Implemented M Coloring Problem

vedas-dixit · vedas-dixit · commit f945eb1c7990 · 2023-10-23T10:28:10.000+05:30
diff --git a/Backtracking/MColoringProblem.js b/Backtracking/MColoringProblem.js
@@ -0,0 +1,65 @@
+/*
+  Problem: M Coloring Problem
+  Given a graph represented as an adjacency matrix and a number M (number of colors), 
+  determine if the graph can be colored with up to M colors such that no two adjacent 
+  vertices share the same color.
+
+  What is the M Coloring Problem?
+  - This problem is about coloring a graph's vertices with at most M different colors 
+    such that no two adjacent vertices have the same color.
+
+  Example:
+  - Consider a triangle (3 nodes connected cyclically). We'd need 3 colors to color each vertex 
+    without adjacent vertices having the same color.
+
+  Solution:
+  - We will be using backtracking to solve this question.
+  - Color a vertex, then move to an adjacent vertex and try all colors. If a color is valid, 
+    continue to the next vertex, else backtrack.
+*/
+
+class MColoring {
+    constructor(graph, m) {
+      this.graph = graph; // adjacency matrix representation
+      this.m = m; 
+      this.colors = new Array(graph.length).fill(0);
+    }
+  
+    isSafe(vertex, color) {
+      for (let i = 0; i < this.graph.length; i++) {
+        if (this.graph[vertex][i] && this.colors[i] === color) {
+          return false;
+        }
+      }
+      return true;
+    }
+  
+    solveColoring(vertex = 0) {
+      if (vertex === this.graph.length) {
+        return true;
+      }
+  
+      for (let color = 1; color <= this.m; color++) {
+        if (this.isSafe(vertex, color)) {
+          this.colors[vertex] = color;
+  
+          if (this.solveColoring(vertex + 1)) {
+            return true;
+          }
+  
+          this.colors[vertex] = 0; // backtrack
+        }
+      }
+      return false;
+    }
+  
+    getSolution() {
+      if (this.solveColoring()) {
+        return this.colors;
+      }
+      return [];
+    }
+  }
+  
+  export { MColoring }
+  
diff --git a/Backtracking/tests/MColoringProblem.test.js b/Backtracking/tests/MColoringProblem.test.js
@@ -0,0 +1,25 @@
+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 test1 = new MColoring(graph, 3);
+    const solution = test1.getSolution();
+    expect(solution).not.toEqual([]);
+  });
+
+  it('should not color a triangle with 2 colors', () => {
+    const graph = [
+      [0, 1, 1],
+      [1, 0, 1],
+      [1, 1, 0]
+    ];
+    const test2 = new MColoring(graph, 2);
+    const solution = test2.getSolution();
+    expect(solution).toEqual([]);
+  });
+});
