ROCK - Sweet and Sour Rock

A manufacturer of sweets has started production of a new type of sweet called rock. Rock comes in sticks composed of one-centimetre-long segments, some of which are sweet, and the rest are sour. Before sale, the rock is broken up into smaller pieces by splitting it at the connections of some segments.

Today's children are very particular about what they eat, and they will only buy a piece of rock if it contains more sweet segments than sour ones. Try to determine the total length of rock which can be sold after breaking up the rock in the best possible way.


The input begins with the integer t, the number of test cases. Then t test cases follow.

For each test case, the first line of input contains one integer N - the length of the stick in centimetres (1<=N<=200). The next line is a sequence of N characters '0' or '1', describing the segments of the stick from the left end to the right end ('0' denotes a sour segment, '1' - a sweet one).


For each test case output a line with a single integer: the total length of rock that can be sold after breaking up the rock in the best possible way.


Sample input:

Sample output:

hide comments
nonushikhar: 2016-07-06 02:42:28

easy :) loved it .... hint : matrix chain multiplication

sarvesh_19: 2016-06-28 22:23:48

recursion with memo accepted !! AC in 1st attempt.

poojan : 2016-06-11 06:25:01

Getting WA I think i have checked all corner case! PS plz check solution!

Last edit: 2016-06-11 06:25:45
prateek1985: 2016-04-14 23:41:15

Great problem to build confidence in dp ! LOVED IT :) !

dev: 2016-03-22 14:47:08

Too easy ! 3 wa due to silly mistake :D

Mohit Rathore: 2016-01-21 07:21:16

Loved solving this :)

bruceoutdoors: 2015-11-14 11:52:53

@saurabh the answer of 1st test case is 9, because you can break 100110001010001 into 3 segments where there are more 1's than 0's: 10011, 101, and 1. The total length of this 3 segments combined is 9, ergo the answer.

Last edit: 2015-11-14 11:58:09
saurabh: 2015-10-24 20:39:10

how come the answer of 1st test case be 9.
can anyone please explain it ?

fool_01: 2015-09-19 18:24:58

creating dynamic arrays for every test case giving TLE ??

Last edit: 2015-09-19 18:26:11
xxbloodysantaxx: 2015-07-11 07:49:23

Problem statement is so unclear!
A segment of length greater than 1 is sweet if number of sweet segments of length 1 are greater than number of sweet segments of length 0

Last edit: 2015-07-11 08:18:29

Added by:adrian
Time limit:7s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Resource:based on a problem from the VII Polish Collegiate Team Programming Contest (AMPPZ), 2002