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Commit a9d2051

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chore: Merge pull request #783 from lvlte/ProjectEuler/018
Project Euler - Problem 18
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‎DIRECTORY.md‎

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* [Problem014](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem014.js)
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* [Problem015](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem015.js)
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* [Problem016](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem016.js)
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* [Problem018](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem018.js)
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* [Problem020](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem020.js)
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* [Problem1](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem1.js)
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* [Problem10](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem10.js)

‎Project-Euler/Problem018.js‎

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/**
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* @file Provides solution for Project Euler Problem 18 - Maximum path sum I
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* @author Eric Lavault {@link https://github.com/lvlte}
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* @license MIT
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*/
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/**
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* Problem 18 - Maximum path sum I
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*
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* @see {@link https://projecteuler.net/problem=18}
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*
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* By starting at the top of the triangle below and moving to adjacent numbers
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* on the row below, the maximum total from top to bottom is 23 :
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*
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* 3
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* 7 4
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* 2 4 6
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* 8 5 9 3
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*
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* That is, 3 +たす 7 +たす 4 +たす 9 =わ 23.
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*
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* Find the maximum total from top to bottom of the triangle below :
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*
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* 75
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* 95 64
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* 17 47 82
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* 18 35 87 10
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* 20 04 82 47 65
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* 19 01 23 75 03 34
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* 88 02 77 73 07 63 67
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* 99 65 04 28 06 16 70 92
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* 41 41 26 56 83 40 80 70 33
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* 41 48 72 33 47 32 37 16 94 29
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* 53 71 44 65 25 43 91 52 97 51 14
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* 70 11 33 28 77 73 17 78 39 68 17 57
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* 91 71 52 38 17 14 91 43 58 50 27 29 48
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* 63 66 04 68 89 53 67 30 73 16 69 87 40 31
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* 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
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*
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* NOTE: As there are only 16384 routes, it is possible to solve this problem
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* by trying every route. However, Problem 67, is the same challenge with a
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* triangle containing one-hundred rows; it cannot be solved by brute force,
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* and requires a clever method! ;o)
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*/
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const triangle = `
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75
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95 64
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17 47 82
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18 35 87 10
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20 04 82 47 65
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19 01 23 75 03 34
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88 02 77 73 07 63 67
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99 65 04 28 06 16 70 92
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41 41 26 56 83 40 80 70 33
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41 48 72 33 47 32 37 16 94 29
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53 71 44 65 25 43 91 52 97 51 14
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70 11 33 28 77 73 17 78 39 68 17 57
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91 71 52 38 17 14 91 43 58 50 27 29 48
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63 66 04 68 89 53 67 30 73 16 69 87 40 31
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04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
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`
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export const maxPathSum = function (grid = triangle) {
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/**
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* If we reduce the problem to its simplest form, considering :
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*
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* 7 -> The max sum depends on the two adjacent numbers below 7,
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* 2 4 not 7 itself.
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*
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* obviously 4 > 2 therefore the max sum is 7 + 4 = 11
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*
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* 6
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* Likewise, with : 4 6 6 > 4 therefore the max sum is 6 + 6 = 12
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*
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* Now, let's say we are given :
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*
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* 3
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* 7 6
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* 2 4 6
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*
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* and we decompose it into sub-problems such that each one fits the simple
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* case above, we got :
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*
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* . . 3
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* 7 . . 6 ? ?
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* 2 4 . . 4 6 . . .
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*
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* Again, considering any number, the best path depends on the two adjacent
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* numbers below it, not the number itself. That's why we have to compute
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* the max sum from bottom to top, replacing each number with the sum of
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* that number plus the greatest of the two adjacent numbers computed from
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* the previous row.
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*
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* . . 3 15
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* 11 . . 12 -> 11 12 -> x x
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* x x . . x x x x x x x x
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*
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* We are simplifying a complicated problem by breaking it down into simpler
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* sub-problems in a recursive manner, this is called Dynamic Programming.
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*/
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grid = grid.split(/\r\n|\n/).filter(l => l).map(r => r.split(' ').map(n => +n))
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for (let i = grid.length - 2; i >= 0; i--) {
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for (let j = 0; j < grid[i].length; j++) {
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grid[i][j] += Math.max(grid[i + 1][j], grid[i + 1][j + 1])
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}
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}
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return grid[0][0]
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}
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import { maxPathSum } from '../Problem018'
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const example = `
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3
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7 4
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2 4 6
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8 5 9 3
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`
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describe('Check Problem 18 - Maximum path sum I', () => {
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it('Check example', () => {
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expect(maxPathSum(example)).toBe(23)
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})
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it('Check solution', () => {
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expect(maxPathSum()).toBe(1074)
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})
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})

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