Count the number of nodes at given level in a tree using BFS.
Last Updated :
28 Mar, 2023
Given a tree represented as an undirected graph. Count the number of nodes at a given level l. It may be assumed that vertex 0 is the root of the tree.
Examples:
Input : 7
0 1
0 2
1 3
1 4
1 5
2 6
2
Output : 4
Input : 6
0 1
0 2
1 3
2 4
2 5
2
Output : 3
BFS is a traversing algorithm that starts traversing from a selected node (source or starting node) and traverses the graph layer-wise thus exploring the neighbour nodes (nodes that are directly connected to the source node). Then, move towards the next-level neighbor nodes.
As the name BFS suggests, traverse the graph breadth wise as follows:
- First move horizontally and visit all the nodes of the current layer.
- Move to the next layer.
In this code, while visiting each node, the level of that node is set with an increment in the level of its parent node i.e., level[child] = level[parent] + 1. This is how the level of each node is determined. The root node lies at level zero in the tree.
Explanation :
0 Level 0
/ \
1 2 Level 1
/ |\ |
3 4 5 6 Level 2
Given a tree with 7 nodes and 6 edges in which node 0 lies at 0 level. Level of 1 can be updated as : level[1] = level[0] +1 as 0 is the parent node of 1. Similarly, the level of other nodes can be updated by adding 1 to the level of their parent.
level[2] = level[0] + 1, i.e level[2] = 0 + 1 = 1.
level[3] = level[1] + 1, i.e level[3] = 1 + 1 = 2.
level[4] = level[1] + 1, i.e level[4] = 1 + 1 = 2.
level[5] = level[1] + 1, i.e level[5] = 1 + 1 = 2.
level[6] = level[2] + 1, i.e level[6] = 1 + 1 = 2.
Then, count of number of nodes which are at level l(i.e, l=2) is 4 (node:- 3, 4, 5, 6)
Implementation:
C++
// C++ Program to print
// count of nodes
// at given level.
#include <iostream>
#include <list>
using namespace std;
// This class represents
// a directed graph
// using adjacency
// list representation
class Graph {
// No. of vertices
int V;
// Pointer to an
// array containing
// adjacency lists
list<int>* adj;
public:
// Constructor
Graph(int V);
// function to add
// an edge to graph
void addEdge(int v, int w);
// Returns count of nodes at
// level l from given source.
int BFS(int s, int l);
};
Graph::Graph(int V)
{
this->V = V;
adj = new list<int>[V];
}
void Graph::addEdge(int v, int w)
{
// Add w to v’s list.
adj[v].push_back(w);
// Add v to w's list.
adj[w].push_back(v);
}
int Graph::BFS(int s, int l)
{
// Mark all the vertices
// as not visited
bool* visited = new bool[V];
int level[V];
for (int i = 0; i < V; i++) {
visited[i] = false;
level[i] = 0;
}
// Create a queue for BFS
list<int> queue;
// Mark the current node as
// visited and enqueue it
visited[s] = true;
queue.push_back(s);
level[s] = 0;
while (!queue.empty()) {
// Dequeue a vertex from
// queue and print it
s = queue.front();
queue.pop_front();
// Get all adjacent vertices
// of the dequeued vertex s.
// If a adjacent has not been
// visited, then mark it
// visited and enqueue it
for (auto i = adj[s].begin();
i != adj[s].end(); ++i) {
if (!visited[*i]) {
// Setting the level
// of each node with
// an increment in the
// level of parent node
level[*i] = level[s] + 1;
visited[*i] = true;
queue.push_back(*i);
}
}
}
int count = 0;
for (int i = 0; i < V; i++)
if (level[i] == l)
count++;
return count;
}
// Driver program to test
// methods of graph class
int main()
{
// Create a graph given
// in the above diagram
Graph g(6);
g.addEdge(0, 1);
g.addEdge(0, 2);
g.addEdge(1, 3);
g.addEdge(2, 4);
g.addEdge(2, 5);
int level = 2;
cout << g.BFS(0, level);
return 0;
}
// Java Program to print
// count of nodes
// at given level.
import java.util.*;
// This class represents
// a directed graph
// using adjacency
// list representation
class Graph
{
// No. of vertices
int V;
Vector<Integer>[] adj;
// Constructor
@SuppressWarnings("unchecked")
Graph(int V)
{
adj = new Vector[V];
for (int i = 0; i < adj.length; i++)
{
adj[i] = new Vector<>();
}
this.V = V;
}
void addEdge(int v, int w)
{
// Add w to v’s list.
adj[v].add(w);
// Add v to w's list.
adj[w].add(v);
}
int BFS(int s, int l)
{
// Mark all the vertices
// as not visited
boolean[] visited = new boolean[V];
int[] level = new int[V];
for (int i = 0; i < V; i++)
{
visited[i] = false;
level[i] = 0;
}
// Create a queue for BFS
Queue<Integer> queue = new LinkedList<>();
// Mark the current node as
// visited and enqueue it
visited[s] = true;
queue.add(s);
level[s] = 0;
int count = 0;
while (!queue.isEmpty())
{
// Dequeue a vertex from
// queue and print it
s = queue.peek();
queue.poll();
Vector<Integer> list = adj[s];
// Get all adjacent vertices
// of the dequeued vertex s.
