Treats for the Cows
Time Limit: 1000MS | Memory Limit: 65536K | |
Total Submissions: 5172 | Accepted: 2697 |
Description
FJ has purchased N (1 <= N <= 2000) yummy treats for the cows who get money for giving vast amounts of milk. FJ sells one treat per day and wants to maximize the money he receives over a given period time.
The treats are interesting for many reasons:
The first treat is sold on day 1 and has age a=1. Each subsequent day increases the age by 1.
The treats are interesting for many reasons:
- The treats are numbered 1..N and stored sequentially in single file in a long box that is open at both ends. On any day, FJ can retrieve one treat from either end of his stash of treats.
- Like fine wines and delicious cheeses, the treats improve with age and command greater prices.
- The treats are not uniform: some are better and have higher intrinsic value. Treat i has value v(i) (1 <= v(i) <= 1000).
- Cows pay more for treats that have aged longer: a cow will pay v(i)*a for a treat of age a.
The first treat is sold on day 1 and has age a=1. Each subsequent day increases the age by 1.
Input
Line 1: A single integer, N
Lines 2..N+1: Line i+1 contains the value of treat v(i)
Lines 2..N+1: Line i+1 contains the value of treat v(i)
Output
Line 1: The maximum revenue FJ can achieve by selling the treats
Sample Input
5 1 3 1 5 2
Sample Output
43
Hint
Explanation of the sample:
Five treats. On the first day FJ can sell either treat #1 (value 1) or treat #5 (value 2).
FJ sells the treats (values 1, 3, 1, 5, 2) in the following order of indices: 1, 5, 2, 3, 4, making 1x1 + 2x2 + 3x3 + 4x1 + 5x5 = 43.
Five treats. On the first day FJ can sell either treat #1 (value 1) or treat #5 (value 2).
FJ sells the treats (values 1, 3, 1, 5, 2) in the following order of indices: 1, 5, 2, 3, 4, making 1x1 + 2x2 + 3x3 + 4x1 + 5x5 = 43.
Source
USACO 2006 February Gold & Silver
题意:给出的一系列的数字,可以看成一个双向队列,每次只能从队首或者队尾出队,第n个出队就拿这个数乘以n,最后将和加起来,求最大和
/*
dp[i][j]记录取i-j能获得的最大价值
从取最后一个开始想,取最后一个i是a[i]*n, 上次取得就是dp[i-1][i]或dp[i][i+1]
状态转移方程:dp[i][j] = max(dp[i+1][j]+(n-k)*a[i], dp[i][j-1]+(n-k)*a[j]), (k是ij区间长度)
*/
#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
const int maxn = 2005;
int a[maxn], dp[maxn][maxn];
int main(void)
{
int n;
while(cin >> n)
{
memset(dp, 0, sizeof(dp));
for(int i = 1; i <= n; i++) scanf("%d", &a[i]), dp[i][i] = n*a[i];
for(int k = 1; k < n; k++)
for(int i = 1; i+k <= n; i++)
{
int j = i+k;
dp[i][j] = max(dp[i+1][j]+(n-k)*a[i], dp[i][j-1]+(n-k)*a[j]);
}
printf("%d\n", dp[1][n]);
}
return 0;
}