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feat(js): add modular solution and documentation for normal challenge 5 - BFS and DFS Graph Traversal
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‎2-NORMAL/JavaScript/5-bfs-dfs-graph-traversal/article.md‎

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# Challenge Description and Solution
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## English Version
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### Challenge Description
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Implement breadth-first search (BFS) and depth-first search (DFS) algorithms to traverse a graph represented by adjacency lists. Ensure coverage of both connected and disconnected graphs.
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### Code Explanation
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The `Graph` class represents an undirected graph using adjacency lists. It supports:
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- `addEdge(u, v)`: Adds an undirected edge between vertices `u` and `v`.
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- `bfs(start)`: Performs BFS traversal starting from a given vertex.
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- `dfs(start)`: Performs DFS traversal starting from a given vertex.
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- `bfsDisconnected()`: Performs BFS traversal covering all vertices, including disconnected components.
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- `dfsDisconnected()`: Performs DFS traversal covering all vertices, including disconnected components.
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### Relevant Code Snippet
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```javascript
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class Graph {
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constructor(vertices) {
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this.V = vertices;
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this.adj = Array.from({ length: vertices }, () => []);
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}
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addEdge(u, v) {
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this.adj[u].push(v);
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this.adj[v].push(u); // Undirected graph
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}
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bfs(start) {
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const visited = new Array(this.V).fill(false);
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const queue = [];
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const result = [];
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visited[start] = true;
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queue.push(start);
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while (queue.length > 0) {
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const vertex = queue.shift();
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result.push(vertex);
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for (const neighbor of this.adj[vertex]) {
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if (!visited[neighbor]) {
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visited[neighbor] = true;
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queue.push(neighbor);
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}
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}
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}
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return result;
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}
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dfsUtil(v, visited, result) {
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visited[v] = true;
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result.push(v);
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for (const neighbor of this.adj[v]) {
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if (!visited[neighbor]) {
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this.dfsUtil(neighbor, visited, result);
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}
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}
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}
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dfs(start) {
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const visited = new Array(this.V).fill(false);
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const result = [];
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this.dfsUtil(start, visited, result);
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return result;
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}
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bfsDisconnected() {
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const visited = new Array(this.V).fill(false);
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const result = [];
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for (let i = 0; i < this.V; i++) {
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if (!visited[i]) {
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const queue = [];
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visited[i] = true;
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queue.push(i);
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while (queue.length > 0) {
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const vertex = queue.shift();
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result.push(vertex);
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for (const neighbor of this.adj[vertex]) {
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if (!visited[neighbor]) {
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visited[neighbor] = true;
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queue.push(neighbor);
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}
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}
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}
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}
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}
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return result;
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}
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dfsDisconnected() {
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const visited = new Array(this.V).fill(false);
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const result = [];
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for (let i = 0; i < this.V; i++) {
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if (!visited[i]) {
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this.dfsUtil(i, visited, result);
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}
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}
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return result;
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}
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}
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```
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### Example Usage
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```javascript
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import Graph from './graph.js';
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const g = new Graph(7);
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const edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [5, 6]];
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for (const [u, v] of edges) {
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g.addEdge(u, v);
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}
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console.log('BFS starting from vertex 0:');
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console.log(g.bfs(0));
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console.log('DFS starting from vertex 0:');
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console.log(g.dfs(0));
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console.log('BFS for disconnected graph:');
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console.log(g.bfsDisconnected());
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console.log('DFS for disconnected graph:');
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console.log(g.dfsDisconnected());
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```
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---
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## Versión en Español
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### Descripción del Reto
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Implementa los algoritmos de búsqueda en anchura (BFS) y búsqueda en profundidad (DFS) para recorrer un grafo representado por listas de adyacencia. Asegura la cobertura de grafos conectados y desconectados.
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### Explicación del Código
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La clase `Graph` representa un grafo no dirigido usando listas de adyacencia. Soporta:
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- `addEdge(u, v)`: Añade una arista no dirigida entre los vértices `u` y `v`.
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- `bfs(start)`: Realiza un recorrido BFS comenzando desde un vértice dado.
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- `dfs(start)`: Realiza un recorrido DFS comenzando desde un vértice dado.
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- `bfsDisconnected()`: Realiza un recorrido BFS cubriendo todos los vértices, incluyendo componentes desconectados.
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- `dfsDisconnected()`: Realiza un recorrido DFS cubriendo todos los vértices, incluyendo componentes desconectados.
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### Fragmento de Código Relevante
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```javascript
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class Graph {
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constructor(vertices) {
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this.V = vertices;
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this.adj = Array.from({ length: vertices }, () => []);
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}
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addEdge(u, v) {
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this.adj[u].push(v);
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this.adj[v].push(u); // Grafo no dirigido
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}
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bfs(start) {
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const visited = new Array(this.V).fill(false);
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const queue = [];
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const result = [];
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visited[start] = true;
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queue.push(start);
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while (queue.length > 0) {
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const vertex = queue.shift();
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result.push(vertex);
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for (const neighbor of this.adj[vertex]) {
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if (!visited[neighbor]) {
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visited[neighbor] = true;
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queue.push(neighbor);
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}
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}
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}
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return result;
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}
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dfsUtil(v, visited, result) {
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visited[v] = true;
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result.push(v);
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for (const neighbor of this.adj[v]) {
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if (!visited[neighbor]) {
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this.dfsUtil(neighbor, visited, result);
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}
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}
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}
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dfs(start) {
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const visited = new Array(this.V).fill(false);
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const result = [];
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this.dfsUtil(start, visited, result);
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return result;
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}
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bfsDisconnected() {
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const visited = new Array(this.V).fill(false);
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const result = [];
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for (let i = 0; i < this.V; i++) {
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if (!visited[i]) {
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const queue = [];
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visited[i] = true;
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queue.push(i);
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while (queue.length > 0) {
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const vertex = queue.shift();
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result.push(vertex);
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for (const neighbor of this.adj[vertex]) {
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if (!visited[neighbor]) {
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visited[neighbor] = true;
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queue.push(neighbor);
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}
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}
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}
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}
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}
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return result;
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}
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dfsDisconnected() {
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const visited = new Array(this.V).fill(false);
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const result = [];
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for (let i = 0; i < this.V; i++) {
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if (!visited[i]) {
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this.dfsUtil(i, visited, result);
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}
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}
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return result;
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}
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}
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```
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### Ejemplo de Uso
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```javascript
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import Graph from './graph.js';
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const g = new Graph(7);
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const edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [5, 6]];
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for (const [u, v] of edges) {
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g.addEdge(u, v);
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}
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console.log('BFS starting from vertex 0:');
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console.log(g.bfs(0));
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console.log('DFS starting from vertex 0:');
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console.log(g.dfs(0));
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console.log('BFS for disconnected graph:');
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console.log(g.bfsDisconnected());
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console.log('DFS for disconnected graph:');
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console.log(g.dfsDisconnected());

