石子合并-区间dp

重点
1. 状态表示：f[i][j] 表示 将区间i-j合并的所有合法方案的集合，属性操作代价最小值
2. 集合划分：根据最后是由哪两部分合并的，来进行划分

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 310;
int f[N][N];
int s[N];
int a[N];

int main() {
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        s[i] = s[i - 1] + a[i];
    }
    for (int len = 1; len <= n; len++) {
        for (int i = 1; i + len  - 1 <= n; i++) {
            int j = i + len - 1;
            if (i == j) {
                f[i][j] = 0;
                continue;
            }
            f[i][j] = f[i][i] + f[i + 1][j] + s[j] - s[i - 1];
            for (int k = i + 1; k <= j; k++) {
                f[i][j] = min(f[i][j], f[i][k] + f[k + 1][j] + s[j] - s[i - 1]);
            }
        }
    }
    cout << f[1][n] << endl;


    return 0;
}