Pythonic way to check diagonals in nested list

Question

I have a nested list of 0s and ones such as :

L = [[1, 0, 1],
     [0, 0, 0],
     [0, 0, 1]]

I want to check if any ones are diagonal to each other. The nested list can come in any size, as long as the length of the sublists is equal to the length of the whole list (it's a square). So if I ran it on the above list, it would return False, because of two ones being diagonal.

My current code is:

for num, i in enumerate(List):
    for count, m in enumerate(i):
        key1 = True
        key2 = True
        key3 = True
        key4 = True
        num1 = num
        num2 = num
        num3 = num
        num4 = num
        count1 = count
        count2 = count
        count3 = count
        count4 = count
        if m == 1:
            while key1 or key2 or key3 or key4:
            #print(key1, key2, key3, key4)
                try:
                    if List[num1 + 1][count1 + 1] == 1:
                        print(List[num1 + 1][count1 + 1])
                        return False
                    num1 += 1
                    count1 += 1
                except IndexError:
                    key1 = False
                try:
                    if List[num2 - 1][count2 + 1] == 1:
                        if num2 > 0:
                            print(List[num2 - 1][count2 + 1])
                            return False
                    num2 -= 1
                    count2 += 1
                except IndexError:
                        key2 = False
                try:
                    if List[num3 + 1][count3 - 1] == 1:
                        if count3 > 0:
                            print(List[num3 + 1][count3 - 1])
                            print(num3 + 1, count3 - 1)
                            return False
                    num3 += 1
                    count3 -= 1
                except IndexError:
                    key3 = False
                try:
                    if List[num4 - 1][count4 - 1] == 1:
                        if count4 > 0 and num4 > 0:
                            print(List[num4 - 1][count4 - 1])
                            return False
                    num4 -= 1
                    count4 -=1
                except IndexError:
                    key4 = False
return True

The code scans the list for 1s, and when one is found, it looks at its four corners and searches them. It continues to search in the direction of the corner, moving one grid at a time. If another 1 is found, it returns false. Once all possible diagonal grids are searched (up to returning index error), the code moves to the next 1 that is found. Once every single 1 is searched and none of them find any diagonal is found, the code returns true.

It feels clunky and inefficient, but I'm not sure how to compact it. Is there a shorter way to do this?

Answer 1

You can access the diagonals like so:

L = [[1, 0, 1],
 [0, 0, 0],
 [0, 0, 1]]

diag1 = [L[i][i] for i in range(len(L))]
diag2 = [L[i][len(L[0])-i-1] for i in range(len(L))]
if diag1 == diag2:
   pass #do something here

Answer 2

You can start by thinking of a means of naming the diagonals. For example, in a 3x3 matrix the indices (x, y) go like this:

(0,0) (1,0) (2,0)
(0,1) (1,1) (2,1)
(0,2) (1,2) (2,2)

If we follow the diagonals, their indices have a simple pattern. The diagonals that run lower left to upper right are:

Diag #1 (0,0)
Diag #2 (0,1) (1,0)
Diag #3 (0,2) (1,1) (2,0)
Diag #4 (1,2) (2,1)
Diag #5 (2,2)

From upper left to lower right they are:

#1 (0,2)
#2 (0,1) (1,2)
#3 (0,0) (1,1) (2,2)
#4 (1,0) (2,1)
#5 (2,0)

Notice that in the lower left to upper right case, every cell (x, y) on the same diagonal has the same value of x + y. In the other case, every cell on the same diagonal has the same value of x - y. Obviously this will be true for any size matrix. We can use x+y and x-y to name the individual diagonals. As we step through the matrix, each time we encounter a "1" we can immediately calculate the names of the two diagonals that intersect there.

This suggests an efficient algorithm for deciding if any two "1"s are on the same diagonal. In Python we can use two sets to keep track of the "occupied" diagonals. If we encounter a "1" on an already-occupied diagonal, we return True, otherwise false. We can step through the matrix in any order provided we visit all the elements.

def has_diagonal_ones(a):
    # a is a 2-dimensional square array of 0's and 1's
    lower_left_upper_right = set()
    upper_left_lower_right = set()
    for x in range(len(a)):
         for y in range(len(a)):
             if a[x][y] == 0:
                 continue
             i_lower_to_upper = x + y
             i_upper_to_lower = x - y
             if i_lower_to_upper in lower_left_upper_right:
                 return True
             if i_upper_to_lower in upper_left_lower_right:
                 return True
             lower_left_upper_right.add(i_lower_to_upper)
             upper_left_lower_right.add(i_upper_to_lower) 
    return False

L = [[1, 0, 1],
 [0, 0, 0],
 [0, 0, 1]]
print(has_diagonal_ones(L))

>>> True

Answer 3

you can use numpy to solve this problem.

import numpy as np
def diagonal(arr):
    d = np.diag(a)

    set_len = len(set(d))
    d_len = len(d)
    if set_len < d_len:
        return False
    else:
        return True

a = np.array([[1, 0, 1], [0, 0, 0], [0, 0, 1]])
print(diagonal(a))

Answer 4

I have a lib for this. Checkout diag and adiag functions! https://github.com/dhilst/funcyou/blob/master/funcyou/indexers.py