def check_matrix(m):
    pass

def get_range_for_cell(m,x,y):
    r = [1,2,3,4,5]
    for j in range(size):
        try:
            i = r.index(m[y][j])
        except ValueError: pass
        else: del r[i]

        try:
            i = r.index(m[j][x])
        except ValueError: pass
        else: del r[i]


    #print(len(r))
    return r

def solve(m):
    d = []
    modified = 0
    while (True):
        for y in range(size):
            for x in range(size):

                if (m[y][x] == 0):
                    rng = get_range_for_cell(m,x,y) # searching possible variants for cell
                    if len(rng) == 1:
                        m[y][x] = rng[0] # just one variant - put it
                        modified += 1
                    else:
                        d.append({'x':x, 'y':y, 'range':rng, 'pos':0 }) # put variants and set pointer to zero
        if (modified == 0):
            break
        modified = 0
    print(m)

matrix = [
    [5,1,0,2,0],
    [0,0,0,5,1],
    [4,5,1,0,0],
    [0,0,0,4,5],
    [0,4,5,0,3]]
size = len(matrix)
solve(matrix)