CF33C - Wonderful Randomized Sum

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Learn, learn and learn again — Valera has to do this every day. He is studying at mathematical school, where math is the main discipline. The mathematics teacher loves her discipline very much and tries to cultivate this love in children. That's why she always gives her students large and difficult homework. Despite that Valera is one of the best students, he failed to manage with the new homework. That's why he asks for your help. He has the following task. A sequence of n numbers is given. A prefix of a sequence is the part of the sequence (possibly empty), taken from the start of the sequence. A suffix of a sequence is the part of the sequence (possibly empty), taken from the end of the sequence. It is allowed to sequentially make two operations with the sequence. The first operation is to take some prefix of the sequence and multiply all numbers in this prefix by  - 1. The second operation is to take some suffix and multiply all numbers in it by  - 1. The chosen prefix and suffix may intersect. What is the maximum total sum of the sequence that can be obtained by applying the described operations?


The first line of the input gives the number of test cases, T. T test cases follow, each with two lines. The first line contains integer n (1 ≤ n ≤ 105) — amount of elements in the sequence. The second line contains n integers ai ( - 104 ≤ ai ≤ 104) — the sequence itself.


For each test case, output one line containing the answer to the problem.


-1 -2 -3
-4 2 0 5 0
-1 10 -5 10 -2


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hamza007: 2014-08-16 08:30:35

Unnecessary use of long long results in tle ...

P.B.MUKUND: 2013-04-20 17:04:47

Is there any test case where intersection of prefix and suffix actually comes into picture ?
AFAIK, intersection is not possible in the sense that the same max sum can be found even without intersection.
Is my understanding correct ?


RR: 2012-07-06 15:47:15

I think it is stated somewhere in Codeforces that it is forbidden to add codeforces' problems to other sites.

Last edit: 2012-07-06 15:53:49
Ashwin Menon: 2011-10-17 14:13:02

(-1) 10 -5 10 (-2)
gives -> 23
How is the maximum sum 18?
Reply - Wear your specs man..
1 + 10 - 5 + 10 + 2 = 18..

Last edit: 2012-06-25 07:50:58
LeppyR64: 2010-10-09 14:41:30

@Kelwin: You only get to choose one preifx and one suffix, not choose each operation multiple times.

Kelwin: 2010-10-09 13:18:58

Hi, please check output.

-1 10 -5 10 (-2)
(-1 10 -5) 10 2
(1 -10) 5 10 2
(1) 10 5 10 2

And total is 28

Added by:Ruslan Sennov
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 NODEJS OBJC VB.NET
Resource:Codeforces #33