51Nod 1021 石子归并（动态规划）

#include <iostream>
#include <algorithm>
#include <string>
#include <iostream>

#define INF 0xfffffff
using namespace std;
const int maxn = 100 + 5;
int a[maxn];
int sum[maxn];
int dp[maxn][maxn];
//dp[i][j]    从i到j所需的最少

int main(){
    ios::sync_with_stdio(false);
    /*
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
    */
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++){
        cin >> a[i];
        sum[i] = sum[i - 1] + a[i];
    }
    //init
    
    for (int l = 2; l <= n; l++){
        //中间的长度
        for (int sta = 1; sta <= n - l + 1; sta++){
            int endd = sta + l - 1;
            int Min = INF;
            for (int k = sta; k < endd; k++){
                if (dp[sta][k] + dp[k + 1][endd] + sum[endd] - sum[sta - 1] < Min){
                    Min = dp[sta][k] + dp[k + 1][endd] + sum[endd] - sum[sta - 1];
                }
            }
            dp[sta][endd] = Min;
        }
    }
    cout << dp[1][n] << endl;
    
    //fclose(stdin);
    //fclose(stdout);
    system("pause");
    return 0;
}