Count number of trees in a forest

Given n nodes of a forest (collection of trees), find the number of trees in the forest.

Examples :

Input :  edges[] = {0, 1}, {0, 2}, {3, 4}
Output : 2
Explanation : There are 2 trees
                   0       3
                  / \       \
                 1   2       4

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

Approach :
1. Apply DFS on every node.
2. Increment count by one if every connected node is visited from one source.
3. Again perform DFS traversal if some nodes yet not visited.
4. Count will give the number of trees in forest.

C++

// CPP program to count number of trees in 
// a forest. 
#include<bits/stdc++.h> 
using namespace std; 
  
// A utility function to add an edge in an 
// undirected graph. 
void addEdge(vector<int> adj[], int u, int v) 
{ 
    adj[u].push_back(v); 
    adj[v].push_back(u); 
} 
  
// A utility function to do DFS of graph 
// recursively from a given vertex u. 
void DFSUtil(int u, vector<int> adj[], 
                    vector<bool> &visited) 
{ 
    visited[u] = true; 
    for (int i=0; i<adj[u].size(); i++) 
        if (visited[adj[u][i]] == false) 
            DFSUtil(adj[u][i], adj, visited); 
} 
  
// Returns count of tree is the forest 
// given as adjacency list. 
int countTrees(vector<int> adj[], int V) 
{ 
    vector<bool> visited(V, false); 
    int res = 0; 
    for (int u=0; u<V; u++) 
    { 
        if (visited[u] == false) 
        { 
            DFSUtil(u, adj, visited); 
            res++; 
        } 
    } 
    return res; 
} 
  
// Driver code 
int main() 
{ 
    int V = 5; 
    vector<int> adj[V]; 
    addEdge(adj, 0, 1); 
    addEdge(adj, 0, 2); 
    addEdge(adj, 3, 4); 
    cout << countTrees(adj, V); 
    return 0; 
} 

Java

// Java program to count number of trees in a forest. 
import java.io.*;  
import java.util.*;  
  
// This class represents a directed graph using adjacency list  
// representation  
class Graph  
{  
    private int V; // No. of vertices  
  
    // Array of lists for Adjacency List Representation  
    private LinkedList<Integer> adj[];  
  
    // Constructor  
    Graph(int v)  
    {  
        V = v;  
        adj = new LinkedList[v];  
        for (int i = 0; i <  v; ++i)  
            adj[i] = new LinkedList();  
    }  
  
    //Function to add an edge into the graph  
    void addEdge(int v, int w)  
    {  
        adj[v].add(w); // Add w to v's list.  
    }  
  
    // A function used by DFS  
    void DFSUtil(int v,boolean visited[])  
    {  
        // Mark the current node as visited and print it  
        visited[v] = true;  
          
        // Recur for all the vertices adjacent to this vertex  
        Iterator<Integer> i = adj[v].listIterator();  
        while (i.hasNext())  
        {  
            int n = i.next();  
            if (!visited[n]) 
            { 
                DFSUtil(n,visited);  
            } 
        } 
    }  
  
    // The function to do DFS traversal. It uses recursive DFSUtil()  
    int countTrees() 
    {  
        // Mark all the vertices as not visited(set as  
        // false by default in java)  
        boolean visited[] = new boolean[V];  
        int res = 0; 
          
        // Call the recursive helper function to print DFS traversal  
        // starting from all vertices one by one  
        for (int i = 0; i < V; ++i)  
        { 
            if (visited[i] == false) 
            {  
                DFSUtil(i, visited);  
                res ++; 
            } 
        } 
        return res; 
    }  
  
    // Driver code 
    public static void main(String args[])  
    {  
        Graph g = new Graph(5);  
  
        g.addEdge(0, 1);  
        g.addEdge(0, 2);  
        g.addEdge(3, 4);  
  
        System.out.println(g.countTrees());  
    }  
}  
  
// This code is contributed by mayankbansal2 

Python3

# Python3 program to count number   
# of trees in a forest. 
  
# A utility function to add an  
# edge in an undirected graph.  
def addEdge(adj, u, v): 
    adj[u].append(v)  
    adj[v].append(u) 
  
# A utility function to do DFS of graph  
# recursively from a given vertex u.  
def DFSUtil(u, adj, visited): 
    visited[u] = True
    for i in range(len(adj[u])): 
        if (visited[adj[u][i]] == False): 
            DFSUtil(adj[u][i], adj, visited) 
  
# Returns count of tree is the  
# forest given as adjacency list.  
def countTrees(adj, V): 
    visited = [False] * V  
    res = 0
    for u in range(V): 
        if (visited[u] == False): 
            DFSUtil(u, adj, visited)  
            res += 1
    return res 
  
# Driver code  
if __name__ == '__main__': 
  
    V = 5
    adj = [[] for i in range(V)]  
    addEdge(adj, 0, 1)  
    addEdge(adj, 0, 2)  
    addEdge(adj, 3, 4)  
    print(countTrees(adj, V)) 
  
# This code is contributed by PranchalK 

Output:

Time Complexity : O(V + E)

My Personal Notes

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

C++

Java

Python3

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