solve11.py

# https://projecteuler.net/problem=11
# Run with: 'python solve11.py'
# using Python 3.6.9
# by Zack Sargent

# Prompt:
# In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
# 
# (see grid)
# 
# 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?
# 
# 
#  grid is taken from the problems page.
grid = """\
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"""
grid = grid.split("\n")
for i in range(0, len(grid)):
    grid[i] = grid[i].split(" ")
# grid is now a multidimenstional array

# prints a multidimensional array, correctly
def print_md_array(arr):
    string = f"{arr}"
    string = string.replace("],", "],\n")
    print(string)

def horizontal(array):
    return array

def vertical(array):
    vertical_array = []
    for height in range(0, len(array)):
        row = []
        for width in range(0, len(array[height])):
            row.append(array[width][height])
        vertical_array.append(row)
    return vertical_array

# diagonals from left to right, going down
# we have to break the scan into two steps
# in order to account for the grid borders.
def ltr_diagonals(array):
    diagonals = []
    # apply to bottom left half of array
    for x in range(0, len(array[0])):
        row = []
        for y in range(0, len(array)):
            try:
                row.append(array[x + y][y])
            except:
                pass
        diagonals.append(row)
    # apply to top right half of array
    for x in range(1, len(array[0])):
        row = []
        for y in range(0, len(array)):
            try:
                row.append(array[y][x + y])
            except:
                pass
        diagonals.append(row)
    return diagonals

def rtl_diagonals(array):
    diagonals = []
    # apply to bottom right, going left to right, up
    for x in reversed(range(0, len(array[0]))):
        row = []
        for y in range(x+1, len(array)):
            row.append(array[x - y][y])
        diagonals.append(row)
    # apply to center diagonal, going left to right, up
    for x in range(0, len(array[0])):
        row = []
        for y in range(0, len(array) - x):
            row.append(array[y][len(array) - y - 1 - x])
        diagonals.append(row)
    return diagonals

def array_product(array):
    product = 1
    for i in array:
        i = int(i)
        product *= i
    return product

STEP_SIZE = 4
def greatest_product(array):
    products = []
    for line in array:
        for i in range(0, len(line)):
            segment = line[i:i+STEP_SIZE]
            product = array_product(segment)
            products.append(product)
    return max(products)


totals = []
totals.append(greatest_product(horizontal(grid)))
totals.append(greatest_product(vertical(grid)))
totals.append(greatest_product(rtl_diagonals(grid)))
totals.append(greatest_product(ltr_diagonals(grid)))
print(max(totals))
# -> 70600674