XorBoardDivTwo | Topcoder Archive

Problem Statement

Fox Jiro has a rectangular board, divided into a grid of square cells. Each cell in the grid contains either the character '0', or the character '1'. The String[] board contains the current state of the board. The j-th character of the i-th element of board is the character in row i, column j of the grid.

Jiro now has to make exactly two flips. In the first flip, he must pick a row and flip all characters in that row. (When flipped, a '0' turns to a '1' and vice versa.) In the second flip, he must pick a column and flip all characters in that column.

You are given the String[] board. Return the maximum number of '1's in the grid after Jiro makes the two flips.

Definition

Class:: XorBoardDivTwo
Method:: theMax
Parameters:: String[]
Returns:: int
Method signature:: int theMax(String[] board)
(be sure your method is public)

Constraints

board will contain between 1 and 50 elements, inclusive.
Each element of board will contain the same number of characters.
Each element of board will contain between 1 and 50 characters, inclusive.
Each character in board will be '0' or '1'.

Examples

```
{"101",
 "010",
 "101"}
```
```
Returns: 9
```
Jiro can obtain 9 '1's by flipping the center row and then the center column.
```
{"111",
 "111",
 "111"}
```
```
Returns: 5
```
Jiro has to make both flips, even if that decreases the number of '1's.
```
{"0101001",
 "1101011"}
```
```
Returns: 9
```

{"000",
 "001",
 "010",
 "011",
 "100",
 "101",
 "110",
 "111"}

Returns: 15

{"000000000000000000000000",
 "011111100111111001111110",
 "010000000100000001000000",
 "010000000100000001000000",
 "010000000100000001000000",
 "011111100111111001111110",
 "000000100000001000000010",
 "000000100000001000000010",
 "000000100000001000000010",
 "011111100111111001111110",
 "000000000000000000000000"}

Returns: 105

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