2s
        Merge(x, y, i, i + s - 1, n - 1);
    else for (int j = i; j <= n - 1; j++)
        y[j] = x[j];
}

template <class Type>
void Merge(Type c[], Type d[], int l, int m, int r)  //合并c[l:m]和c[m+1:r]到d[l:r],其中c[l:m]和c[m+1:r]都是已经经过升序排好的数组
{
    int i = l, j = m + 1, k = l;
    while ((i <= m) && (j <= r))
    {
        if (c[i] <= c[j])
            d[k++] = c[i++];
        else
            d[k++] = c[j++];
    }
    if (i > m)
        for (int q = j; q <= r; q++)
            d[k++] = c[q];
    else for (int q = i; q <= m; q++)
        d[k++] = c[q];
}

//main.cpp
#include <iostream>
#include "merge_sort.h"

using namespace std;

#define Type int  //定义Type类型

int main()
{
    int size;  //数组大小
    cout << "请输入数组大小： ";
    cin >> size;
    Type *a = new Type[size];  //定义一个数组
    cout << "请输入数组中元素：" << endl;
    for (int i = 0; i < size; i++)
    {
        cin >> a[i];
    }
    MergeSort(a, size);  //对数组进行升序排序
    cout << "输出合并排序后的数组： " << endl;
    for (int j = 0; j < size; j++)
    {
        cout << a[j] << "  ";
    }
    system("pause");
    delete a;
    return 0;
}