区间DP模板题。
区间DP就是在区间上进行动态规划，通过合并小区间的最优解进而得出大区间上最优解的dp算法。
#include <bits/stdc++.h>
using namespace std;
int dp[110][110];
int a[110];
int sum[110];
int main()
{
int n;
cin >> n;
for (int i = 1; i <= n; i++)
cin >> a[i];
for (int i = 1; i <= n; i++)
sum[i] = sum[i - 1] + a[i];
memset(dp, 0x3f3f3f3f, sizeof dp);
for (int i = 1; i <= n; i++)
dp[i][i] = 0;
for (int len = 2; len <= n; len++) //枚举区间长度
{
for (int beg = 1; beg + len - 1 <= n; beg++) //枚举开始位置
{
int end = beg + len - 1; //结束位置
for (int mid = beg; mid < end; mid++) //枚举分界点
dp[beg][end] = min(dp[beg][mid] + dp[mid + 1][end] + sum[end] - sum[beg - 1], dp[beg][end]);
}
}
cout << dp[1][n] << endl;
return 0;
}
