Python Implementation of Problem 11
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Includes
Problem Solution
Project Euler Problem 11
This one was tedious but pretty easy. I think I could even make it a generic version of this problem if I could figure out how to do the type expressions correctly.
Problem:
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?
1"""
2Project Euler Problem 11
3
4This one was tedious but pretty easy. I think I could even make it a generic version of this problem if I could figure
5out how to do the type expressions correctly.
6
7Problem:
8
9In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
10
1108 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
1249 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
1381 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
1452 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
1522 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
1624 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
1732 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
1867 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
1924 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
2021 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
2178 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
2216 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
2386 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
2419 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
2504 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
2688 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
2704 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
2820 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
2920 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
3001 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
31
32The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
33
34What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in
35the 20×20 grid?
36"""
37from functools import reduce
38from itertools import chain
39from operator import mul
40from typing import Iterable, List, Tuple, cast
41
42from .lib.iters import groupwise
43
44
45def text_to_grid(text: str) -> List[List[int]]:
46 return [[int(x) for x in row.split()] for row in text.split('\n')]
47
48
49def rows_by_4(grid: List[List[int]]) -> Iterable[Tuple[int, int, int, int]]:
50 for row in grid:
51 yield from cast(Iterable[Tuple[int, int, int, int]], groupwise(row, 4))
52
53
54def cols_by_4(grid: List[List[int]]) -> Iterable[Tuple[int, int, int, int]]:
55 transposed = [[0] * len(grid[0])] * len(grid)
56 for x, row in enumerate(grid):
57 for y, value in enumerate(row):
58 transposed[y][x] = value
59 yield from rows_by_4(transposed)
60
61
62def down_diags_by_4(grid: List[List[int]]) -> Iterable[Tuple[int, int, int, int]]:
63 for x in range(len(grid) - 4):
64 for y in range(len(grid[x]) - 4):
65 try:
66 yield cast(Tuple[int, int, int, int], tuple(grid[x+z][y+z] for z in range(4)))
67 except IndexError: # pragma: no cover
68 break
69
70
71def up_diags_by_4(grid: List[List[int]]) -> Iterable[Tuple[int, int, int, int]]:
72 for x in range(4, len(grid)):
73 for y in range(len(grid[x]) - 4):
74 try:
75 yield cast(Tuple[int, int, int, int], tuple(grid[x-z][y+z] for z in range(4)))
76 except IndexError: # pragma: no cover
77 break
78
79
80def main() -> int:
81 text = (
82 "08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\n"
83 "49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\n"
84 "81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\n"
85 "52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91\n"
86 "22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80\n"
87 "24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50\n"
88 "32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70\n"
89 "67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\n"
90 "24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\n"
91 "21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\n"
92 "78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\n"
93 "16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\n"
94 "86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\n"
95 "19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\n"
96 "04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\n"
97 "88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\n"
98 "04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36\n"
99 "20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16\n"
100 "20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\n"
101 "01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"
102 )
103 grid = text_to_grid(text)
104 answer = 0
105 for group in chain(rows_by_4(grid), cols_by_4(grid), down_diags_by_4(grid), up_diags_by_4(grid)):
106 product = reduce(mul, group, 1)
107 if product > answer:
108 answer = product
109 return answer