POJ3186 Treats for the Cows —— 區間DP
阿新 • • 發佈:2017-10-06
ref making script inf desc acc memset nes lap
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.
Lines 2..N+1: Line i+1 contains the value of treat v(i)
Line 1: The maximum revenue FJ can achieve by selling the treats
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.
題目鏈接: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.
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, NLines 2..N+1: Line i+1 contains the value of treat v(i)
Output
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 題解: 代碼如下: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
POJ3186 Treats for the Cows —— 區間DP