Finding the path from one vertex to rest using BFS

Given an adjacency list representation of a directed graph, the task is to find the path from source to every other node in the graph using BFS.

Examples:

Input:
Example
Output:
0 <- 2
1 <- 0 <- 2
2
3 <- 1 <- 0 <- 2
4 <- 5 <- 2
5 <- 2
6 <- 2

Approach: In the images shown below:



  • que[] array stores the vertices reached and we will enqueue a vertex only if it has not been visited and dequeue it once all its child node have been considered.
  • In order to distinguish whether the node has been visited or not we will put 1 in visited[] array at the respective index to signify it has been visited and if at given index 0 is present it will signify that it has not been visited.
  • Parent array is to store the parent node of each vertex. For ex. In case of 0 connected to 2, 2 will be the parent node of 0 and we will put 2 at the index 0 in the parent array.










Below is the implementation of the above approach:

Java

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// Java implementation of the approach
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
  
class GFG {
  
    // Function to print the path from
    // source (s) to destination (d)
    static void print(int parent[], int s, int d)
    {
        // The while loop will stop only when the
        // destination and the source node become equal
        while (s != d) {
  
            // Print the destination and store the parent
            // of the node in the destination since parent
            // stores the node through which
            // the current node has been reached
            System.out.print(d + " <- ");
            d = parent[d];
        }
  
        System.out.println(d);
    }
  
    // Finding Path using BFS ALgorithm
    static void bfs(List<List<Integer> > adjList, int source, int n)
    {
        int parent[] = new int[n];
        int que[] = new int[n];
        Arrays.fill(parent, 0);
        Arrays.fill(que, 0);
  
        int front = -1, rear = -1;
        int visited[] = new int[n];
        Arrays.fill(visited, 0);
        visited = 1;
        parent = source;
  
        // To add any non visited node we will increment the rear
        // and add that vertex to the end of the array (enqueuing)
        que[++rear] = source;
  
        int k;
  
        // The loop will continue till the rear and front are equal
        while (front != rear) {
  
            // Here Dequeuing is nothing but to increment the front int
            k = que[++front];
            List<Integer> list = adjList.get(k);
            for (int i = 0; i < list.size(); i++) {
                int j = list.get(i);
                if (visited[j] == 0) {
                    que[++rear] = j;
                    visited[j] = 1;
                    parent[j] = k;
                }
            }
        }
  
        // Print the path from source to every other node
        for (k = 0; k < n; k++)
            print(parent, source, k);
    }
  
    // Driver code
    public static void main(String args[])
    {
  
        // Adjacency list representation of the graph
        List<List<Integer> > adjList = new ArrayList<>();
  
        // Vertices 1 and 2 have an incoming edge
        // from vertex 0
        List<Integer> tmp = new ArrayList<Integer>(Arrays.asList(1, 2));
        adjList.add(tmp);
  
        // Vertex 3 has an incoming edge from vertex 1
        tmp = new ArrayList<Integer>(Arrays.asList(3));
        adjList.add(tmp);
  
        // Vertices 0, 5 and 6 have an incoming
        // edge from vertex 2
        tmp = new ArrayList<Integer>(Arrays.asList(0, 5, 6));
        adjList.add(tmp);
  
        // Vertices 1 and 4 have an incoming edge
        // from vertex 3
        tmp = new ArrayList<Integer>(Arrays.asList(1, 4));
        adjList.add(tmp);
  
        // Vertices 2 and 3 have an incoming edge
        // from vertex 4
        tmp = new ArrayList<Integer>(Arrays.asList(2, 3));
        adjList.add(tmp);
  
        // Vertices 4 and 6 have an incoming edge
        // from vertex 5
        tmp = new ArrayList<Integer>(Arrays.asList(4, 6));
        adjList.add(tmp);
  
        // Vertex 5 has an incoming edge from vertex 6
        tmp = new ArrayList<Integer>(Arrays.asList(5));
        adjList.add(tmp);
  
        int n = adjList.size();
  
        int source = 2;
        bfs(adjList, source, n);
    }
}

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Python3














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# Python3 implementation of the approach  


  


# Function to print the path from  


# src (s) to destination (d)  


def printfunc(parent, s, d):  


      


    # The while loop will stop only when  


    # the destination and the src node  


    # become equal  


    while s != d:  


  


        # Print the destination and store  


        # the parent of the node in the  


        # destination since parent stores 


        # the node through which the current 


        # node has been reached  


        print(str(d) + " <-", end = " ")  


        d = parent[d]  


          


    print(d)  


  


# Finding Path using BFS ALgorithm  


def bfs(adjList, src, n):  


      


    parent = [0] * (n)  


    que = [0] * (n)  


      


    front, rear = -1, -1


    visited = [0] * (n)  


    visited[src] = 1


    parent[src] = src 


  


    # To add any non visited node we will  


    # increment the rear and add that vertex  


    # to the end of the array (enqueuing)  


    rear += 1


    que[rear] = src  


  


    # The loop will continue till the rear  


    # and front are equal  


    while front != rear:  


  


        # Here Dequeuing is nothing but to 


        # increment the front int  


        front += 1


        k = que[front]  


        List = adjList[k]  


        for i in range(0, len(List)):  


            j = List[i] 


              


            if visited[j] == 0: 


                rear += 1


                que[rear] = j  


                visited[j] = 1


                parent[j] = k  


                  


    # Print the path from src to every  


    # other node  


    for k in range(0, n):  


        printfunc(parent, src, k)  


      


# Driver code  


if __name__ == "__main__":  


  


    # Adjacency list representation 


    # of the graph  


    adjList = []  


  


    # Vertices 1 and 2 have an incoming edge  


    # from vertex 0  


    adjList.append([1, 2])  


  


    # Vertex 3 has an incoming edge  


    # from vertex 1  


    adjList.append([3])  


  


    # Vertices 0, 5 and 6 have an incoming  


    # edge from vertex 2  


    adjList.append([0, 5, 6])  


  


    # Vertices 1 and 4 have an incoming edge  


    # from vertex 3  


    adjList.append([1, 4])  


  


    # Vertices 2 and 3 have an incoming edge  


    # from vertex 4  


    adjList.append([2, 3])  


  


    # Vertices 4 and 6 have an incoming edge  


    # from vertex 5  


    adjList.append([4, 6])  


  


    # Vertex 5 has an incoming edge  


    # from vertex 6  


    adjList.append([5])  


  


    n = len(adjList)  


  


    src = 2


    bfs(adjList, src, n)  


      


# This code is contributed by Rituraj Jain 



















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Output:


0 <- 2
1 <- 0 <- 2
2
3 <- 1 <- 0 <- 2
4 <- 5 <- 2
5 <- 2
6 <- 2






          
          
          

          

    

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