Project Euler 11 - Largest product in a Grid

'''
In the 20×20 grid below, four numbers along a diagonal line have been marked in red.

08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 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 03 45 02 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 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 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 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
'''
# FUNCTION 1
def maxProductHorizontal(array, m):
    product = 0
    for i in range(n-m+1):
        for j in range(n):
            value = array[i][j] * array[i+1][j] * array[i+2][j] * array[i+3][j]
            if value > product:
                product = value
    return product

# FUNCTION 2
def maxProductVertical(array, m):
    product = 0
    for i in range(n):
        for j in range(n-m+1):
            value = array[i][j] * array[i][j+1] * array[i][j+2] * array[i][j+3]
            if value > product:
                product = value
    return product

# FUNCTION 3
def maxProductDiagRight(array, m):
    product = 0
    for i in range(n):
        for diag in range(-(n-m), n-m+1):
            j = i + diag
            if i >= 0 and j >= 0 and i+3 < n and j+3 < n:
                value = array[i][j] * array[i+1][j+1] * array[i+2][j+2] * array[i+3][j+3]
                if value > product:
                    product = value
    return product

# FUNCTION 4
def maxProductDiagLeft(array, m):
    sum = n-1
    product = 0
    for i in range(n):
        for diag in range(sum+1):
            j = diag - i
            if i >= 3 and j >= 0 and i < n and j+3 < n:
                value = array[i][j] * array[i-1][j+1] * array[i-2][j+2] * array[i-3][j+3]
                if value > product:
                    product = value
    return product


n = 20
m = 4

matrixWord = "08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 \
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 \
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 \
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 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 03 45 02 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 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 \
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 \
21 36 23 09 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 03 80 04 62 16 14 09 53 56 92 \
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 \
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 \
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 \
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 \
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 \
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 \
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 \
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 \
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"

matrixNumbers = matrixWord.split(" ")
counter = -1
array = [[0 for __ in range(n)] for _ in range(n)]
for i in range(n):
    for j in range(n):
        counter += 1
        array[i][j] = matrixNumbers[counter]

# Now, "array" is a 20x20 matrix with string numbers
for i in range(n):
    for j in range(n):
        array[i][j] = int(array[i][j])

prodHoriz = maxProductHorizontal(array, m)
print("**** 1. Horizontally ****")
print(prodHoriz)
print()
prodVert = maxProductVertical(array, m)
print("**** 2. Vertically ****")
print(prodVert)
print()
prodDiagRight = maxProductDiagRight(array, m)
print("**** 3. Diagonally Right ****")
print(prodDiagRight)
print()
prodDiagLeft = maxProductDiagLeft(array, m)
print("**** 4. Diagonally Left ****")
print(prodDiagLeft)
print()