GESP 7级客观题｜二维动态规划｜课堂讲解

考试频率：高频。本卷共 2 题。

1. 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 - 1; 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];
}

{{ select(1) }}

• $f(i,j) = \min_{i \le k < j} (f(i,j),f(i,k)+f(k+1,j)+s(j)-(s-1))$
• $f(i,j) = \min_{i \le k < j} (f(i,j),f(i,k)+f(k+1,j)+\sum_{k=i}^{j}a(k))$
• $f(i,j) = \min_{i \le k \le j} (f(i,k)+f(k+1,j)+\sum_{k=i}^{j+1}a(k))$
• $f(i,j) = \min_{i \le k < j} (f(i,k)+f(k+1,j)+\sum_{k=i}^{j}a(k))$

2. 动态规划只要推导出状态转移方程，就可以写出递归程序来求出最优解。( )

   {{ select(2) }}

• 对
• 错