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Largest area of rectangle with permutations


Problem Setter: amitkgupta94 Problem Tester: RAMBO_tejasv

Problem Description

Given a binary grid A of size N x M consisting of 0's and 1's, find the area of the largest rectangle inside the grid such that all the cells inside the chosen rectangle should have 1 in them.

You are allowed to permutate the columns matrix i.e. you can arrange each of the column in any order in the final grid.

Please follow the sample input and explanation for more clarity.



Input Format

First and only argument is an 2D binary array A.



Output Format

Return a single integer denoting the area of the largest rectangle inside the grid such that all the cells inside the chosen rectangle should have 1 in them.



Example Input

Input 1:

 A = [  [1, 0, 1]
        [0, 1 ,0]
        [1, 0, 0]
    ]



Example Output

Output 1:

 2



Example Explanation

Explanation 1:

    1 0 1
    0 1 0
    1 0 0

At present we can see that max rectangle satisfying the criteria mentioned in the problem is of 1 * 1 = 1 area i.e either of the 4 cells which contain 1 in it.

Now since we are allowed to permutate the columns of the given matrix, we can take column 1 and column 3 and make them neighbours. One of the possible configuration of the grid can be: 1 1 0 0 0 1 1 0 0

Now In this grid, first column is column 1, second column is column 3 and third column is column 2 from the original given grid.

Now, we can see that if we calculate the max area rectangle, we get max area as 1 * 2 = 2 which is bigger than the earlier case. Hence 2 will be the answer in this case.



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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