TopCoder problem "LampsGrid" used in SRM 432 (Division I Level One , Division II Level Two)



Problem Statement

    

Jack has bought a rectangular table containing a grid of lamps. Each lamp is initially either "on" or "off". There is a switch underneath each column, and when the switch is flipped, all the lamps in that column reverse their states ("on" lamps become "off" and vice versa).



A row in the grid is considered lit if all the lamps in that row are "on". Jack must make exactly K flips. The K flips do not necessarily have to be performed on K distinct switches. His goal is to have as many lit rows as possible after making those flips.



You are given a String[] initial, where the j-th character of the i-th element is '1' (one) if the lamp in row i, column j is initially "on", and '0' (zero) otherwise. Return the maximal number of rows that can be lit after performing exactly K flips.
 

Definition

    
Class:LampsGrid
Method:mostLit
Parameters:String[], int
Returns:int
Method signature:int mostLit(String[] initial, int K)
(be sure your method is public)
    
 

Constraints

-initial will contain between 1 and 50 elements, inclusive.
-Each element of initial will contain between 1 and 50 characters, inclusive.
-Each element of initial will contain the same number of characters.
-Each element of initial will contain only the digits '0' and '1'.
-K will be between 0 and 1000, inclusive.
 

Examples

0)
    
{"01",
 "10",
 "10"}
1
Returns: 2
Here, Jack must flip exactly one switch. If he flips the switch for the second column, the bottom two rows become lit.
1)
    
{"101010"}
2
Returns: 0
2)
    
{"00", "11"}
999
Returns: 0
No row can be lit after exactly 999 flips.
3)
    
{"0", "1", "0", "1", "0"}

1000
Returns: 2
4)
    
{"001", "101", "001", "000", "111", "001", "101", "111", "110", "000", "111", "010", "110", "001"}
6
Returns: 4
5)
    
{"01", "10", "01", "01", "10"}
1
Returns: 3

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10154

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=13694&pm=10154

Writer:

nika

Testers:

PabloGilberto , Olexiy , ivan_metelsky

Problem categories:

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