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problem_11.py
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problem_11.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
'''
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?
'''
grid = (
( 8, 2,22,97,38,15, 0,40, 0,75, 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, 0,),
(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, 0,76,44,20,45,35,14, 0,61,33,97,34,31,33,95,),
(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, 0,17,54,24,36,29,85,57,),
(86,56, 0,48,35,71,89, 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,),
)
def sequence(grid, row, col):
width = len(grid[row])
height = len(grid)
# # left -> right
if col + 4 <= width:
yield grid[row][col:col + 4]
# top -> bottom
if row + 4 <= height:
yield list(grid[row + n][col] for n in xrange(4))
# diagonally left -> right
if col + 4 <= width and row + 4 <= height:
yield list(grid[row + n][col + n] for n in xrange(4))
# diagonally left -> right
if col >= 3 and row + 4 <= height:
yield list(grid[row + n][col - n] for n in xrange(4))
max = 0
for row in xrange(len(grid)):
for col in xrange(len(grid[row])):
for line in sequence(grid, row, col):
c = reduce(lambda x, y: x * y, line)
if c > max:
max = c
print max