g7-02296. GESP-7级-2023-12-单选-第02题 未做

对于下面动态规划方法实现的函数，以下选项中最适合表达其状态转移函数的为（ ）。

int s[MAX_N], f[MAX_N][MAX_N];
int stone_merge(int n, int a[]) {
    for (int i = 1; i <= n; i++)
        s[i] = s[i - 1] + a[i];
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++)
            if (i == j)
                f[i][j] = 0;
            else
                f[i][j] = MAX_F;
    for (int l = 1; l < n; l++)
        for (int i = 1; i <= n - l; i++) {
            int j = i + l;
            for (int k = i; k < j; k++)
                f[i][j] = min(f[i][j], f[i][k] + f[k + 1][j] + s[j] - s[i - 1]);
        }
    return f[1][n];
}

• A. $f(i,j)={\min }_{i\le k<j}(f(i,j),f(i,k)+f(k+1,j)+s(j)-s(i-1))$
• B. $f(i,j)={\min }_{i\le k<j}(f(i,j),f(i,k)+f(k+1,j)+{\sum }_{k=i}^{j}a(k))$
• C. $f(i,j)={\min }_{i\le k\le j}(f(i,k)+f(k+1,j)+{\sum }_{k=i}^{j+1}a(k))$
• D. $f(i,j)={\min }_{i\le k<j}(f(i,k)+f(k+1,j))+{\sum }_{k=i}^{j}a(k)$