Count the number of nodes at a given level in a tree using DFS

Given an integer l and a tree represented as an undirected graph rooted at vertex 0. The task is to print the number of nodes present at level l.

Examples:

Input: l = 2

Output: 4



We have already discussed the BFS approach, in this post we will solve it using DFS.

Approach: The idea is to traverse the graph in a DFS manner. Take two variables, count and curr_level. Whenever the curr_level = l increment the value of the count.

Below is the implementation of the above approach:

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Class to represent a graph
class Graph {
  
    // No. of vertices
    int V;
  
    // Pointer to an array containing
    // adjacency lists
    list<int>* adj;
  
    // A function used by NumOfNodes
    void DFS(vector<bool>& visited, int src, int& curr_level,
             int level, int& NumberOfNodes);
  
public:
    // Constructor
    Graph(int V);
  
    // Function to add an edge to graph
    void addEdge(int src, int des);
  
    // Returns the no. of nodes
    int NumOfNodes(int level);
};
  
Graph::Graph(int V)
{
    this->V = V;
    adj = new list<int>[V];
}
  
void Graph::addEdge(int src, int des)
{
    adj[src].push_back(des);
    adj[des].push_back(src);
}
  
// DFS function to keep track of
// number of nodes
void Graph::DFS(vector<bool>& visited, int src, int& curr_level,
                int level, int& NumberOfNodes)
{
    // Mark the current vertex as visited
    visited[src] = true;
  
    // If current level is equal
    // to the given level, increment
    // the no. of nodes
    if (level == curr_level) {
        NumberOfNodes++;
    }
    else if (level < curr_level)
        return;
    else {
        list<int>::iterator i;
  
        // Recur for the vertices
        // adjacent to the current vertex
        for (i = adj[src].begin(); i != adj[src].end(); i++) {
            if (!visited[*i]) {
                curr_level++;
                DFS(visited, *i, curr_level, level, NumberOfNodes);
            }
        }
    }
    curr_level--;
}
  
// Function to return the number of nodes
int Graph::NumOfNodes(int level)
{
    // To keep track of current level
    int curr_level = 0;
  
    // For keeping track of visited
    // nodes in DFS
    vector<bool> visited(V, false);
  
    // To store count of nodes at a
    // given level
    int NumberOfNodes = 0;
  
    DFS(visited, 0, curr_level, level, NumberOfNodes);
  
    return NumberOfNodes;
}
  
// Driver code
int main()
{
    int V = 8;
  
    Graph g(8);
    g.addEdge(0, 1);
    g.addEdge(0, 4);
    g.addEdge(0, 7);
    g.addEdge(4, 6);
    g.addEdge(4, 5);
    g.addEdge(4, 2);
    g.addEdge(7, 3);
  
    int level = 2;
  
    cout << g.NumOfNodes(level);
  
    return 0;
}

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Output:

4


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