A Game

Problem Description

Little Hi and Little Ho are playing a game. There is an integer array in front of them. They take turns (Little Ho goes first) to select a number from either the beginning or the end of the array. The number will be added to the selecter’s score and then be removed from the array.

Given the array what is the maximum score Little Ho can get? Note that Little Hi is smart and he always uses the optimal strategy.

Input

The first line contains an integer N denoting the length of the array. (1 ≤ N ≤ 1000)

The second line contains N integers A1, A2, … AN, denoting the array. (-1000 ≤ Ai ≤ 1000)

Output

Output the maximum score Little Ho can get.

Sample Input

4
-1 0 100 2

Sample Output

99

題意：

每次輪到小Hi或者小Ho時，他們都面臨同樣的二選一決策：是拿走最左邊的數，還是拿走最右邊的數？
問最後小Ho能拿到的最大點數是多少？

解題思路：

Code：

#include <cstdio>
#include <iostream>

using namespace std;

const int maxn=1000+5
 
;
int a[maxn];
int sum[maxn];
int dp[maxn][maxn];
int main()
{
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        scanf("%d",a+i);
        sum[i]=sum[i-1]+a[i];
        dp[i][i]=a[i];
    }
    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=n-i;j++)
        {
            dp[j][i+j]=sum[i+j]-sum[j-1]-min(dp[j+1][i+j],dp[j][i+j-1]);
        }
    }

    printf("%d\n",dp[1][n]);
    return 0;
}