Find the level of given node in an Undirected Graph

Given an undirected graph with V vertices and E edges and a node X, The task is to find the level of node X in the undirected graph. If X does not exist in the graph then return -1.

Note: Traverse the graph starting from vertex 0.

Examples:

Input: V = 5, Edges = {{0, 1}, {0, 2}, {1, 3}, {2, 4}}, X = 3
Output: 2
Explanation: Starting from vertex 0, at level 0 we have node 0, at level 1 we have nodes 1 and 2 and at level 2 we have nodes 3 and 4. So the answer is 2

The example graph

Input: V = 5, Edges = {{0, 1}, {0, 2}, {1, 3}, {2, 4}}, X = 5
Output: -1
Explanation: Vertex 5 is not present in the given graph so answer is -1

An example graph

Approach: The problem can be solved based on the following idea:

The given problem can be solved with the help of level order traversal. We can perform a BFS traversal in order to find the level of the given vertex

Follow the steps mentioned below to implement the idea:

• Find the maximum vertex of the graph and store it in a variable (say maxVertex).
• create adjacency list adj[] of size maxVertex+1.
• Check if X is present or not, if not then return -1.
• To traverse the graph, create a queue for level order traversal.
• Push vertex 0 in a queue, and set a counter level to 0.
• Create a visited array of size maxVertex+1 to mark the visited nodes. 
• Start BFS traversal if the value of X is found in front of the queue then return the level.
  • Keep popping nodes from the queue till it becomes empty and increment the counter level
  • In one iteration, push all the unvisited nodes in the queue connected with the current node
  • Increment the level variable to jump to the next level.

Below is the implementation of the above approach.

C++

// C++ code to implement the approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the level of the given node
int findLevel(int N, vector<vector<int> >& edges, int X)
{

    // Variable to store maximum vertex of graph
    int maxVertex = 0;
    for (auto it : edges) {
        maxVertex = max({ maxVertex, it[0], it[1] });
    }

    // Creating adjacency list
    vector<int> adj[maxVertex + 1];
    for (int i = 0; i < edges.size(); i++) {
        adj[edges[i][0]].push_back(edges[i][1]);
        adj[edges[i][1]].push_back(edges[i][0]);
    }

    // If X is not present then return -1
    if (X > maxVertex || adj[X].size() == 0)
        return -1;

    // Initialize a Queue for BFS traversal
    queue<int> q;
    q.push(0);
    int level = 0;

    // Visited array to mark the already visited nodes
    vector<int> visited(maxVertex + 1, 0);
    visited[0] = 1;

    // BFS traversal
    while (!q.empty()) {
        int sz = q.size();
        while (sz--) {
            auto currentNode = q.front();
            q.pop();
            if (currentNode == X) {
                return level;
            }

            for (auto it : adj[currentNode]) {
                if (!visited[it]) {
                    q.push(it);
                    visited[it] = 1;
                }
            }
        }
        level++;
    }

    return -1;
}

// Driver Code
int main()
{
    int V = 5;
    vector<vector<int> > edges
        = { { 0, 1 }, { 0, 2 }, { 1, 3 }, { 2, 4 } };
    int X = 3;

    // Function call
    int level = findLevel(V, edges, X);
    cout << level << endl;

    return 0;
}

Java

// Java code to implement the approach

import java.util.*;
class GFG {

    // Driver code
    public static void main(String[] args)
    {
        int V = 5;
        int[][] edges
            = { { 0, 1 }, { 0, 2 }, { 1, 3 }, { 2, 4 } };
        int X = 3;

        // Function call
        int level = findLevel(V, edges, X);
        System.out.println(level);
    }

    // Function to find the level of the node
    public static int findLevel(int N, int[][] edges, int X)
    {
        int maxVertex = 0;
        for (int[] it : edges) {
            maxVertex = Math.max(maxVertex,
                                 Math.max(it[0], it[1]));
        }

        // Creating adjacency list
        ArrayList<Integer>[] adj
            = new ArrayList[maxVertex + 1];

        for (int i = 0; i <= maxVertex; i++)
            adj[i] = new ArrayList<>();

        for (int i = 0; i < edges.length; i++) {
            adj[edges[i][0]].add(edges[i][1]);
            adj[edges[i][1]].add(edges[i][0]);
        }

        // X is not present
        if (X > maxVertex || adj[X].size() == 0)
            return -1;

        // Queue for BFS traversal
        LinkedList<Integer> q = new LinkedList<>();
        q.offer(0);
        int level = 0;

        boolean[] visited = new boolean[maxVertex + 1];

        // BFS traversal
        while (!q.isEmpty()) {
            int sz = q.size();
            while (sz-- > 0) {
                int currentNode = q.poll();

                if (currentNode == X)
                    return level;

                for (int it : adj[currentNode]) {
                    if (!visited[it]) {
                        q.offer(it);
                        visited[it] = true;
                    }
                }
            }
            level++;
        }

        return -1;
    }
}

Python3

# Python code to implement the approach

# Function to find the level of the given node
def findLevel(N,edges,X):
    # Variable to store maximum vertex of graph
    maxVertex=0
    for it in edges:
        maxVertex=max(maxVertex,max(it[0],it[1]))

