BFS-BREADTH FIRST SEARCH CODE

JAVA PYTHON GO KOTLIN C# RUBY C++ Java Script

Example :

import java.util.Iterator;
import java.util.LinkedList;
import java.util.Queue;

public class BFS {

    static LinkedList<String> vertices;
    static LinkedList<LinkedList<String>>  adjacencyList;
    static boolean visited[];
    static int level[];

    void insertVertex(String vertex) {

        vertices.add(vertex);
    }

    void constructAdjacencyList(String vtx, String adjcVertex) {

        int vtxIndex = vertices.indexOf(vtx);

        adjacencyList.add(new LinkedList<String>());
        adjacencyList.get(vtxIndex).add(adjcVertex);
    }

    void breadthFirstSearch(String source) {

        Queue<Integer> queue = new LinkedList<Integer>();

        int sourceIndex = vertices.indexOf(source);

        visited[sourceIndex] = true;
        queue.add(sourceIndex);

        while (queue.size() != 0) {

            sourceIndex = queue.poll();

            for (Iterator<String> iter = adjacencyList.get(sourceIndex).iterator(); iter.hasNext(); ) {

                String str = iter.next();

                int i = vertices.indexOf(str);

                if (visited[i] == false) {

                    visited[i] = true;
                    level[i] = level[sourceIndex] + 1;

                    queue.add(i);
                }
            }
            System.out.print(vertices.get(sourceIndex)+" of level "+level[sourceIndex]+" --> ");
        }
        System.out.print("\b\b\b\b");
    }

    public static void main(String[ ] args) {

        int V = 5;

        BFS bfs = new BFS();

        visited = new boolean[V];

        level = new int[V];

        adjacencyList = new LinkedList<LinkedList<String>>();

        vertices = new LinkedList<>();

        // Insert Vertices

        bfs.insertVertex("a");
        bfs.insertVertex("b");
        bfs.insertVertex("c");
        bfs.insertVertex("d");
        bfs.insertVertex("e");
        
        // Construct Adjacency List

        bfs.constructAdjacencyList("a", "b");
        bfs.constructAdjacencyList("a", "c");
        bfs.constructAdjacencyList("a", "d");

        bfs.constructAdjacencyList("b", "a");
        bfs.constructAdjacencyList("b" ,"e");

        bfs.constructAdjacencyList("c", "a");
        bfs.constructAdjacencyList("c", "d");
        bfs.constructAdjacencyList("c", "e");

        bfs.constructAdjacencyList("d", "a");
        bfs.constructAdjacencyList("d" ,"c");
        bfs.constructAdjacencyList("d", "e");

        bfs.constructAdjacencyList("e", "b");
        bfs.constructAdjacencyList("e", "c");
        bfs.constructAdjacencyList("e", "d");

        bfs.breadthFirstSearch("c");

    }
}

Output :

c of level 0 --> a of level 1 --> d of level 1 --> e of level 1 --> b of level 2

Code Explanation for BFS - Breadth First Search

Let's list out, what all do we need to support Breadth First Search Data Structure.

We need a Linked List to store the vertices.
We need a doubly Linked List to store the adjacency linked list.
We need a Queue and an array to store its Levels.
We need a boolean array to store the Vertices that are already visited.

Now, let us see the above code.

We have a Linked List to store the Vertices.

static LinkedList<String> vertices;

We also have a doubly Linked List to store the Adjacency List.

static LinkedList<LinkedList<String>>  adjacencyList;

Similarly, we have a Queue defined inside the method 'breadthFirstSearch(...)'.

Queue<Integer> queue = new LinkedList<Integer>();

And, we have an array to store the Levels.

static int level[];

And, there is a boolean array to store the Vertices that are visited.

static boolean visited[];

Note :The variables are marked as static, so that they could be accessed from main(...) method.

