Python Implementation of Problem 18
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Includes
Problem Solution
Project Euler Problem 18
Thinking from the bottom up got the answer
Problem:
By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.
3
7 4
2 4 6
8 5 9 3
That is, 3 + 7 + 4 + 9 = 23.
Find the maximum total from top to bottom of the triangle below:
75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)
1"""
2Project Euler Problem 18
3
4Thinking from the bottom up got the answer
5
6Problem:
7
8By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top
9to bottom is 23.
10
11.. code-block::
12
13 3
14 7 4
15 2 4 6
16 8 5 9 3
17
18That is, 3 + 7 + 4 + 9 = 23.
19
20Find the maximum total from top to bottom of the triangle below:
21
22.. code-block::
23
24 75
25 95 64
26 17 47 82
27 18 35 87 10
28 20 04 82 47 65
29 19 01 23 75 03 34
30 88 02 77 73 07 63 67
31 99 65 04 28 06 16 70 92
32 41 41 26 56 83 40 80 70 33
33 41 48 72 33 47 32 37 16 94 29
34 53 71 44 65 25 43 91 52 97 51 14
35 70 11 33 28 77 73 17 78 39 68 17 57
36 91 71 52 38 17 14 91 43 58 50 27 29 48
37 63 66 04 68 89 53 67 30 73 16 69 87 40 31
38 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
39
40NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67,
41is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a
42clever method! ;o)
43
44"""
45from .lib.triangles import reduce_triangle
46
47
48def main() -> int:
49 rows = (
50 (75, ),
51 (95, 64),
52 (17, 47, 82),
53 (18, 35, 87, 10),
54 (20, 4, 82, 47, 65),
55 (19, 1, 23, 75, 3, 34),
56 (88, 2, 77, 73, 7, 63, 67),
57 (99, 65, 4, 28, 6, 16, 70, 92),
58 (41, 41, 26, 56, 83, 40, 80, 70, 33),
59 (41, 48, 72, 33, 47, 32, 37, 16, 94, 29),
60 (53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14),
61 (70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57),
62 (91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48),
63 (63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31),
64 (4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23)
65 )
66 return reduce_triangle(rows)