// If a adjacent has not been
// visited, then mark it
// visited and enqueue it
for (int i : list)
{
if (!visited[i])
{
visited[i] = true;
level[i] = level[s] + 1;
queue.add(i);
}
}
count = 0;
for (int i = 0; i < V; i++)
if (level[i] == l)
count++;
}
return count;
}
}
class GFG {
// Driver code
public static void main(String[] args)
{
// Create a graph given
// in the above diagram
Graph g = new Graph(6);
g.addEdge(0, 1);
g.addEdge(0, 2);
g.addEdge(1, 3);
g.addEdge(2, 4);
g.addEdge(2, 5);
int level = 2;
System.out.print(g.BFS(0, level));
}
}
// This code is contributed by Rajput-Ji
# Python3 program to print
# count of nodes at given level.
from collections import deque
adj = [[] for i in range(1001)]
def addEdge(v, w):
# Add w to v’s list.
adj[v].append(w)
# Add v to w's list.
adj[w].append(v)
def BFS(s, l):
V = 100
# Mark all the vertices
# as not visited
visited = [False] * V
level = [0] * V
for i in range(V):
visited[i] = False
level[i] = 0
# Create a queue for BFS
queue = deque()
# Mark the current node as
# visited and enqueue it
visited[s] = True
queue.append(s)
level[s] = 0
while (len(queue) > 0):
# Dequeue a vertex from
# queue and print
s = queue.popleft()
#queue.pop_front()
# Get all adjacent vertices
# of the dequeued vertex s.
# If a adjacent has not been
# visited, then mark it
# visited and enqueue it
for i in adj[s]:
if (not visited[i]):
# Setting the level
# of each node with
# an increment in the
# level of parent node
level[i] = level[s] + 1
visited[i] = True
queue.append(i)
count = 0
for i in range(V):
if (level[i] == l):
count += 1
return count
# Driver code
if __name__ == '__main__':
# Create a graph given
# in the above diagram
addEdge(0, 1)
addEdge(0, 2)
addEdge(1, 3)
addEdge(2, 4)
addEdge(2, 5)
level = 2
print(BFS(0, level))
# This code is contributed by mohit kumar 29
// C# program to print count of nodes
// at given level.
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
// This class represents
// a directed graph
// using adjacency
// list representation
class Graph{
// No. of vertices
private int _V;
LinkedList<int>[] _adj;
public Graph(int V)
{
_adj = new LinkedList<int>[V];
for(int i = 0; i < _adj.Length; i++)
{
_adj[i] = new LinkedList<int>();
}
_V = V;
}
public void AddEdge(int v, int w)
{
// Add w to v’s list.
_adj[v].AddLast(w);
}
public int BreadthFirstSearch(int s,int l)
{
// Mark all the vertices
// as not visited
bool[] visited = new bool[_V];
int[] level = new int[_V];
for(int i = 0; i < _V; i++)
{
visited[i] = false;
level[i] = 0;
}
// Create a queue for BFS
LinkedList<int> queue = new LinkedList<int>();
// Mark the current node as
// visited and enqueue it
visited[s] = true;
level[s] = 0;
queue.AddLast(s);
while(queue.Any())
{
// Dequeue a vertex from
// queue and print it
s = queue.First();
// Console.Write( s + " " );
queue.RemoveFirst();
LinkedList<int> list = _adj[s];
foreach(var val in list)
{
if (!visited[val])
{
visited[val] = true;
level[val] = level[s] + 1;
queue.AddLast(val);
}
}
}
int count = 0;
for(int i = 0; i < _V; i++)
if (level[i] == l)
count++;
return count;
}
}
// Driver code
class GFG{
static void Main(string[] args)
{
// Create a graph given
// in the above diagram
Graph g = new Graph(6);
g.AddEdge(0, 1);
g.AddEdge(0, 2);
g.AddEdge(1, 3);
g.AddEdge(2, 4);
g.AddEdge(2, 5);
int level = 2;
Console.WriteLine(g.BreadthFirstSearch(0, level));
}
}
// This code is contributed by anvudemy1
<script>
// JavaScript Program to print
// count of nodes
// at given level.
let V;
let adj=new Array(1001);
for(let i=0;i<adj.length;i++)
{
adj[i]=[];
}
function addEdge(v,w)
{
// Add w to v’s list.
adj[v].push(w);
// Add v to w's list.
adj[w].push(v);
}
function BFS(s,l)
{
V=100;
// Mark all the vertices
// as not visited
let visited = new Array(V);
let level = new Array(V);
for (let i = 0; i < V; i++)
{
visited[i] = false;
level[i] = 0;
}
// Create a queue for BFS
let queue = [];
// Mark the current node as
// visited and enqueue it
visited[s] = true;
queue.push(s);
level[s] = 0;
let count = 0;
while (queue.length!=0)
{
// Dequeue a vertex from
// queue and print it
s = queue[0];
queue.shift();
let list = adj[s];
// Get all adjacent vertices
// of the dequeued vertex s.
// If a adjacent has not been
// visited, then mark it
// visited and enqueue it
for (let i=0;i<list.length;i++)
{
if (!visited[list[i]])
{
visited[list[i]] = true;
level[list[i]] = level[s] + 1;
queue.push(list[i]);
}
}
count = 0;
for (let i = 0; i < V; i++)
if (level[i] == l)
count++;
}
return count;
}
// Driver code
// Create a graph given
// in the above diagram
addEdge(0, 1)
addEdge(0, 2)
addEdge(1, 3)
addEdge(2, 4)
addEdge(2, 5)
let level = 2;
document.write(BFS(0, level));
// This code is contributed by unknown2108
</script>
Time Complexity: O(V+E)
Auxiliary Space: O(V)
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