python - Checking diagonal adjacent numbers greatest product in a grid

Question

As mentioned in the title, I'm trying to find the greatest product of diagonal adjacent numbers in a grid but without using the numpy library.

dataa = [
    [1,2,3,4,5],
    [1,2,3,4,5],
    [2,3,4,5,6],
    [5,6,8,9,10],
    [1,2,3,4,5]
]


def search_dr(data, length): # length = how many adjacent numbers to check
    result, size = 0, len(data[0])
    for i in range(size):
        for y in range(0, len(data) - (length - 1)):
            part, counter = [], 0
            while len(part) < length:
                if size >= i + (length - 1): # for downward diagonal
                    part.append(data[y + counter][i + counter])
                    counter += 1
                product = 1
                for x in part:
                    product *= x
                if product > result:
                    result = product
                if length - 1 <= i: # for upward diagonal
                    part.append(data[y + counter][i - counter])
                    counter += 1
                product = 1
                for x in part:
                    product *= x
                if product > result:
                    result = product
    return result


search_dr(dataa, 4)

expected output is 480 since it is the result of 5 * 4 * 4 * 6 which are adjacent numbers and their product would be the greatest product among other 4 adjacent number in the sample grid.

But I can't understand why it doesn't work and in most cases it gives an index error. I would appreciate it a lot if anyone could help me to understand my code problem.

main sample:

   [8,2,22,97,38,15,00,40,00,75,4,5,7,78,52,12,50,77,91,8],
    [49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,4,56,62,00],
    [81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,3,49,13,36,65],
    [52,70,95,23,4,60,11,42,69,24,68,56,1,32,56,71,37,2,36,91],
    [22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80],
    [24,47,32,60,99,3,45,2,44,75,33,53,78,36,84,20,35,17,12,50],
    [32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70],
    [67,26,20,68,2,62,12,20,95,63,94,39,63,8,40,91,66,49,94,21],
    [24,55,58,5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72],
    [21,36,23,9,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95],
    [78,17,53,28,22,75,31,67,15,94,3,80,4,62,16,14,9,53,56,92],
    [16,39,5,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57],
    [86,56,00,48,35,71,89,7,5,44,44,37,44,60,21,58,51,54,17,58],
    [19,80,81,68,5,94,47,69,28,73,92,13,86,52,17,77,4,89,55,40],
    [4,52,8,83,97,35,99,16,7,97,57,32,16,26,26,79,33,27,98,66],
    [88,36,68,87,57,62,20,72,3,46,33,67,46,55,12,32,63,93,53,69],
    [4,42,16,73,38,25,39,11,24,94,72,18,8,46,29,32,40,62,76,36],
    [20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,4,36,16],
    [20,73,35,29,78,31,90,1,74,31,49,71,48,86,81,16,23,57,5,54],
    [1,70,54,71,83,51,54,69,16,92,33,48,61,43,52,1,89,19,67,48]

expected output: 70600674 [89, 94, 97, 87]

question from:https://stackoverflow.com/questions/66064251/checking-diagonal-adjacent-numbers-greatest-product-in-a-grid

Answer 1

You should take a simpler approach and only process positions that are part of a 4 value diagonal. This can be obtained by identifying the subset of the matrix that contains the top left items and going down 4 positions from those.

For example:

data = [
    [1,2,3,4,5],
    [1,2,3,4,5],
    [2,3,4,5,6],
    [5,6,8,9,10],
    [1,2,3,4,5]]

result  = 0
values  = []
diagLen = 4
for diagDir in (1,-1):
    for r in range(len(data)-diagLen+1):
        for c in range(len(data[0])-diagLen+1):
            if diagDir<0 : c = len(data[0])-1-c
            prod = 1
            for i in range(diagLen): prod *= data[r+i][c+i*diagDir]
            if prod<result: continue
            result = prod
            values = [data[r+i][c+i*diagDir] for i in range(diagLen)]

print(result,values)
# 480 [5, 4, 4, 6]