TWENDS  Two Ends
In the twoplayer game “Two Ends”, an even number of cards is laid out in a row. On each card, face up, is written a positive integer. Players take turns removing a card from either end of the row and placing the card in their pile. The player whose cards add up to the highest number wins the game. Now one strategy is to simply pick the card at the end that is the largest — we’ll call this the greedy strategy. However, this is not always optimal, as the following example shows: (The first player would win if she would first pick the 3 instead of the 4.)
3 2 10 4
You are to determine exactly how bad the greedy strategy is for different games when the second player uses it but the first player is free to use any strategy she wishes.
Input
There will be multiple test cases. Each test case will be contained on one line. Each line will start with an even integer n followed by n positive integers. A value of n = 0 indicates end of input. You may assume that n is no more than 1000. Furthermore, you may assume that the sum of the numbers in the list does not exceed 1,000,000.
Output
For each test case you should print one line of output of the form:
In game m, the greedy strategy might lose by as many as p points.
where m is the number of the game (starting at game 1) and p is the maximum possible difference between the first player’s score and second player’s score when the second player uses the greedy strategy. When employing the greedy strategy, always take the larger end. If there is a tie, remove the left end.
Example
Input: 4 3 2 10 4 8 1 2 3 4 5 6 7 8 8 2 2 1 5 3 8 7 3 0 Output: In game 1, the greedy strategy might lose by as many as 7 points. In game 2, the greedy strategy might lose by as many as 4 points. In game 3, the greedy strategy might lose by as many as 5 points.
hide comments
Aman Verma:
20140617 08:57:21
My first question DP :) 

Divyank Duvedi:
20140521 14:14:53
@Vijay Jain,@New_Bullet,@sagar gandhi


paras meena:
20140520 20:58:48
maja aa gaya.. :D 

Sanjeev Kumar:
20140515 16:39:55
Easy DP!!! 

Pratik kumar:
20140423 13:09:57
The period '.' at the end is necessary. 

Tigran Galstyan:
20140223 10:50:16
@New_Bullet n is easy 

Python:
20140115 16:14:09
"If there is a tie, remove the left end."


:`(:
20140115 14:54:21
very


New_Bullet:
20131231 11:07:27
5 1 2 1 2 1


Vijay Jain:
20130730 07:42:00
interesting problem

Added by:  Camilo Andrés Varela León 
Date:  20070726 
Time limit:  0.100s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  East Central North America 2005 