solMatrix.py

#!/usr/bin/env python

import random
import itertools

def rindex(alist, value):
    return len(alist) - alist[-1::-1].index(value) - 1

def getAvailability(arr, val):
    return [i.count(val) > 0 for i in arr]

def getDistances(arr, val1, val2):
    horizontal_dist = []
    for i in arr:
        try:
            horizontal_dist.append(max(
                abs(i.index(val1) - rindex(i, val2)),
                abs(i.index(val2) - rindex(i, val1))))
        except ValueError:
            horizontal_dist.append(None)
    return horizontal_dist

def maxArea(distances, availability):
    max_area = -1
    for id_i, i in enumerate(distances):
        if not i == None:
            for id_j, j in enumerate(availability):
                if j == True:
                    max_area = max(max_area, (0.5 * i * (abs(id_j - id_i))))
    return max_area

def main():
    x = 4
    arr = [[random.randint(0,2) for i in xrange(x)] for j in xrange(x)]
    transposed_arr = zip(*arr)
    for i in arr: print i

    all_values = set([0, 1, 2])
    max_in_horizontal = max([maxArea(getDistances(arr, i[0], i[1]), getAvailability(arr, all_values.difference(i).pop())) for i in itertools.combinations(all_values, 2)])
    max_in_vertical = max([maxArea(getDistances(transposed_arr, i[0], i[1]), getAvailability(transposed_arr, all_values.difference(i).pop())) for i in itertools.combinations(all_values, 2)])
    print "Answer: ", max(max_in_horizontal, max_in_vertical)

if __name__ == '__main__':
    main()