‎2-NORMAL/JavaScript/5-bfs-dfs-graph-traversal/proposed-solution/graph.js‎

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// graph.js - Graph class with BFS and DFS traversals
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class Graph {
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constructor(vertices) {
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this.V = vertices;
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this.adj = Array.from({ length: vertices }, () => []);
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}
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addEdge(u, v) {
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this.adj[u].push(v);
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this.adj[v].push(u); // Undirected graph
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}
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bfs(start) {
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const visited = new Array(this.V).fill(false);
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const queue = [];
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const result = [];
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visited[start] = true;
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queue.push(start);
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while (queue.length > 0) {
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const vertex = queue.shift();
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result.push(vertex);
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for (const neighbor of this.adj[vertex]) {
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if (!visited[neighbor]) {
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visited[neighbor] = true;
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queue.push(neighbor);
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}
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}
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}
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return result;
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}
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dfsUtil(v, visited, result) {
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visited[v] = true;
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result.push(v);
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for (const neighbor of this.adj[v]) {
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if (!visited[neighbor]) {
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this.dfsUtil(neighbor, visited, result);
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}
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}
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}
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dfs(start) {
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const visited = new Array(this.V).fill(false);
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const result = [];
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this.dfsUtil(start, visited, result);
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return result;
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}
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bfsDisconnected() {
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const visited = new Array(this.V).fill(false);
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const result = [];
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for (let i = 0; i < this.V; i++) {
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if (!visited[i]) {
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const queue = [];
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visited[i] = true;
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queue.push(i);
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while (queue.length > 0) {
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const vertex = queue.shift();
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result.push(vertex);
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for (const neighbor of this.adj[vertex]) {
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if (!visited[neighbor]) {
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visited[neighbor] = true;
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queue.push(neighbor);
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}
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}
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}
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}
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}
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return result;
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}
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dfsDisconnected() {
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const visited = new Array(this.V).fill(false);
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const result = [];
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for (let i = 0; i < this.V; i++) {
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if (!visited[i]) {
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this.dfsUtil(i, visited, result);
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}
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}
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return result;
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}
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}
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export default Graph;

‎2-NORMAL/JavaScript/5-bfs-dfs-graph-traversal/proposed-solution/main.js‎

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// main.js - Example usage of Graph with BFS and DFS traversals
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import Graph from './graph.js';
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/*
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Challenge: Implement breadth-first search (BFS) and depth-first search (DFS) algorithms to traverse a graph represented by adjacency lists.
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Ensure coverage of both connected and disconnected graphs.
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*/
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function main() {
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const g = new Graph(7);
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const edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [5, 6]];
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for (const [u, v] of edges) {
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g.addEdge(u, v);
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}
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console.log('BFS starting from vertex 0:');
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console.log(g.bfs(0));
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console.log('DFS starting from vertex 0:');
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console.log(g.dfs(0));
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console.log('BFS for disconnected graph:');
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console.log(g.bfsDisconnected());
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console.log('DFS for disconnected graph:');
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console.log(g.dfsDisconnected());
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}
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main();

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