UVa 10891 Game of Sum / 记忆化搜索

记忆化搜索

dp[i][j] 表示第i~j个元素组成的子序列 先手得分的最大值

dp[i][j] = sum(i,j) - min(dp[i+1][j],dp[i+2][j],.....dp[j][j],dp[i][j-1],dp[i][j-2],.....dp[i][i],0) ,0 代表取完所有数

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int MAX = 110;
int dp[MAX][MAX];
bool vis[MAX][MAX];
int a[MAX];
int sum[MAX];
int dfs(int s,int e)
{
	if(vis[s][e])
		return dp[s][e];
	vis[s][e] = true;
	int k;
	int m = 0;
	for(k = s + 1; k <= e; k++)
		m = min(m,dfs(k,e));
	for(k = s; k < e; k++)
		m = min(m,dfs(s,k));
	dp[s][e] = sum[e] - sum[s-1] - m;
	return dp[s][e];
}
int main()
{
	int n;
	int i;
	while(scanf("%d",&n),n)
	{
		for(i = 1;i <= n; i++)
		{
			scanf("%d",&a[i]);
			sum[i] = sum[i-1] + a[i];
		}
		memset(vis,false,sizeof(vis));
		printf("%d\n",2*dfs(1,n)-sum
);
	}
	return 0;
}