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problem-11.py
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# -*- coding: utf-8 -*-
"""
Largest product in a grid
https://projecteuler.net/problem=11
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?
----------------------------------------
Наибольшее произведение в таблице
В таблице 20×20 (внизу) четыре числа на одной диагонали выделены красным.
Произведение этих чисел 26 × 63 × 78 × 14 = 1788696.
Каково наибольшее произведение четырёх подряд идущих чисел в таблице 20×20 ,
расположенных в любом направлении (вверх, вниз, вправо, влево или по диагонали)?
"""
import time
DATA = '''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'''
#todo optimize?
def main():
start = time.time()
temp_strings = DATA.split('\n')
data_array = []
for arr in temp_strings:
data_array.append(arr.split(" "))
product = 0
# diagonals: left down to right
for column in range(0, 17):
for row in range(0, 17):
first = int(data_array[row][column])
second = int(data_array[row+1][column+1])
third = int(data_array[row+2][column+2])
forth = int(data_array[row+3][column+3])
temp = first * second * third * forth
if temp > product:
product = temp
#diagonals: right down to left
for column in reversed(range(3, 20)):
for row in range(0, 17):
first = int(data_array[row][column])
second = int(data_array[row+1][column-1])
third = int(data_array[row+2][column-2])
forth = int(data_array[row+3][column-3])
temp = first * second * third * forth
if temp > product:
product = temp
#horizontal and vertical
for column in range(0, 17):
for row in range(0, 20):
#horizontal
first = int(data_array[row][column])
second = int(data_array[row][column+1])
third = int(data_array[row][column+2])
forth = int(data_array[row][column+3])
temp = first * second * third * forth
if temp > product:
product = temp
#vertical
first = int(data_array[column][row])
second = int(data_array[column+1][row])
third = int(data_array[column+2][row])
forth = int(data_array[column+3][row])
temp = first * second * third * forth
if temp > product:
product = temp
elapsed = (time.time() - start)
print(product)
print "%s seconds" % (elapsed)
if __name__ == "__main__":
main()