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>
This commit is contained in:
Vedas Dixit
2023-10-24 12:18:59 +05:30
committed by GitHub
parent 7d7f109e6f
commit fb134b10b0
3 changed files with 74 additions and 0 deletions

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/**
* 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 };