Implemented M Coloring Problem (TheAlgorithms#1562)

* Implemented M Coloring Problem * Implemented M Coloring Problem * Switch to a functional approach instead of class-based. Use proper JSDoc comments. Refine the comments and remove redundancies. * Updated Documentation in README.md * Proper JSDoc comment --------- Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com>

Author: 3 people

Backtracking/MColoringProblem.js

@@ -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 };

Backtracking/tests/MColoringProblem.test.js

@@ -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();
+ });
+});

DIRECTORY.md

@@ -3,6 +3,7 @@
  * [generateParentheses](Backtracking/generateParentheses.js)
  * [GeneratePermutations](Backtracking/GeneratePermutations.js)
  * [KnightTour](Backtracking/KnightTour.js)
+ * [MColoringProblem](Backtracking/MColoringProblem.js)
  * [NQueens](Backtracking/NQueens.js)
  * [RatInAMaze](Backtracking/RatInAMaze.js)
  * [Sudoku](Backtracking/Sudoku.js)
@@ -166,6 +167,7 @@
  * [Area](Maths/Area.js)
  * [ArithmeticGeometricMean](Maths/ArithmeticGeometricMean.js)
  * [ArmstrongNumber](Maths/ArmstrongNumber.js)
+ * [AutomorphicNumber](Maths/AutomorphicNumber.js)
  * [AverageMean](Maths/AverageMean.js)
  * [AverageMedian](Maths/AverageMedian.js)
  * [BinaryConvert](Maths/BinaryConvert.js)