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Implemented M Coloring Problem#1562
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raklaptudirm merged 6 commits intoTheAlgorithms:masterfromvedas-dixit:m-coloring-backtrackingOct 24, 2023
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a6edadf Implemented M Coloring Problem
vedas-dixitf945eb1 Implemented M Coloring Problem
vedas-dixit95cab08 Switch to a functional approach instead of class-based.
vedas-dixit8c8f1dd Merge branch 'm-coloring-backtracking' of https://github.com/vedas-di…
vedas-dixiteafd7fb Updated Documentation in README.md
9300adc Proper JSDoc comment
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,49 @@ | ||
| /** | ||
| * Colors a graph using up to m colors such that no two adjacent vertices share the same color. | ||
| * @param {number[][]} graph - Adjacency matrix of the graph, using 0 for no edge. | ||
| * @param {number} m - The number of colors to use. | ||
| * @returns {?Array.<number>} A valid M-coloring of the graph using colors 1 to m, or null if none exists. | ||
| * @see https://en.wikipedia.org/wiki/Graph_coloring | ||
| */ | ||
| function mColoring(graph, m) { | ||
| const colors = new Array(graph.length).fill(0); | ||
| // Check if it's safe to color a vertex with a given color. | ||
| function isSafe(vertex, color) { | ||
| for (let i = 0; i < graph.length; i++) { | ||
| if (graph[vertex][i] && colors[i] === color) { | ||
| return false; | ||
| } | ||
| } | ||
| return true; | ||
| } | ||
| // Use backtracking to try and color the graph. | ||
| function solveColoring(vertex = 0) { | ||
| if (vertex === graph.length) { | ||
| return true; | ||
| } | ||
| for (let color = 1; color <= m; color++) { | ||
| if (isSafe(vertex, color)) { | ||
| colors[vertex] = color; | ||
| if (solveColoring(vertex + 1)) { | ||
| return true; | ||
| } | ||
| // If no solution, backtrack. | ||
| colors[vertex] = 0; | ||
| } | ||
| } | ||
| return false; | ||
| } | ||
| // If coloring is possible, return the colors. | ||
| if (solveColoring()) { | ||
| return colors; | ||
| } | ||
| return null; | ||
| } | ||
| export { mColoring }; |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,23 @@ | ||
| import { mColoring } from '../MColoringProblem'; | ||
| describe('MColoringProblem', () => { | ||
| it('should color a triangle with 3 colors', () => { | ||
| const graph = [ | ||
| [0, 1, 1], | ||
| [1, 0, 1], | ||
| [1, 1, 0] | ||
| ]; | ||
| const solution = mColoring(graph, 3); | ||
| expect(solution).not.toBeNull(); | ||
| }); | ||
| it('should not color a triangle with 2 colors', () => { | ||
| const graph = [ | ||
| [0, 1, 1], | ||
| [1, 0, 1], | ||
| [1, 1, 0] | ||
| ]; | ||
| const solution = mColoring(graph, 2); | ||
| expect(solution).toBeNull(); | ||
| }); | ||
| }); |
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