Largest submatrix with equal no of 1's and 0's

Question

Given a matrix of size mxn containing 0\'s and 1\'s only. I need to find the largest sub-matrix which has equal number of 1\'s and 0\'s in it. Brute force appro

Answer 1

This algorithm assumes that we search a sub-matrix with contiguous rows and columns and with the largest possible product of height and width.

Start with the following pre-processing:

A = substitute_zero_with_minus_one(InputMatrix)
B = prefix_sum_for_each_column(A)
C = prefix_sum_for_each_row(B)

Now for each pair of rows (i, j) do the folowing:

for each column k:
  d = C[k, j] - C[k, i]
  if h[d] not empty:
    if (k - h[d]) * (j - i) is greater than best result:
      update best result
  else:
    h[d] = k

Time complexity is O(N² * M), extra space is O(N * M).