How to DRY up directional logic from a try/except mess

Question

I'm trying to simplify my solution to Project Euler's problem 11 (find the greatest product of 4-in-a-row numbers in a 20x20 grid).

My main gripe with my answer are the four try/except clauses in the definition of sub_lists_at_xy. I have one for each direction (east, south, southeast, and southwest) of 4-in-a-row lists that could possibly run off the board. Do you have any suggestions for simplifying or DRYing up this implementation?

from operator import mul

with open("11.txt") as f:
    nums = [[int(num) for num in line.split(' ')] for line in f.read().split('\n')]

def prod(lst):
    return reduce(mul, lst, 1)

def sub_lists_at_xy(array, length, x, y):

    try:
        east=array[y][x:x+length]
    except IndexError:
        east=[0]*length

    try:
        south=[list[x] for list in array[y:y+length]] 
    except IndexError:
        south=[0]*length

    try:
        southeast=[array[y+i][x+i] for i in range(length)]
    except IndexError:
        southeast=[0]*length

    try:
        southwest=[array[y+i][x-i] for i in range(length)]
    except IndexError:
        southwest=[0]*length    

    return east, south, southeast, southwest

sub_lists=[]

for x in range(len(nums[0])):
    for y in range(len(nums)):
        sub_lists += sub_lists_at_xy(nums, 4, x, y)
best = max(prod(lst) for lst in sub_lists)
print(best)

Answer 1

To follow the don't-repeat-yourself rule, you could pull out the direction logic:

def sub_lists_at_xy(array, length, x, y):
    directions = [(1, 0), (0, 1), (1, 1), (-1, 1)]
    sublists = []
    for dx, dy in directions:
        try:
            seq = [array[y+dy*i][x+dx*i] for i in range(length)]
            sublists.append(seq)
        except IndexError:
            pass
    return sublists

You might want to check that I didn't get the directions wrong -- I usually make sign errors all over the place -- but you get the idea.

[Note: this isn't how I myself would do it, but it's how I would simplify your code.]

Answer 2

You could check the input, but you could also pad your array

with open("11.txt") as f:
    nums = [["X"] + [int(num) for num in line.split(' ')] + ["X"] for line in f.read().split('\n')]
    nums = ["X"]*(len(nums[0])+2) + nums + ["X"]*(len(nums[0])+2)

You can then filter your data

reduce(mul, [x for x in lst if x != "X"], 1)