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

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

C#

// C# program to count number of trees in a forest.
using System;
using System.Collections.Generic;

// 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 List<int> []adj;

    // Constructor
    Graph(int v)
    {
        V = v;
        adj = new List<int>[v];
        for (int i = 0; i < v; ++i)
            adj[i] = new List<int>();
    }

    // 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, bool []visited)
    {
        // Mark the current node as
        // visited and print it
        visited[v] = true;

        // Recur for all the vertices
        // adjacent to this vertex
        foreach(int i in adj[v])
        {
            int n = i;
            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)
        bool []visited = new bool[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);

        Console.WriteLine(g.countTrees());
    }
}

// This code is contributed by PrinciRaj1992

Javascript

<script>
// Javascript program to count number of trees in a forest.

// This class represents a directed graph
// using adjacency list representation
var V; // No. of vertices

// Array of lists for
// Adjacency List Representation
var adj;
// Constructor
function Graph( v)
{
    V = v;
    adj = Array.from(Array(v), ()=>Array());
}
// Function to add an edge into the graph
function addEdge(v, w)
{
    adj[v].push(w); // Add w to v's list.
}
// A function used by DFS
function DFSUtil(v, visited)
{
    // Mark the current node as
    // visited and print it
    visited[v] = true;

    // Recur for all the vertices
    // adjacent to this vertex
    for(var i of adj[v])
    {
        var n = i;
        if (!visited[n])
        {
            DFSUtil(n, visited);
        }
    }
}
// The function to do DFS traversal.
// It uses recursive DFSUtil()
function countTrees()
{
    // Mark all the vertices as not visited
    // (set as false by default in java)
    var visited = Array(V).fill(false);
    var res = 0;

    // Call the recursive helper function
    // to print DFS traversal starting from
    // all vertices one by one
    for(var i = 0; i < V; ++i)
    {
        if (visited[i] == false)
        {
            DFSUtil(i, visited);
            res ++;
        }
    }
    return res;
}

// Driver code
Graph(5);
addEdge(0, 1);
addEdge(0, 2);
addEdge(3, 4);
document.write(countTrees());

// This code is contributed by rutvik_56.
</script>

Output:

2

Time Complexity : O(V + E)