# 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: Output:
0 <- 2
1 <- 0 <- 2
2
3 <- 1 <- 0 <- 2
4 <- 5 <- 2
5 <- 2
6 <- 2
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 `// 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 > 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 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 > adjList = ``new` `ArrayList<>(); ` ` `  `        ``// Vertices 1 and 2 have an incoming edge ` `        ``// from vertex 0 ` `        ``List tmp = ``new` `ArrayList(Arrays.asList(``1``, ``2``)); ` `        ``adjList.add(tmp); ` ` `  `        ``// Vertex 3 has an incoming edge from vertex 1 ` `        ``tmp = ``new` `ArrayList(Arrays.asList(``3``)); ` `        ``adjList.add(tmp); ` ` `  `        ``// Vertices 0, 5 and 6 have an incoming ` `        ``// edge from vertex 2 ` `        ``tmp = ``new` `ArrayList(Arrays.asList(``0``, ``5``, ``6``)); ` `        ``adjList.add(tmp); ` ` `  `        ``// Vertices 1 and 4 have an incoming edge ` `        ``// from vertex 3 ` `        ``tmp = ``new` `ArrayList(Arrays.asList(``1``, ``4``)); ` `        ``adjList.add(tmp); ` ` `  `        ``// Vertices 2 and 3 have an incoming edge ` `        ``// from vertex 4 ` `        ``tmp = ``new` `ArrayList(Arrays.asList(``2``, ``3``)); ` `        ``adjList.add(tmp); ` ` `  `        ``// Vertices 4 and 6 have an incoming edge ` `        ``// from vertex 5 ` `        ``tmp = ``new` `ArrayList(Arrays.asList(``4``, ``6``)); ` `        ``adjList.add(tmp); ` ` `  `        ``// Vertex 5 has an incoming edge from vertex 6 ` `        ``tmp = ``new` `ArrayList(Arrays.asList(``5``)); ` `        ``adjList.add(tmp); ` ` `  `        ``int` `n = adjList.size(); ` ` `  `        ``int` `source = ``2``; ` `        ``bfs(adjList, source, n); ` `    ``} ` `} `

## Python3

 `# 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 `

Output:

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

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