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

hide comments
rishi_07: 2017-03-03 12:30:59

Very Nice Question!

hasan356: 2017-03-02 18:27:24

My first memo!!

vladimira: 2017-02-25 15:44:05

Can be implemented easily with just O(n) memory without some matrix chain multiplications. But you must work first with your pen and sheet of paper a little. My solving function was 10 lines.

nilabja16180: 2017-02-22 19:02:54

Not easy as it seems!

sarthakshah30: 2017-01-27 19:49:22

AC in one Go ;)
Bottom Up DP
Hint ->Matrix chain Multiplication Variation

epsilonalpha: 2016-12-22 00:05:27

Got TLE once because I'm used to dealing with vectors instead of arrays and I forgot to pass by reference!
Always pass a vector as this if you don't intend to change it's values:
const vector<int> &v
Otherwise remove const.

For those still struggling, scroll halfway down to this page:
https://www.hackerearth.com/practice/notes/dynamic-programming-i-1/

sayedathar11: 2016-11-25 19:19:21

Got a tle just because forgot to memoize fixed that and Got an ac

siddharth_0196: 2016-10-05 10:58:49

Recursion+Memoization: AC!
Try TWENDS after this!

Last edit: 2016-10-05 13:23:42
davidgalehouse: 2016-09-09 05:28:56

If you're stuck I recommend you try to solve the problem recursively in the most obvious way, study the recursive calls being made and try to make an important observation, turn the observation into memoization, then turn that into DP.

mahmood_2000: 2016-08-27 12:53:21

My first time I get AC on the first go on spoj :)


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