From 98ee73447e5f4cf1f5df6ad4e658ece30df24beb Mon Sep 17 00:00:00 2001 From: Eric Lavault <39483232+lvlte@users.noreply.github.com> Date: Wed, 13 Oct 2021 11:36:22 +0200 Subject: [PATCH 1/3] Project Euler : add solution for problem 18 (Max Path Sum I) + test. --- Project-Euler/Problem018.js | 112 ++++++++++++++++++++++++++ Project-Euler/test/Problem018.test.js | 18 +++++ 2 files changed, 130 insertions(+) create mode 100644 Project-Euler/Problem018.js create mode 100644 Project-Euler/test/Problem018.test.js diff --git a/Project-Euler/Problem018.js b/Project-Euler/Problem018.js new file mode 100644 index 000000000..43e8a9e62 --- /dev/null +++ b/Project-Euler/Problem018.js @@ -0,0 +1,112 @@ +/** + * @file Provides solution for Project Euler Problem 18 - Maximum path sum I + * @author Eric Lavault {@link https://github.com/lvlte} + * @license MIT + */ + +/** + * Problem 18 - Maximum path sum I + * + * @see {@link https://projecteuler.net/problem=18} + * + * 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) + */ + +const triangle = ` +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 +` + +export const maxPathSum = function (grid = triangle) { + /** + * If we reduce the problem to its simplest form, considering : + * + * 7 -> The max sum depends on the two adjacent numbers below 7, + * 2 4 not 7 itself. + * + * obviously 4 > 2 therefore the max sum is 7 + 4 = 11 + * + * 6 + * Likewise, with : 4 6 6 > 4 therefore the max sum is 6 + 6 = 12 + * + * Now, let's say we are given : + * + * 3 + * 7 6 + * 2 4 6 + * + * and we decompose it into sub-problems such that each one fits the simple + * case above, we got : + * + * . . 3 + * 7 . . 6 ? ? + * 2 4 . . 4 6 . . . + * + * Again, considering any number, the best path depends on the two adjacent + * numbers below it, not the number itself. That's why we have to compute + * the max sum from bottom to top, replacing each number with the sum of + * that number plus the greatest of the two adjacent numbers computed from + * the previous row. + * + * . . 3 15 + * 11 . . 12 -> 11 12 -> x x + * x x . . x x x x x x x x + * + * We are simplifying a complicated problem by breaking it down into simpler + * sub-problems in a recursive manner, this is called Dynamic Programming. + */ + + grid = grid.split(/\r\n|\n/).filter(l => l).map(r => r.split(' ').map(n => +n)) + + for (let i = grid.length - 2; i >= 0; i--) { + for (let j = 0; j < grid[i].length; j++) { + grid[i][j] += Math.max(grid[i + 1][j], grid[i + 1][j + 1]) + } + } + + return grid[0][0] +} diff --git a/Project-Euler/test/Problem018.test.js b/Project-Euler/test/Problem018.test.js new file mode 100644 index 000000000..cebb49ec4 --- /dev/null +++ b/Project-Euler/test/Problem018.test.js @@ -0,0 +1,18 @@ +import { maxPathSum } from '../Problem018' + +const example = ` +3 +7 4 +2 4 6 +8 5 9 3 +` + +describe('Check Problem 18 - Maximum path sum I', () => { + it('Check example', () => { + expect(maxPathSum(triangle)).toBe(23) + }) + + it('Check solution', () => { + expect(maxPathSum()).toBe(1074) + }) +}) From db7a28305e7a6ddb5e320151460bcc7b0f2f4866 Mon Sep 17 00:00:00 2001 From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Date: Wed, 13 Oct 2021 09:37:07 +0000 Subject: [PATCH 2/3] Auto-update DIRECTORY.md --- DIRECTORY.md | 1 + 1 file changed, 1 insertion(+) diff --git a/DIRECTORY.md b/DIRECTORY.md index 8290405c9..7328922d7 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -197,6 +197,7 @@ * [Problem014](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem014.js) * [Problem015](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem015.js) * [Problem016](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem016.js) + * [Problem018](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem018.js) * [Problem020](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem020.js) * [Problem1](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem1.js) * [Problem10](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem10.js) From 177f843195cd4583c26b242009b1bb1912df296e Mon Sep 17 00:00:00 2001 From: Eric Lavault <39483232+lvlte@users.noreply.github.com> Date: Wed, 13 Oct 2021 11:49:10 +0200 Subject: [PATCH 3/3] Fix renamed variable after testing ! --- Project-Euler/test/Problem018.test.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Project-Euler/test/Problem018.test.js b/Project-Euler/test/Problem018.test.js index cebb49ec4..a9b3f2109 100644 --- a/Project-Euler/test/Problem018.test.js +++ b/Project-Euler/test/Problem018.test.js @@ -9,7 +9,7 @@ const example = ` describe('Check Problem 18 - Maximum path sum I', () => { it('Check example', () => { - expect(maxPathSum(triangle)).toBe(23) + expect(maxPathSum(example)).toBe(23) }) it('Check solution', () => {