# 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; ` `} ` |

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## 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)

## Recommended Posts:

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- Program to count Number of connected components in an undirected graph
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- Disjoint Set Union on trees | Set 1
- Minimum number of operation required to convert number x into y

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