    # Creating adjacency list
    adj=[[] for j in range(maxVertex+1)]
    for i in range(len(edges)):
        adj[edges[i][0]].append(edges[i][1])
        adj[edges[i][1]].append(edges[i][0])

    # If X is not present then return -1
    if(X>maxVertex or len(adj[X])==0):
        return -1

    # Initialize a Queue for BFS traversal
    q=[]
    q.append(0)
    level=0

    # Visited array to mark the already visited nodes
    visited=[0]*(maxVertex+1)
    visited[0]=1

    # BFS traversal
    while(len(q)>0):
        sz=len(q)
        while(sz>0):
            currentNode=q[0]
            q.pop(0)
            if(currentNode==X):
                return level
            for it in adj[currentNode]:
                if(not visited[it]):
                    q.append(it)
                    visited[it]=1
            sz=sz-1
        level=level+1

    return -1

# Driver Code
V=5
edges=[[0,1],[0,2],[1,3],[2,4]]
X=3

#Function call
level=findLevel(V,edges,X)
print(level)

# This code is contributed by Pushpesh Raj.

C#

// C# code to implement the approach
using System;
using System.Collections.Generic;
using System.Collections;
class GFG {

    // Function to find the level of the given node
    static int findLevel(int N, int[, ] edges, int X)
    {

        // Variable to store maximum vertex of graph
        int maxVertex = 0;
        for (int i = 0; i < edges.GetLength(0); i++) {
            maxVertex = Math.Max(
                maxVertex,
                Math.Max(edges[i, 0], edges[i, 1]));
        }
        // Creating adjacency list
        List<int>[] adj = new List<int>[ maxVertex + 1 ];
        for (int i = 0; i <= maxVertex; i++)
            adj[i] = new List<int>();
        for (int i = 0; i < edges.GetLength(0); i++) {
            adj[edges[i, 0]].Add(edges[i, 1]);
            adj[edges[i, 1]].Add(edges[i, 0]);
        }

        // If X is not present then return -1
        if (X > maxVertex || adj[X].Count == 0)
            return -1;

        // Initialize a Queue for BFS traversal
        Queue q = new Queue();
        q.Enqueue(0);
        int level = 0;
        // Visited array to mark the already visited nodes
        int[] visited = new int[maxVertex + 1];
        for (int i = 0; i <= maxVertex; i++)
            visited[i] = 0;
        visited[0] = 1;
        // BFS traversal
        while (q.Count != 0) {
            int sz = q.Count;
            while (sz-- != 0) {
                int currentNode = (int)q.Dequeue();
                if (currentNode == X) {
                    return level;
                }

                for (int i = 0; i < adj[currentNode].Count;
                     i++) {
                    int it = adj[currentNode][i];
                    if (visited[it] == 0) {
                        q.Enqueue(it);
                        visited[it] = 1;
                    }
                }
            }
            level++;
        }
        return -1;
    }

    static void Main()
    {
        int V = 5;
        int[, ] edges = new int[, ] {
            { 0, 1 }, { 0, 2 }, { 1, 3 }, { 2, 4 }
        };
        int X = 3;

        // Function call
        int level = findLevel(V, edges, X);
        Console.Write(level);
    }
}

// This code is contributed by garg28harsh.

Javascript

// JS code to implement the approach

// Function to find the level of the given node
function findLevel( N, edges, X)
{
    // Variable to store maximum vertex of graph
    let maxVertex = 0;
    for (let i=0;i<edges.length;i++){
        let it = edges[i];
        let a = Math.max(it[0],it[1]);
        maxVertex = Math.max(maxVertex,a);
    }

    // Creating adjacency list
    let adj = [];
    for(let i=0;i<maxVertex+1;i++){
        adj.push([]);
    }
    for (let i = 0; i < edges.length; i++) {
        adj[edges[i][0]].push(edges[i][1]);
        adj[edges[i][1]].push(edges[i][0]);
    }

    // If X is not present then return -1
    if (X > maxVertex || adj[X].length == 0)
        return -1;

    // Initialize a Queue for BFS traversal
    let q = [];
    q.push(0);
    let level = 0;

    // Visited array to mark the already visited nodes
    let visited = [];
    for(let i=0;i<maxVertex+1;i++)
    {
        visited.push(0);
    }
    visited[0] = 1;

    // BFS traversal

    while (q.length > 0) {
        let sz = q.length;
        while (sz--) {
            let currentNode = q[0];
            q.shift();
            if (currentNode == X) {
                return level;
            }

            for(let k =0;k<adj[currentNode].length;k++){
                let it = adj[currentNode][k];
                if (visited[it]==0) {
                    q.push(it);
                    visited[it] = 1;
                }
            }
        }
        level++;
    }

    return -1;
}

// Driver Code
let V = 5;
let edges
    = [ [ 0, 1 ], [ 0, 2 ], [ 1, 3 ], [ 2, 4 ] ];
let X = 3;

// Function call
let level = findLevel(V, edges, X);
console.log(level);

// This code is contributed by ksam24000

Output

2

Time Complexity: O(V + E) For traversing all of the nodes.
Auxiliary Space: O(V) to store all the nodes in the queue.