归并排序

归并排序重点在治，即合并两个有序数组：

void merge(int A[], int p, int q, int r)
{
    int i = 0, j = 0, k = p;
    int m = q - p + 1;
    int n = r - q;
    int *S = new int[m];
    int *T = new int[n];
    for (i = 0; i < m; i++)
        S[i] = A[p + i]; 
    for (j = 0; j < n; j++)
        T[j] = A[q + j + 1]; 

    i = j = 0;
    while ((i < m) && (j < n)) 
        if (S[i] < T[j])
            A[k++] = S[i++];
        else
            A[k++] = T[j++];
    while (i < m)
        A[k++] = S[i++];
    while (j < n)
        A[k++] = T[j++];
    
    delete[] S;
    delete[] T;
}

有了merge函数，就可以使用up-down的方式分治，使用递归解决。

void merge_sort(int A[], int p, int r)
{
    int q;
    if (p < r)
    {
        q = (p + r) / 2;
        merge_sort(A, p, q);
        merge_sort(A, q + 1, r);
        merge(A, p, q, r);
    }
}

 或者采用bottom-up的方法，非递归解决。

void merge_sort(int A[], int p, int r)
{
    int step, low, mid, high;

    for (step = 1; step <= r; step *= 2)
    {   
        low = p;
        while (low + step <= r)
        {   
            mid = low + step - 1;
            high = mid + step;
            if (high >= r)
                high = r;
            merge(A, low, mid, high);
            low = high + 1;
        }   
    }   
}