# Java Program to do a Breadth First Search/Traversal on a graph non-recursively

Problem Description

Given a graph in the form of an adjacency matrix and a source vertex, write a program to perform a breadth-first search of the graph. In breadth-first search traversal, nodes are traversed level by level.Problem Solution

The idea is to store the source vertex in the queue. Now, iterate through the queue until it is empty. For every vertex retrieved from the queue, check which of its neighbours are still not processed. Add those neighbours to the queue.Program/Source Code

Here is the source code of the Java Program to do a Breadth First Search/Traversal on a graph non-recursively. The program is successfully compiled and tested using IDE IntelliJ Idea in Windows 7. The program output is also shown below.

//Java Program to do a Breadth First Search/Traversal on a graph non-recursively

import java.io.IOException;
import java.util.Queue;

// Function to perform breadth first search
static void breadthFirstSearch(int[][] matrix, int source){
boolean[] visited = new boolean[matrix.length];
visited[source-1] = true;
while(!queue.isEmpty()){
System.out.println(queue.peek());
int x = queue.poll();
int i;
for(i=0; i<matrix.length;i++){
if(matrix[x-1][i] == 1 && visited[i] == false){
visited[i] = true;
}
}
}
}
// Function to read user input
public static void main(String[] args) {
int vertices;
System.out.println("Enter the number of vertices in the graph");
try{
}catch(IOException e){
System.out.println("An error occurred");
return;
}
int[][] matrix = new int[vertices][vertices];
int i,j;
for(i=0; i<vertices; i++){
for(j=0; j<vertices; j++){
try{
}catch (IOException e){
System.out.println("An error occurred");
}
}
}
int source;
System.out.println("Enter the source vertex");
try{
}catch(IOException e){
System.out.println("An error occurred");
return;
}
}
}


Program Explanation

1. In function breadthFirstSearch(), a boolean array is created and visited value of the source is set to true.
2. Then a queue is created and source vertex is added to it.
3. The loop while(!queue.isEmpty()) traverses until the queue is empty.
4. The nested loop for(i=0; i&ltmatrix.length; i++) traverses through all the neighbours of the currently polled vertex from the queue.
5. The condition if(matrix[x-1][i] == 1 && visited[i] == false) looks for all the neighbours of the currently polled vertex and adds the non-visited vertices to the queue.

Time Complexity: O(n2) where n is the number of elements in the array.

Runtime Test Cases

Case 1 (Simple Test Case):

Enter the number of vertices in the graph
4
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
Enter the source vertex
3
3
1
2

Case 2 (Simple Test Case - another example):

Enter the number of vertices in the graph
3
0
0
0
1
0
1
1
1
1
Enter the source vertex
2