poj 3186 dp（按天出手的最大值）

题意：给定n个物品，重量分别为s1...sn。分n天卖出，第一天单价为1，第n天为n。已知每次卖出只能从n个物品的头或尾挑一个。求最大收益值。

思路：一开始以为是加括号，提交TLE。参考（http://blog.youkuaiyun.com/libin56842/article/details/9735231）知道应该是由里向外逆推区间。

#include <stdio.h>
#include <string.h>
#define max(a,b) ((a)>(b)?(a):(b))
#define N 2005
int dp[N][N],s[N];
int n;
int main(){
	freopen("a.txt","r",stdin);
	while(scanf("%d",&n)!=EOF){
		int i,j,k;
		memset(dp,0,sizeof(dp));
		for(i = 1;i<=n;i++){
			scanf("%d",&s[i]);
			dp[i][i] = n*s[i];
		}
		for(k = 1;k<n;k++){
			for(i = 1;i<=n-k;i++){
				j = i+k;
				dp[i][j] = max(dp[i+1][j]+(n-k)*s[i],dp[i][j-1]+(n-k)*s[j]);
			}
		}
		printf("%d\n",dp[1][n]);
	}
	return 0;
}

TLE的加括号思路：

#include <stdio.h>
#include <string.h>
#define max(a,b) ((a)>(b)?(a):(b))
#define N 2005
int dp[N][N],sum[N][N];
int n;
int main(){
	freopen("a.txt","r",stdin);
	while(scanf("%d",&n)!=EOF){
		int i,j,k,p;
		memset(sum,0,sizeof(sum));
		memset(dp,0,sizeof(dp));
		for(i = 1;i<=n;i++){
			scanf("%d",&sum[i][i]);
			dp[i][i] = sum[i][i];
			for(j = i-1;j>=1;j--)
				sum[j][i] = sum[j+1][i]+sum[j][j];
		}

		for(k = 1;k<n;k++)
			for(i = 1;i<=n-k;i++){
				j = i+k;
				for(p = i;p<j;p++){
					dp[i][j] = max(dp[i][j],max(sum[i][p],sum[p+1][j])+dp[i][p]+dp[p+1][j]);
				}
			}
		printf("%d\n",dp[1][n]);
	}
	return 0;
}