poj3186

dp

f[i][j] = max(f[i + 1][j] + sum(i + 1,j) + v[i],f[i][j - 1] + sum(i,j - 1) + v[j])

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
using namespace std;

#define maxn 2005

int n;
int v[maxn];
int f[maxn][maxn];
int sum[maxn];

void input()
{
    scanf("%d", &n);
    for (int i = 1; i <= n; i++)
        scanf("%d", &v[i]);
    v[0] = 0;
    sum[0] = v[0];
    for (int i = 1; i <= n; i++)
        sum[i] = sum[i - 1] + v[i];
}

int work()
{
    for (int i = 1; i <= n; i++)
        f[i][i] = v[i];
    for (int k = 1; k < n; k++)
    {
        for (int i = 1; i <= n - k; i++)
        {
            int j = i + k;
            f[i][j] = max(f[i + 1][j] + (sum[j] - sum[i]) + v[i],f[i][j - 1] + (sum[j - 1] - sum[i - 1]) + v[j]);
        }
    }
    return f[1][n];
}

int main()
{
//    freopen("t.txt", "r", stdin);
    input();
    printf("%d\n", work());
    return 0;
}