Implemented M Coloring Problem (#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>

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)