132 lines
5.1 KiB
Python
132 lines
5.1 KiB
Python
#!/usr/bin/env python3
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# In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
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#
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# 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
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# 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
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# 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
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# 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
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# 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
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# 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
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# 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
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# 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
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# 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
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# 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
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# 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
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# 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
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# 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
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# 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
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# 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
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# 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
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# 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
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# 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
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# 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
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# 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
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#
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# The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
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#
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# What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
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from projecteuler import timing
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@timing
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def p011() -> None:
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grid = [[8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8],
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[49, 49, 99, 40, 17, 81, 18, 57, 60, 87,
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17, 40, 98, 43, 69, 48, 4, 56, 62, 0],
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[81, 49, 31, 73, 55, 79, 14, 29, 93, 71,
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40, 67, 53, 88, 30, 3, 49, 13, 36, 65],
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[52, 70, 95, 23, 4, 60, 11, 42, 69, 24,
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68, 56, 1, 32, 56, 71, 37, 2, 36, 91],
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[22, 31, 16, 71, 51, 67, 63, 89, 41, 92,
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36, 54, 22, 40, 40, 28, 66, 33, 13, 80],
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[24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33,
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53, 78, 36, 84, 20, 35, 17, 12, 50],
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[32, 98, 81, 28, 64, 23, 67, 10, 26, 38,
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40, 67, 59, 54, 70, 66, 18, 38, 64, 70],
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[67, 26, 20, 68, 2, 62, 12, 20, 95, 63,
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94, 39, 63, 8, 40, 91, 66, 49, 94, 21],
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[24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78,
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78, 96, 83, 14, 88, 34, 89, 63, 72],
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[21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35,
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14, 0, 61, 33, 97, 34, 31, 33, 95],
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[78, 17, 53, 28, 22, 75, 31, 67, 15, 94,
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3, 80, 4, 62, 16, 14, 9, 53, 56, 92],
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[16, 39, 5, 42, 96, 35, 31, 47, 55, 58,
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88, 24, 0, 17, 54, 24, 36, 29, 85, 57],
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[86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44,
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37, 44, 60, 21, 58, 51, 54, 17, 58],
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[19, 80, 81, 68, 5, 94, 47, 69, 28, 73,
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92, 13, 86, 52, 17, 77, 4, 89, 55, 40],
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[4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57,
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32, 16, 26, 26, 79, 33, 27, 98, 66],
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[88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33,
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67, 46, 55, 12, 32, 63, 93, 53, 69],
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[4, 42, 16, 73, 38, 25, 39, 11, 24, 94,
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72, 18, 8, 46, 29, 32, 40, 62, 76, 36],
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[20, 69, 36, 41, 72, 30, 23, 88, 34, 62,
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99, 69, 82, 67, 59, 85, 74, 4, 36, 16],
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[20, 73, 35, 29, 78, 31, 90, 1, 74, 31,
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49, 71, 48, 86, 81, 16, 23, 57, 5, 54],
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[1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]]
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_max = 0
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# Brute-force approach: for each number in the grid, try products with its three
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# adjacent numbers in every direction (horizontal, vertical and the two diagonals).
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# If the product is larger than the current maximum, save it.
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for i in range(17):
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for j in range(17):
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# Horizontal direction.
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prod = 1
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k = j
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while k < j + 4:
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prod = prod * grid[i][k]
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k = k + 1
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_max = max(_max, prod)
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# Vertical direction.
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prod = 1
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k = i
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while k < i + 4:
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prod = prod * grid[k][j]
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k = k + 1
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_max = max(_max, prod)
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# Diagonal direction, from top left to bottom right.
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prod = 1
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k = i
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w = j
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while k < i + 4 and w < j + 4:
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prod = prod * grid[k][w]
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k = k + 1
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w = w + 1
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_max = max(_max, prod)
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# The last diagonal is handled separately
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for i in range(17):
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for j in range(3, 20):
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# Diagonal direction, from top right to bottom left.
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prod = 1
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k = i
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w = j
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while k < i + 4 and w > j - 4:
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prod = prod * grid[k][w]
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k = k + 1
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w = w - 1
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_max = max(_max, prod)
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print('Project Euler, Problem 11')
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print(f'Answer: {_max}')
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if __name__ == '__main__':
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p011()
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