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TRT - Treats for the Cows |
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
The maximum revenue FJ can achieve by selling the treats
Example
Input: 5 1 3 1 5 2 Output: 43
| Added by: | Nguyen Van Quang Huy |
| Date: | 2006-02-15 |
| Time limit: | 1s |
| Source limit: | 50000B |
| Memory limit: | 1536MB |
| Cluster: | Cube (Intel G860) |
| Languages: | All except: NODEJS PERL6 VB.NET |
| Resource: | USACO FEB06 Gold Division |
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2012-11-10 14:51:08 Shubham Somani
very good question for beginners.. top down worked for me :) |
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2012-08-15 13:50:06 AC Srinivas
Everyday he HAS to sell EXACTLY ONE treat from either end. Last edit: 2012-08-15 13:50:41 |
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2011-10-04 09:50:07 iamthewalrus
I'm using recursion, gives TLE !! |
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2011-06-15 17:47:53 Kunal Kapadia
Done :) |
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2011-03-05 09:30:48 The Financier
Tornike Mandzulashvili, isn't. Try 6 98 98 98 98 1 99 , correct is 1865 What is the optimal logik ? I solved using bruteforce with caching. But it's too slow |
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2012-01-16 13:53:18 Tornike Mandzulashvili
if c[l]<=c[r] then take c[l]*a and l++; else choose c[r]*a and r--; this is o(n) solution . isnt it right??? |
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2010-12-19 02:42:14 yyf
The treats are numbered 1..N and stored sequentially in single file in a long box that is open at both ends |
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2010-05-26 11:34:53 pantop
@ ~!(*(@*!@^& why did he sell the treats ( values 1,3,1,5,2) in this order (1,5,2,3,4)of indices....why not in (1,3,5,2,4) making 1*1 + 2*1 + 3*2 + 4*3 + 5*5 = 46 > 43 ...?????????? Pls read the problem statement carefully !! Last edit: 2010-05-27 05:56:13 |
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2009-03-27 06:36:10 ~!(*(@*!@^&
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 - Insert example explaination pls. |
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