So, the first thing we will do is, insert the Vertices to the 'LinkedList<String> vertices' Linked List.

vertices = new LinkedList<>();
	
bfs.insertVertex("a");
bfs.insertVertex("b");
bfs.insertVertex("c");
bfs.insertVertex("d");
bfs.insertVertex("e");

Explanation of 'void insertVertex(String vertex)' method

void insertVertex(String vertex) {

    vertices.add(vertex);
}

'void insertVertex(String vertex)' is quite simple.

There is just one statement in it.

vertices.add(vertex);

It accepts 'String vertex' as a parameter and adds it to the Linked List, 'vertices'.

The next thing we will do is, create an Adjacency List to track the Adjacent Vertices.

Let us take the example of vertex 'a', to explain the creation of Adjacency List.

As we have seen, 'a' has three adjacent vertices(i.e. b, c and d). And we have used the constructAdjacencyList(...) method to construct the Adjacency Matrix.

bfs.constructAdjacencyList("a", "b");
bfs.constructAdjacencyList("a", "c");
bfs.constructAdjacencyList("a", "d");

Note :Just remember, creating an Adjacency List above is same as creating an Edge. As the Adjacency List is actually a group of Edges.

Explanation of 'void constructAdjacencyList(String vtx, String adjcVertex)' method

void constructAdjacencyList(String vtx, String adjcVertex) {

    int vtxIndex = vertices.indexOf(vtx);

    adjacencyList.add(new LinkedList<String>());
    adjacencyList.get(vtxIndex).add(adjcVertex);
}

Although, the above method is explained in 'Adjacency List Code' tutorial. I will give a brief explanation in this tutorial.

When a method call is made,

The variable 'vtx' is assigned with value "a" and 'adjcVertex' is assigned with "b".

Now, the first line,

int vtxIndex = vertices.indexOf(vtx);

Calculates the index/position of Vertex 'a'. And as we can see the index 'a' is 0.

Now, in the next line,

adjacencyList.add(new LinkedList<String>());

We are initialising the first row of the 2D Linked List, 'adjacencyList'.

But with what?

We are initialising it with a Linked List 'new LinkedList<String>()',

adjacencyList.add(new LinkedList<String>());

So that the first row can hold the Adjacency List for vertex 'a'.

Similarly, the second row should hold the Adjacency List for vertex 'b' and so on.

And in this iteration, our target is to find out the first row(To create an Adjacency List for vertex 'a') and insert vertex 'b' to it.

And the below code does that.

adjacencyList.get(vtxIndex).add(adjcVertex);

We get the index of vertex 'a'

vtxIndex = vertices.indexOf(vtx);

As we know 'vtx' is 'a'.

Then add 'adjcVertex'(That contains vertex 'b') to the 0th index of 'adjacencyList'.

adjacencyList.get(0).add("b");

And following it we form the Adjacency List.

Then we come across the most important method 'void breadthFirstSearch(String source)' that performs the Breadth First Search (BFS).

Explanation of 'void breadthFirstSearch(String source)' method

void breadthFirstSearch(String source) {

    Queue<Integer> queue = new LinkedList<Integer>();

    int sourceIndex = vertices.indexOf(source);

    visited[sourceIndex] = true;
    queue.add(sourceIndex);

    while (queue.size() != 0) {

        sourceIndex = queue.poll();

        for (Iterator<String> iter = adjacencyList.get(sourceIndex).iterator(); iter.hasNext(); ) {

            String str = iter.next();

            int i = vertices.indexOf(str);

            if (visited[i] == false) {

                visited[i] = true;
                level[i] = level[sourceIndex] + 1;

                queue.add(i);
            }
        }
        System.out.print(vertices.get(sourceIndex)+" of level "+level[sourceIndex]+" --> ");
    }
	 	System.out.print("\b\b\b\b");
}

So, we are calling the method

bfs.breadthFirstSearch("c");

Passing the vertex 'c' as source.

Below is the graph on which we had to perform a Breadth First Search (BFS).

To perform Breadth First Search (BFS), all we need is a Linked List to keep track of Vertices. Which we have in place.

