Largest rectangular sub matrix with the same number

Question

I am trying to come up with a dynamic programming algorithm that finds the largest sub matrix within a matrix that consists of the same number:

example:

Answer 1

This question is a duplicate. I have tried to flag it as a duplicate. Here is a Python solution, which also returns the position and shape of the largest rectangular submatrix:

#!/usr/bin/env python3

import numpy

s = '''5 5 8
5 5 7
3 4 1'''

nrows = 3
ncols = 3
skip_not = 5
area_max = (0, [])

a = numpy.fromstring(s, dtype=int, sep=' ').reshape(nrows, ncols)
w = numpy.zeros(dtype=int, shape=a.shape)
h = numpy.zeros(dtype=int, shape=a.shape)
for r in range(nrows):
    for c in range(ncols):
        if not a[r][c] == skip_not:
            continue
        if r == 0:
            h[r][c] = 1
        else:
            h[r][c] = h[r-1][c]+1
        if c == 0:
            w[r][c] = 1
        else:
            w[r][c] = w[r][c-1]+1
        minw = w[r][c]
        for dh in range(h[r][c]):
            minw = min(minw, w[r-dh][c])
            area = (dh+1)*minw
            if area > area_max[0]:
                area_max = (area, [(r, c, dh+1, minw)])

print('area', area_max[0])
for t in area_max[1]:
    print('coord and shape', t)

Output:

area 4
coord and shape (1, 1, 2, 2)