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 codeint 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 |
Output:
2
Time Complexity : O(V + E)
