hihoCoder 1338 : A Game（dp）

A Game

Time limit:1000ms Memory limit:256MB

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

题意：

每次轮到小Hi或者小Ho时，他们都面临同样的二选一决策：是拿走最左边的数，还是拿走最右边的数？

问最后小Ho能拿到的最大点数是多少？

解题思路：

官方题解：《A Game》题目分析

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]
);
return 0;
}