# Challenge: Implement Breadth First Search

In this lesson, you have to implement the breadth first search algorithm. A solution is placed in the "solution" section to help you, but we suggest trying to solve it on your own first.

## We'll cover the following

## Problem statement

In this exercise, you have to implement the *breadth first search* traversal in Java. It is a level-by-level searching algorithm for the graph, so we are going to use our already-implemented *graph* class for this task (since we have already covered the implementation of graph).

Note:Your solution should work for both connected and unconnected graphs. For an unconnected graph, the order of output should depend upon indices in ascending order.

To solve this problem, all the previously implemented data structures will be available to us.

### Input

The input is a graph in the form of an adjacency list.

### Output

The output is a string containing the vertices of the graph listed in the correct order of traversal.

### Sample input

**Graph:**

Vertex |
Edges |
---|---|

0 | 1, 2 |

1 | 3, 4 |

2 | None |

3 | None |

4 | None |

In the

inputcolumn of test cases, this graph is represented as:`|V|=5, E:[(0,1)(0,2)(1,3)(1,4)]`

, where,`|V|`

represents the number of vertices and`E`

represents the edges.

### Sample output

`"01234"`

## Coding exercise

First, take a close look and design a step-by-step algorithm before jumping to the implementation. This problem is designed for your practice, so initially try to solve it on your own. If you get stuck, you can always refer to the solution provided in the solution section. Good Luck!

public class DoublyLinkedList<T> {//Node inner class for DLLpublic class Node {public T data;public Node nextNode;public Node prevNode;}public Node headNode;public Node tailNode;public int size;public DoublyLinkedList() {this.headNode = null;this.tailNode = null;}public boolean isEmpty() {if (headNode == null && tailNode == null)return true;return false;}public Node getHeadNode() {return headNode;}public Node getTailNode() {return tailNode;}public int getSize() {return size;}public void insertAtHead(T data) {Node newNode = new Node();newNode.data = data;newNode.nextNode = this.headNode; //Linking newNode to head's nextNodenewNode.prevNode = null;if (headNode != null)headNode.prevNode = newNode;elsetailNode = newNode;this.headNode = newNode;size++;}public void insertAtEnd(T data) {if(isEmpty()) {insertAtHead(data);return;}Node newNode = new Node();newNode.data = data;newNode.nextNode = null;newNode.prevNode = tailNode;tailNode.nextNode = newNode;tailNode = newNode;size++;}public void printList() {if (isEmpty()) {System.out.println("List is Empty!");return;}Node temp = headNode;System.out.print("List : null <- ");while (temp.nextNode != null) {System.out.print(temp.data.toString() + " <-> ");temp = temp.nextNode;}System.out.println(temp.data.toString() + " -> null");}public void printListReverse() {if (isEmpty()) {System.out.println("List is Empty!");}Node temp = tailNode;System.out.print("List : null <- ");while (temp.prevNode != null) {System.out.print(temp.data.toString() + " <-> ");temp = temp.prevNode;}System.out.println(temp.data.toString() + " -> null");}public void deleteAtHead() {if (isEmpty())return;headNode = headNode.nextNode;if (headNode == null)tailNode = null;elseheadNode.prevNode = null;size--;}public void deleteAtTail() {if (isEmpty())return;tailNode = tailNode.prevNode;if (tailNode == null)headNode = null;elsetailNode.nextNode = null;size--;}}