Euler-11.py

# elementary arrays I'll use to define directions
pos = [i for i in range(4)]
neg = [-i for i in pos]
zer = [0]*4

# First, compute the direction vectors. Given a coordinate and a direction vector,
# we can generate four coordinates in a desired direction. We'll care about 8 directions.
# Even though left/right, and up/down are the same, let's no worry about that for now.
#   1 2 3
#   \ | /
# 4 -   - 5
#   / | \
#   6 7 8

dirs = [
    list(zip(neg, neg)), # 1
    # [(0, 0), (-1, -1), (-2, -2), (-3, -3)]
    list(zip(zer, neg)), # 2
    # [(0, 0), (0, -1), (0, -2), (0, -3)],
    list(zip(pos, pos)), # 3
    # etc
    list(zip(neg, zer)), # 4
    list(zip(pos, zer)), # 5
    list(zip(neg, pos)), # 6
    list(zip(zer, pos)), # 7
    list(zip(pos, pos))  # 8
]

input = """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"""

def read_input(input):
    """
    Util function to read in the input array.
    """
    rows_str = input.split('\n')
    rows = []
    for row in rows_str:
        nums_str = row.split(' ')
        rows.append([int(n) for n in nums_str])
    return rows

arr = read_input(input)


def add(p1, p2):
    """
    Util function for adding two tuples, element-wise.
    """
    return (p1[0]+p2[0], p1[1]+p2[1])

def get_coords(p):
    """
    Given a coordinate `p`, generate points in all 8 directions.
    """
    points = []
    for i, d in enumerate(dirs):
        points.append([add(p, p2) for p2 in d])
    return points

def check_bounds(coords, n=20):
    """
    Given a list of coordinates, check if any of them falls outside of matrix bounds.
    """
    for coord in coords:
        x = coord[0]
        y = coord[1]
        if x < 0 or x >= n or y < 0 or y >= n:
            return False
    return True

# Generate all possible indices into our 20x20 matrix, as 2-tuples
idxs = []
for i in range(20):
    for j in range(20):
        idxs.append((i, j))

# Walk through all those indices, generating lists of continous lines, in the shape of indices
vecs = []
for idx in idxs:
    for coord in get_coords(idx):
        vecs.append(coord)

# Filter out lines that lead outside the matrix
good_coords = []
for v in vecs:
    if check_bounds(v):
        good_coords.append(v)

def get_product(coords, arr=arr):
    """
    Given vector of indices into arr, get all of them and get the product.

    [(0, 0), (1, 1), (2, 2), (3, 3)]
    """
    # idxs = [(i, j) for i in range(4) for j in range(2)]
    vals = 1
    for c in coords:
        v = arr[c[0]][c[1]]
        vals *= v
    return vals

# This is the running larges product
max_prod = 0

# Go through all "good" coordinates, compute their product, and update max if needed
for coords in good_coords:
    prod = get_product(coords)
    print('Temp prod', prod)
    if prod > max_prod:
        max_prod = prod

print('Maximum product found is ', max_prod)