Get Path using BFS

Posted: 22 Jul, 2021
Difficulty: Easy

PROBLEM STATEMENT

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You are given an undirected graph G(V, E), where ‘V’ is the number of vertices and ‘E’ is the number of edges present in the graph and two integers ‘v1’ and ‘v2’ denoting vertices of the graph, find and print the path from ‘v1’ to ‘v2’ (if exists) in reverse order. Print an empty list if there is no path between ‘v1’ and ‘v2’.

Find the path using BFS and print the first path that you encountered.

Note:
Vertices are numbered through 0 to V - 1.
Input Format :
The first line contains a single integer ‘T’ denoting the number of test cases. Then each testcase follow.

The first line of each test case contains two integers ‘V’ and ‘E’ denoting the number of vertices and edges in the graph.

The next ‘E’ lines of the test case contain two space-separated integers ‘a’ and ‘b’ denoting that there exists an edge between ‘a’ and ‘b’.

The last line of the test case contains two space-separated integers ‘v1’ and ‘v2’ denoting the starting vertex and ending vertex.
Output Format :
For each test case, print the path from ‘v1’ to ‘v2’ in reverse order.

Output for each test case will be printed in a separate line.
Note :
You are not required to print anything; it has already been taken care of. Just implement the function and return a list of paths.

If there is no path between the vertices return an empty list.If the path is valid then it will print true else it will print false.
Constraints :
1 <= T <= 10
1 <= V <= 1000
1 <= E <= (V * (V - 1)) / 2
0 <= v1, v2 <= V-1


Time Limit: 1sec
Approach 1

In this approach, iterate through the whole graph using BFS and whenever you encounter a new node, update the parent of the new node by the current node.

The steps are as follows :
 

  1. Initialize a list par with -1 to store the parent of nodes.
  2. Create a graph using the given nodes and a queue for storing the nodes to iterate through breadth-first search.
  3. Push v1 to the queue and start Breadth-first search till the queue is not empty.
  4. Iterate through all the connected nodes from the current node.
  5. Update the parent of new nodes.
  6. Push the current element in the queue to iterate all the nodes connected to this node.
  7. After the completion of BFS, push the parent of the current node in a list answer and go to the index of the par to find the parent of parent till we get -1.
  8. If the final node in the answer list is not v1 return an empty list.
  9. Return answer.
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