Merge Sort Back

• 歸併排序: 分治思想(Divide, Conquer and Combination)
• Divide: 二分
• Conquer: 直到只有一個的時候合併
• Combination: 每次比較隊頭,較小的先放進隊列
• 时间复杂度: (最好,平均,最壞情況)
• 空間複雜度:
• 稳定性: 稳定
• 适用情况: 額外空間可以接受的情況下

void Merge(int A[], int p, int m, int q)
{
    int n1 = m - p + 1;
    int n2 = q - (m + 1) + 1;
    int L[MAXSIZE], R[MAXSIZE];                
    for (int i = 1; i <= n1; i++)
    {
        L[i] = A[p + i - 1];
    }
    for (int j = 1; j <= n2; j++)
    {
        R[j] = A[m + j];
    }
    L[n1 + 1] = INFINITY;
    R[n2 + 1] = INFINITY;
    int i = 1;
    int j = 1;
    for (int k = p; k <= q; k++)                
    {
        if (L[i] <= R[j])
        {
            A[k] = L[i];
            i++;
        }
        else
        {
            A[k] = R[j];
            j++;
        }
    }
}

void MergeSort(int A[], int p, int q)
{
    if (p < q)
    {
        int m = (p + q) / 2;
        MergeSort(A, p, m);
        MergeSort(A, m + 1, q);
        Merge(A, p, m, q);
    }
}

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