And, we need a 2D Adjacency List to keep a track of Adjacent Vertices. And we also have that in place.

We also need a boolean array to keep a track of which all vertices are visited. Which we also have in place. All the values default to false.

Lastly, we need the integer array to store the Levels, that is initialised with '0'.

Now, since we have everything in place. Let us understand the 'void breadthFirstSearch(...)' method.

So, if we see the first line of the above method,

Queue<Integer> queue = new LinkedList<Integer>();

We have declared the Queue to maintain the order of Breadth First Search (BFS).

Next, we will try to find the index of the source vertex,

int sourceIndex = vertices.indexOf(source);

In this case our source vertex is 'c'. i.e. We will start traversing the graph from 'c'. And the index of vetex 'c' is 2.

So, the next thing we will do is mark vertex 'c' as visited. i.e. We will mark the position of Vertex 'c' to 'true' in the Visited Array.

visited[sourceIndex] = true;

And add the vertex 'c' to the Queue.

queue.add(sourceIndex);

Next, we come to the 'while()' loop, that will continue until the Queue is not empty.

while (queue.size() != 0) {

    sourceIndex = queue.poll();

    for (Iterator<String> iter = adjacencyList.get(sourceIndex).iterator(); iter.hasNext(); ) {

        String str = iter.next();

        int i = vertices.indexOf(str);

        if (visited[i] == false) {

            visited[i] = true;
            level[i] = level[sourceIndex] + 1;

            queue.add(i);
        }
    }
    System.out.print(vertices.get(sourceIndex)+" of level "+level[sourceIndex]+" --> ");
}

Inside the 'while()' loop, we write the below statement to get the vertex 'c' out of the Queue and get its index in 'sourceIndex'.

sourceIndex = queue.poll();

The next task we do is, try finding the Adjacent Vertices of vertex 'c'.

As we know the Adjacent Vertices of vertex 'c' are,

To find the Adjacent Vertices of 'c', we have used the below 'for' loop,

for (Iterator<String> iter = adjacencyList.get(sourceIndex).iterator(); iter.hasNext(); )

And the 'for' loop itself needs a little explanation.(HIDE THE BELOW POINTS UNDER DROPDOWN)

The first statement of the 'for' loop (i.e. The initialisation section of the loop),
```
Iterator<String> iter = adjacencyList.get(sourceIndex).iterator()
```
is where we get the Adjacent Vertices of vertex 'c' in the 'Iterator<String> iter'.

Thinking How?

Well! The 'adjacencyList' is a 2D Linked List that stores the adjacent vertices. And the trick is played in,
```
adjacencyList.get(sourceIndex).iterator()
```
As we have seen, the sourceIndex is 2 (Because the index of vertex 'c' is 2).

And the 'iter' variable of 'Iterator<String> iter' gets the adjacency list of vertex 'c' in it.
The next statement,
```
iter.hasNext()
```
tells the 'for' loop to continue until there are elements in the list.
And! Well! There is no increment section. We have left it blank

Moral of the story

'iter' variable of 'Iterator<String> iter', stores the Adjacency List of vertex 'c' in it.So, 'iter' has the elements 'a', 'd' and 'e' in it.

Inside the 'for' loop, firstly we collect the first element(i.e. 'a') of the Adjacency List of vertex 'c'.

String str = iter.next();

As we know the variable 'str' contains 'a'. Now, it's time to check the index of 'a'.

Which we have done in the next line.

int i = vertices.indexOf(str);

And found that the index of 'a' is 0.

Then in the next few lines, we check, if we have visited vertex 'a' or not. So we check in the visited[] array.

And find that visited[0] is set to false. So, we get into the below 'if' condition.

if (visited[i] == false) {

    visited[i] = true;
    level[i] = level[sourceIndex] + 1;

    queue.add(i);
}

Firstly, we mark visited[0] to true. Then increase the level[] array by 1.

And finally add the vertex 'a' to the Queue.

We keep on checking the adjacency lists of the individual vertices and continue the same process until the Queue is empty.

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