JavaScript Implementation of Problem 18
View source code here on GitHub!
- p0018()
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)
- Returns:
number --
1/**
2 * Project Euler Problem 18
3 *
4 * Thinking from the bottom up got the answer
5 *
6 * Problem:
7 *
8 * By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from
9 * top to bottom is 23.
10 *
11 * .. code-block::
12 *
13 * 3
14 * 7 4
15 * 2 4 6
16 * 8 5 9 3
17 *
18 * That is, 3 + 7 + 4 + 9 = 23.
19 *
20 * Find 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 *
40 * NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem
41 * 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and
42 * requires a clever method! ;o)
43 *
44 * @return {number}
45 */
46exports.p0018 = function() {
47 const rows = [
48 [75],
49 [95, 64],
50 [17, 47, 82],
51 [18, 35, 87, 10],
52 [20, 4, 82, 47, 65],
53 [19, 1, 23, 75, 3, 34],
54 [88, 2, 77, 73, 7, 63, 67],
55 [99, 65, 4, 28, 6, 16, 70, 92],
56 [41, 41, 26, 56, 83, 40, 80, 70, 33],
57 [41, 48, 72, 33, 47, 32, 37, 16, 94, 29],
58 [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14],
59 [70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57],
60 [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48],
61 [63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
62 [4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23],
63 ];
64 return triangles.reduceTriangle(rows);
65};
66
67const triangles = require('./lib/triangles.js');