分治算法----合并排序

算法：MERGESORT

伪代码如下：

输入：n个元素的数组A[1...n]

输出：按非降序排列的数组A[1...n]

mergesort(A,1,n)

mergesort(low,high)

if low

    mid←(low+high)/2

    mergesort(A,low,mid)

    mergesort(A,mid+1,high)

    MERGE(A,low,mid,high)

end if

此算法时间复杂度为：Θ（nlogn）

详细代码如下：

#include

using namespace std;

#define length 500

//合并的辅助函数

void merge(int *data, int low, int mid, int high)

{

    std::cout << "merge low is" << low << " mid is:" << mid << " high is" << high << std::endl;

    int newLength = high - low + 1;

    int *newData = new int[newLength];

    int i = low, j = mid + 1, k = 0;

    //分解2个数组，并且合并完其中的一个数组

    while (i <= mid && j <= high)

    {

        if (data[i] <= data[j])

            newData[k++] = data[i++];

        else

            newData[k++] = data[j++];

    }

    //合并另外一个数组

    while (i <= mid) 

        newData[k++] = data[i++];

    while (j <= high) 

        newData[k++] = data[j++];

    //把新数据的数组拷贝到原始数组里面去

    for (int i = low, k = 0; i <= high; ++i)

    {

        data[i] = newData[k++];

        std::cout << "data[" << i << "] is" << data[i] << "\t";

    }

    delete[] newData;

    std::cout << std::endl;

}

//合并排序

void mergeSort(int *data, int low, int high)

{

    std::cout << "mergeSort low is" << low << " high is" << high << std::endl;

    if (low < high)

    {

        int mid = (low + high) / 2;

        mergeSort(data, low, mid);

        mergeSort(data, mid + 1, high);

        merge(data, low, mid, high);

    }

}

int main()

{

    int all, data[length];

    std::cout << "请输入需要排序的数据的个数" << std::endl;

    std::cin >> all;

    if (all <= 0)

        std::cout << "输入的数据有误" << std::endl;

     //input data

    for (int i = 0; i < all; ++i)

    {

        std::cin >> data[i];

    }

    //分治排序

    mergeSort(data, 0, all - 1);

    //printf data

    for (int i = 0; i < all; ++i)

    {

        std::cout << data[i] << "\t";

    }

    std::cout << std::endl;

    return 0;

}

参考：分治算法之合并排序 - No talent - CSDN博客