BFS in Graph

Posted: 7 Dec, 2020
Difficulty: Easy

PROBLEM STATEMENT

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You are given an undirected and disconnected graph G(V, E) having V vertices numbered from 0 to V-1 and E edges. Your task is to print its BFS traversal starting from the 0th vertex.

BFS or Breadth-First Traversal of a graph is an algorithm used to visit all of the nodes of a given graph. In this traversal algorithm, one node is selected, and then all of the adjacent nodes are visited one by one.

An undirected graph is a graph where all the edges are bidirectional, i.e., they point from source to destination and destination to source.

A graph is disconnected if at least two vertices of the graph are not connected by a path.

Note:

1. Here, you need to consider that you need to print the BFS path starting from vertex 0 only. 
2. V is the number of vertices present in graph G, and all vertices are numbered from 0 to V-1. 
3. E is the number of edges present in graph G.
4. Graph input is provided as the number of vertices and a list of edges.
5. Handle for Disconnected Graphs as well.

For Example: Consider graph:

example

Here, starting from 0, it is connected to 1 and 2 so, BFS traversal from here will be [0, 1, 2 ]. Now, 3 is also connected to 2. So, BFS traversal becomes [0, 1, 2, 3].

Note:

For each node, the correct order of printing the connected nodes will be sorted order, i.e., if {3,6,9,4} are connected to 1, then the correct order of their printing is {1,3,4,6,9}.

Input Format :

The first line of input contains two integers that denote the value of V and E.
Each of the following E lines contains space-separated two integers that denote an edge between vertex A and B.

Output Format :

For each test case, print the BFS Traversal, as described in the task.
Output for each test case will be printed in a separate line.

Note:

You do not need to print anything; it has already been taken care of. Just implement the given function.

Constraints :

0 <= V <= 10^4
0 <= E <= (V * (V - 1)) / 2
0 <= A <= V - 1
0 <= B <= V - 1

Where 'V' is the number of vertices, 'E' is the number of edges, 'A' and 'B' are the vertex numbers.
Time Limit: 1 second
Approach 1

Let us consider a function BFS that accepts a list of edges, EDGES, and the number of vertices VERTEX as a parameter and do: 

  1. Create ADJACENCYMATRIX from EDGES.
  2. Define a boolean array VISITED to store nodes that are already visited.
  3. Iterate over VISITED[i] for each 0<= i < VISITED.LENGTH, and check:
    1. If VISITED[i] is FALSE, call BFSHELPER function for ADJACENCYMATRIX, i and VISITED.

Now, the function BFSHELPER accepts as parameters, an adjacency matrix of edges ADJACENCYMATRIX, an integer SOURCE and boolean array VISITED and do:

  1. Define a queue, ADJNODE, to store nodes under consideration but not added to the result.
  2. Create an ArrayList RESULT.
  3. Mark VISITED[SOURCE] as TRUE.
  4. Add SOURCE to queue ADJNODE.
  5. Iterate over queue elements until queue ADJNODE is EMPTY:
    1. Remove front element from ADJNODE and store it to FRONT
    2. Append FRONT to RESULT.
    3. Iterate over ADJACENCYMATRIX[FRONT][i] for 0<= i < ADJACENCYMATRIX.LENGTH and check:
      1. If any edge exists between FRONT and i, and i is not VISITED, mark VISITED[i] as TRUE and add i to ADJNODE.
  6. Return RESULT.
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