# 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 ` `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[], ``int` `V) ` `{ ` `    ``vector<``bool``> visited(V, ``false``); ` `    ``int` `res = 0; ` `    ``for` `(``int` `u=0; u 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 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 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:

```2
```

Time Complexity : O(V + E)

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