Added Breath First Search Algorithm

src/Algorithms/Breath First Search/BreathFirstSearch.java

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+import java.util.*;
+
+
+public class BreathFirstSearch {
+    // Graph adjacency list
+    private List<List<Integer>> adjList;
+
+    //BFS class constructor to the adjacency list
+    public BreathFirstSearch(int numVertices){
+        adjList = new ArrayList<>();
+        for (int i = 0; i < numVertices; i++){
+            adjList.add(new ArrayList<>());
+        }
+    }
+
+    //Add edge to the graph
+    public void addEdge(int from, int to){
+        adjList.get(from).add(to);
+        adjList.get(to).add(from); // This makes the graph undirected
+    }
+
+    //Iterative BFS for a given starting point
+    public void bfsIterative(int start){
+        boolean[] visited = new boolean[adjList.size()];
+        Queue<Integer> queue = new LinkedList<>();
+
+        visited[start] = true;
+        queue.add(start);
+
+        System.out.println("Iterative: ");
+        while(!queue.isEmpty()){
+            int vertex = queue.poll();
+            System.out.print(vertex + " ");
+
+            //Traverse all adjacent vertices
+            for (int adj : adjList.get(vertex)){
+                if (!visited[adj]) {
+                    visited[adj] = true;
+                    queue.add(adj);
+                }
+            }
+        }
+    }
+
+    //Recursive BFS for a given starting point
+    public void bfsRecursive(int start){
+        boolean[] visited = new boolean[adjList.size()];
+        Queue<Integer> queue = new LinkedList<>();
+        queue.add(start);
+
+        System.out.println("Recursive: ");
+        bfsRecursiveUtil(queue, visited);
+    }
+
+    //Auxiliar method to perform BFS recursively
+    private void bfsRecursiveUtil(Queue<Integer> queue, boolean[] visited){
+        //Base case: stop if the queue is empty
+        if (queue.isEmpty()) {
+            return;
+        }
+        int vertex = queue.poll();
+
+        //Not visited yet case
+        if (!visited[vertex]) {
+            visited[vertex] = true;
+            System.out.print(vertex + " ");
+
+            //Enqueue all unvisited adjacent vertices
+            for (int adj : adjList.get(vertex)){
+                if (!visited[adj]) {
+                    queue.add(adj);
+                }
+            }
+        }
+        //Recursive call
+        bfsRecursiveAux(queue, visited);
+    }
+
+    //Main method to demonstrate BFS
+    public static void main(String[] args) {
+        BreathFirstSearch graph = new BreathFirstSearch(6);
+
+        //Adding edges to the graph
+        graph.addEdge(0, 1);
+        graph.addEdge(1, 3);
+        graph.addEdge(1, 4);
+        graph.addEdge(2, 5);
+
+        //Perform both BFS approaches
+        graph.bfsIterative(0);
+        System.out.println("");
+        graph.bfsRecursive(0);
+    }
+
+}

