SDE - 1

You have been given an array/list 'HEIGHTS' of length ‘N. 'HEIGHTS' represents the histogram and each element of 'HEIGHTS' represents the height of the histogram bar. Consider that the width of each histogram is 1.

You are supposed to return the area of the largest rectangle possible in the given histogram.

For example :

In the below histogram where array/list elements are {2, 1, 5, 6, 2, 3}.

The area of largest rectangle possible in the given histogram is 10.

You are given an 'N' * 'M' sized binary-valued matrix 'MAT, where 'N' is the number of rows and 'M' is the number of columns. You need to return the maximum size (area) of the submatrix which consists of all 1’s i.e. the maximum area of a submatrix in which each cell has only the value ‘1’.

In the above image, areas in green, red, and violet color are all submatrices of the original 4x4 matrix.

Note:

1. Binary valued matrix has only two values in each cell : 0 and 1.
2. A submatrix is a matrix formed by selecting certain rows and columns from a larger matrix.
3. The area of a matrix with 'h' rows and 'w' columns is equal to 'h' * 'w'. 

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