POJ3186 Treats for the Cows —— 区间DP

Posted 2020-10-09 h_z_cong

题目链接：http://poj.org/problem?id=3186

 

Treats for the Cows

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 6548		Accepted: 3446

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 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.

Given the values v(i) of each of the treats lined up in order of the index i in their box, what is the greatest value FJ can receive for them if he orders their sale optimally? 

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)

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.

Source

USACO 2006 February Gold & Silver

 

 

 

题解：

 

 

 

代码如下：

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cmath>
 5 #include <algorithm>
 6 #include <vector>
 7 #include <queue>
 8 #include <stack>
 9 #include <map>
10 #include <string>
11 #include <set>
12 #define ms(a,b) memset((a),(b),sizeof((a)))
13 using namespace std;
14 typedef long long LL;
15 const double EPS = 1e-8;
16 const int INF = 2e9;
17 const LL LNF = 2e18;
18 const int MAXN = 2e3+10;
19 
20 int n;
21 int a[MAXN], dp[MAXN][MAXN];
22 
23 int main()
24 {
25     while(scanf("%d", &n)!=EOF)
26     {
27         for(int i = 1; i<=n; i++)
28             scanf("%d", &a[i]);
29 
30         for(int i = 1; i<=n; i++)
31             dp[i][i] = a[i]*n;
32 
33         for(int len = 2; len<=n; len++)
34         for(int i = 1; i+len-1<=n; i++)
35         {
36             int j = i+len-1;
37             dp[i][j] = max(dp[i+1][j]+(n-len+1)*a[i], dp[i][j-1]+(n-len+1)*a[j]);
38         }
39 
40         printf("%d\n", dp[1][n]);
41     }
42 }

View Code