# Even size subtree in n-ary tree

Given an n-ary tree of n vertices and n-1 edges. The tree is given in the form of adjacency list. Find number of subtrees of even size in given tree.

**Examples:**

Input :1 / \ 2 3 / \ \ 4 5 6 / \ 7 8Output :2 Subtree rooted at 1 and 3 are of even size.Input :1 / \ 2 3 / | \ \ 4 5 6 7 / | \ 8 9 10Output :3 Subtree rooted at 1, 3 and 5 are of even size.

A **simple** solution is to perform dfs starting from every node and find size of subtree rooted at that node. If size is even increment count. Time complexity of above solution is O(n^{2}).

A **better** solution is to perform single dfs on given tree. The idea is to first find recursively size of subtree of all childeren nodes, then find size of subtree rooted at current node by taking sum of size of children node subtrees and increment count if size is even.

Below is the implementation of above approach:

`// CPP program to find number of subtrees of even size. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// DFS function to traverse the tree and find ` `// number of even size subtree. ` `int` `dfs(vector<` `int` `> adj[], ` `int` `n, ` `int` `v, ` `int` `& ans) ` `{ ` ` ` `// Size of subtree is minimum possible 1 for ` ` ` `// leaf node. ` ` ` `int` `size = 1; ` ` ` ` ` `// Find size of subtree rooted at children nodes ` ` ` `// and add the size to current subtree size. ` ` ` `for` `(` `auto` `ele : adj[v]) { ` ` ` `size += dfs(adj, n, ele, ans); ` ` ` `} ` ` ` ` ` `// If size is even then increment count. ` ` ` `if` `(size % 2 == 0) ` ` ` `ans++; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `n; ` ` ` `n = 10; ` ` ` ` ` `vector<` `int` `> adj[n + 1]; ` ` ` `/* ` ` ` `1 ` ` ` `/ \ ` ` ` `2 3 ` ` ` `/ \ \ ` ` ` `4 5 6 ` ` ` `/ \ ` ` ` `7 8 ` ` ` `*/` ` ` `adj[1].push_back(2); ` ` ` `adj[1].push_back(3); ` ` ` `adj[2].push_back(4); ` ` ` `adj[2].push_back(5); ` ` ` `adj[3].push_back(6); ` ` ` `adj[5].push_back(7); ` ` ` `adj[5].push_back(8); ` ` ` ` ` `/* ` ` ` `1 ` ` ` `/ \ ` ` ` `2 3 ` ` ` `/ | \ \ ` ` ` `4 5 6 7 ` ` ` `/ | \ ` ` ` `8 9 10 ` ` ` `*/` ` ` `/*adj[1].push_back(2); ` ` ` `adj[1].push_back(3); ` ` ` `adj[2].push_back(4); ` ` ` `adj[2].push_back(5); ` ` ` `adj[2].push_back(6); ` ` ` `adj[3].push_back(7); ` ` ` `adj[5].push_back(8); ` ` ` `adj[5].push_back(9); ` ` ` `adj[5].push_back(10); ` ` ` `*/` ` ` `int` `ans = 0; ` ` ` ` ` `dfs(adj, n, 1, ans); ` ` ` ` ` `cout << ans; ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

Output:2

**Time Complexity:** O(n)

**Auxiliary Space:** O(1)

## Recommended Posts:

- Subtree of all nodes in a tree using DFS
- Subtree with given sum in a Binary Tree
- Queries for DFS of a subtree in a tree
- Duplicate subtree in Binary Tree | SET 2
- Find largest subtree sum in a tree
- Euler Tour | Subtree Sum using Segment Tree
- Check if the given Binary Tree have a Subtree with equal no of 1's and 0's
- Find the largest BST subtree in a given Binary Tree | Set 1
- Find the Kth node in the DFS traversal of a given subtree in a Tree
- Number of leaf nodes in the subtree of every node of an n-ary tree
- Find the largest Perfect Subtree in a given Binary Tree
- Find the largest Complete Subtree in a given Binary Tree
- Convert a Binary Tree such that every node stores the sum of all nodes in its right subtree
- Change a Binary Tree so that every node stores sum of all nodes in left subtree
- Check if a binary tree is subtree of another binary tree | Set 2

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.