#3428. [GESP202409 五级 C++] 第 10 题

[GESP202409 五级 C++] 第 10 题

考虑以下C++代码实现的归并排序算法:

void merge(int arr[], int left, int mid, int right) {
    int n1 = mid - left + 1;
    int n2 = right - mid;

    int L[n1], R[n2];

    for (int i = 0; i < n1; i++)
        L[i] = arr[left + i];
    for (int j = 0; j < n2; j++)
        R[j] = arr[mid + 1 + j];

    int i = 0, j = 0, k = left;
    while (i < n1 && j < n2) {
        if (L[i] <= R[j]) {
            arr[k] = L[i];
            i++;
        }
        else {
            arr[k] = R[j];
            j++;
        }
        k++;
    }

    while (i < n1) {
        arr[k] = L[i];
        i++;
        k++;
    }

    while (j < n2) {
        arr[k] = R[j];
        j++;
        k++;
    }
}

void merge_sort(int arr[], int left, int right) {
    if (left < right) {
        int mid = left + (right - left) / 2;

        merge_sort(arr, left, mid);
        merge_sort(arr, mid + 1, right);

        merge(arr, left, mid, right);
    }
}

对长度为 n 的数组 arr,调用函数 merge_sort(a, 0, n-1),在排序过程中 merge 函数的递归调用次数大约是( )。

{{ select(1) }}

  • O(1)O(1)
  • O(n)O(n)
  • O(logn)O(\log n)
  • O(nlogn)O(n \log n)