src/Algorithms/Breath First Search/BreathFirstSearch.md

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+# Overview of the Depth First Search (DFS) Code in Java 💻
+
+## What's Happening in the Code? ❓
+The provided Java code implements Breath First Search (BFS), a fundamental graph traversal algorithm. Let's walk through the details!
+
+### 1. **Setting Up the Graph** 📝
+We start by creating a graph structure using an **adjacency list**, represented by a `List` of `List<Integer>`. Each index in the main list corresponds to a vertex, and each sublist contains its neighboring vertices. This makes it easy to keep track of which nodes are connected.
+
+```java
+private List<List<Integer>> adjList;
+```
+
+### 2. **Constructing the Graph** ⚙️
+The `BreathFirstSearch` constructor initializes the adjacency list with `numVertices` empty lists:
+
+```java
+public BreathFirstSearch(int numVertices){
+    adjList = new ArrayList<>();
+    for (int i = 0; i < numVertices; i++){
+        adjList.add(new ArrayList<>());
+    }
+}
+```
+
+### 3. **Adding Edges** ➕
+The `addEdge` method links two vertices, `from` and `to`, by adding each to the other's adjacency list:
+
+```java
+public void addEdge(int from, int to){
+    adjList.get(from).add(to);
+    adjList.get(to).add(from);
+}
+```
+
+This makes it an **undirected graph**, where the connection between nodes goes both ways.
+
+### 4. **The BFS Iterative Method** ↪️
+The `bfsIteratice` method sets up an array called `visited` to keep track of which nodes have been visited during the traversal,
+as well setting up a `queue` to process the vertices level by level:
+
+```java
+public void bfsIterative(int start){
+    boolean[] visited = new boolean[adjList.size()];
+    Queue<Integer> queue = new LinkedList<>();
+
+    visited[start] = true;
+    queue.add(start);
+
+    System.out.println("Iterative: ");
+    while(!queue.isEmpty()){
+        int vertex = queue.poll();
+        System.out.print(vertex + " ");
+
+        //Traverse all adjacent vertices
+        for (int adj : adjList.get(vertex)){
+            if (!visited[adj]) {
+                visited[adj] = true;
+                queue.add(adj);
+            }
+        }
+    }
+}
+```
+
+### 5. **The BFS Recursive Method** 🔄
+The main `bfsRecursive` method sets up an array called `visited` to keep track of which nodes have been visited during the traversal,
+as well setting up a `queue` to process the vertices level by level then, it calls the util function:
+
+```java
+public void bfsRecursive(int start){
+    boolean[] visited = new boolean[adjList.size()];
+    Queue<Integer> queue = new LinkedList<>();
+    queue.add(start);
+
+    System.out.println("Recursive: ");
+    bfsRecursiveUtil(queue, visited);
+}
+```
+
+### 6. **BFS Utility Method** ❤️
+The `bfsRecursiveUtil` method is the heart of the algorithm. It recursively visits nodes, prints and dequeues them as it goes:
+
+```java
+private void bfsRecursiveUtil(Queue<Integer> queue, boolean[] visited){
+    //Base case: stop if the queue is empty
+    if (queue.isEmpty()) {
+        return;
+    }
+    int vertex = queue.poll();
+
+    //Not visited yet case
+    if (!visited[vertex]) {
+        visited[vertex] = true;
+        System.out.print(vertex + " ");
+
+        //Enqueue all unvisited adjacent vertices
+        for (int adj : adjList.get(vertex)){
+            if (!visited[adj]) {
+                queue.add(adj);
+            }
+        }
+    }
+    //Recursive call
+    bfsRecursiveAux(queue, visited);
+}
+```
+- **Visit**: The current node is marked as visited and printed.
+- **Recur**: For each unvisited neighbor, `bfsUtil` is called recursively.
+
+### 6. **Main Method** 💪
+Finally, the `main` method demonstrates the DBFS by building a sample graph and starting the traversal from vertex `0`:
+
+```java
+public static void main(String[] args) {
+    BreathFirstSearch graph = new BreathFirstSearch(6);
+
+    //Adding edges to the graph
+    graph.addEdge(0, 1);
+    graph.addEdge(1, 3);
+    graph.addEdge(1, 4);
+    graph.addEdge(2, 5);
+
+    //Perform both BFS approaches
+    graph.bfsIterative(0);
+    System.out.println("");
+    graph.bfsRecursive(0);
+}
+```
+
+## What Happens When You Run It? ⏳
+1. The graph is created with 6 vertices.
+2. Edges are added between the vertices to form connections.
+3. BFS starts from vertex `0` and traverses reachable vertices layer by layer.
+
+### Example Output: ✅
+If you run the code, you might see an output like:
+```
+Depth First Search starting from vertex 0:
+0 1 3 4
+```
+This output shows the order in which the vertices are visited during the BFS traversal.
+
+## Fun Fact: 🧐
+DFS is great for finding the shortest path in unweighted graphs, which is very useful for GPS Navigation systems.
+
+
+And that’s how BFS works in Java!
+
+### Created by
+David Bernal based on the job done by Nkeiruka Whenu