# Number of nodes greater than a given value in n-ary tree

Given a **n-ary** tree and a number **x**, find and return the number of nodes which are greater than x.

Example:

In the given tree, x = 7 Number of nodes greater than x are 4.

**Approach :**

The idea is maintain a count variable initialize to 0. Traverse the tree and compare root data with x. If root data is greater than x, increment the count variable and recursively call for all its children.

Below is the implementation of idea.

`// CPP program to find number of nodes ` `// greater than x ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Structure of a node of n-ary tree ` `struct` `Node { ` ` ` `int` `key; ` ` ` `vector<Node*> child; ` `}; ` ` ` `// Utility function to create ` `// a new tree node ` `Node* newNode(` `int` `key) ` `{ ` ` ` `Node* temp = ` `new` `Node; ` ` ` `temp->key = key; ` ` ` `return` `temp; ` `} ` ` ` `// Function to find nuber of nodes ` `// gretaer than x ` `int` `nodesGreaterThanX(Node* root, ` `int` `x) ` `{ ` ` ` `if` `(root == NULL) ` ` ` `return` `0; ` ` ` ` ` `int` `count = 0; ` ` ` ` ` `// if current root is greater ` ` ` `// than x increment count ` ` ` `if` `(root->key > x) ` ` ` `count++; ` ` ` ` ` `// Number of children of root ` ` ` `int` `numChildren = root->child.size(); ` ` ` ` ` `// recursively calling for every child ` ` ` `for` `(` `int` `i = 0; i < numChildren; i++) { ` ` ` `Node* child = root->child[i]; ` ` ` `count += nodesGreaterThanX(child, x); ` ` ` `} ` ` ` ` ` `// return the count ` ` ` `return` `count; ` `} ` ` ` `// Driver program ` `int` `main() ` `{ ` ` ` `/* Let us create below tree ` `* 5 ` `* / | \ ` `* 1 2 3 ` `* / / \ \ ` `* 15 4 5 6 ` `*/` ` ` ` ` `Node* root = newNode(5); ` ` ` `(root->child).push_back(newNode(1)); ` ` ` `(root->child).push_back(newNode(2)); ` ` ` `(root->child).push_back(newNode(3)); ` ` ` `(root->child[0]->child).push_back(newNode(15)); ` ` ` `(root->child[1]->child).push_back(newNode(4)); ` ` ` `(root->child[1]->child).push_back(newNode(5)); ` ` ` `(root->child[2]->child).push_back(newNode(6)); ` ` ` ` ` `int` `x = 5; ` ` ` ` ` `cout << ` `"Number of nodes greater than "` ` ` `<< x << ` `" are "` `; ` ` ` `cout << nodesGreaterThanX(root, x) ` ` ` `<< endl; ` ` ` ` ` `return` `0; ` `} ` |

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Output:

Number of nodes greater than 5 are 2

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