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# Count of nodes in a Binary Tree whose immediate children are co-prime

Given a Binary Tree, the task is to count the nodes whose immediate children are co-prime.

Examples:

```Input:
1
/   \
15     5
/  \   /  \
11   2 4     15
\    /
2  3
Output: 2
Explanation:
Children of 15 (11, 2) are co-prime
Children of 5 (4, 15) are co-prime

Input:
7
/  \
21     14
/  \      \
77   16     3
/ \         / \
2   5       10  11
/
23
Output:3
Explanation:
Children of 21 (77, 8) are co-prime
Children of 77 (2, 5) are co-prime
Children of 3 (10, 11) are co-prime ```

Approach: The idea is to:

1. Do level order traversal of the tree
2. For each node check that its both children are not Null
3. If true, then check whether greatest common divisor of both children is 1.
4. If yes, then count such nodes and print at the end.

Below is the implementation of the above approach:

## C++

 `// C++ program for Counting nodes``// whose immediate children``// are co-prime` `#include ``using` `namespace` `std;` `// Structure of node``struct` `Node {``    ``int` `key;``    ``struct` `Node *left, *right;``};` `// Utility function to``// create a new node``Node* newNode(``int` `key)``{``    ``Node* temp = ``new` `Node;``    ``temp->key = key;``    ``temp->left = temp->right = NULL;``    ``return` `(temp);``}` `// Function to check and print if``// two nodes are co-prime or not``bool` `coprime(``struct` `Node* a,``             ``struct` `Node* b)``{` `    ``if` `(__gcd(a->key, b->key) == 1)``        ``return` `true``;``    ``else``        ``return` `false``;``}` `// Function to get the count of``// Nodes whose immediate children``// are co-prime in a binary tree``unsigned ``int` `getCount(``struct` `Node* node)``{``    ``// Base Case``    ``if` `(!node)``        ``return` `0;` `    ``queue q;` `    ``// Do level order traversal``    ``// starting from root``    ``int` `count = 0;``    ``q.push(node);` `    ``while` `(!q.empty()) {``        ``struct` `Node* temp = q.front();``        ``q.pop();` `        ``if` `(temp->left && temp->right) {``            ``if` `(coprime(temp->left,``                        ``temp->right))``                ``count++;``        ``}` `        ``if` `(temp->left != NULL)``            ``q.push(temp->left);``        ``if` `(temp->right != NULL)``            ``q.push(temp->right);``    ``}``    ``return` `count;``}` `// Function to find total``// number of nodes``// In a given binary tree``int` `findSize(``struct` `Node* node)``{``    ``// Base condition``    ``if` `(node == NULL)``        ``return` `0;` `    ``return` `1``           ``+ findSize(node->left)``           ``+ findSize(node->right);``}` `// Function to create Tree``// and find the count of nodes``// whose immediate children``// are co-prime``void` `findCount()``{``    ``/*         10``            ``/  \``          ``48   12``              ``/  \``            ``18    35``           ``/ \    / \``          ``21 29  43 16``                 ``/``                ``7``    ``*/` `    ``// Create Binary Tree``    ``Node* root = newNode(10);``    ``root->left = newNode(48);``    ``root->right = newNode(12);` `    ``root->right->left = newNode(18);``    ``root->right->right = newNode(35);` `    ``root->right->left->left = newNode(21);``    ``root->right->left->right = newNode(29);``    ``root->right->right->left = newNode(43);``    ``root->right->right->right = newNode(16);``    ``root->right->right->right->left = newNode(7);` `    ``// Print all nodes``    ``// with Co-Prime children``    ``cout << getCount(root) << endl;``}` `// Driver Code``int` `main()``{``    ``// Function Call``    ``findCount();` `    ``return` `0;``}`

## Java

 `// Java program for Counting nodes``// whose immediate children``// are co-prime``import` `java.util.*;` `class` `GFG{`` ` `// Structure of node``static` `class` `Node {``    ``int` `key;``    ``Node left, right;``};`` ` `// Utility function to``// create a new node``static` `Node newNode(``int` `key)``{``    ``Node temp = ``new` `Node();``    ``temp.key = key;``    ``temp.left = temp.right = ``null``;``    ``return` `(temp);``}`` ` `// Function to check and print if``// two nodes are co-prime or not``static` `boolean` `coprime(Node a,``             ``Node b)``{`` ` `    ``if` `(__gcd(a.key, b.key) == ``1``)``        ``return` `true``;``    ``else``        ``return` `false``;``}`` ` `// Function to get the count of``// Nodes whose immediate children``// are co-prime in a binary tree``static` `int` `getCount(Node node)``{``    ``// Base Case``    ``if` `(node == ``null``)``        ``return` `0``;`` ` `    ``Queue q = ``new` `LinkedList();`` ` `    ``// Do level order traversal``    ``// starting from root``    ``int` `count = ``0``;``    ``q.add(node);`` ` `    ``while` `(!q.isEmpty()) {``        ``Node temp = q.peek();``        ``q.remove();`` ` `        ``if` `(temp.left != ``null` `&& temp.right != ``null``) {``            ``if` `(coprime(temp.left,``                        ``temp.right))``                ``count++;``        ``}`` ` `        ``if` `(temp.left != ``null``)``            ``q.add(temp.left);``        ``if` `(temp.right != ``null``)``            ``q.add(temp.right);``    ``}``    ``return` `count;``}`` ` `// Function to find total``// number of nodes``// In a given binary tree``static` `int` `findSize(Node node)``{``    ``// Base condition``    ``if` `(node == ``null``)``        ``return` `0``;`` ` `    ``return` `1``           ``+ findSize(node.left)``           ``+ findSize(node.right);``}`` ` `// Function to create Tree``// and find the count of nodes``// whose immediate children``// are co-prime``static` `void` `findCount()``{``    ``/*         10``            ``/  \``          ``48   12``              ``/  \``            ``18    35``           ``/ \    / \``          ``21 29  43 16``                 ``/``                ``7``    ``*/`` ` `    ``// Create Binary Tree``    ``Node root = newNode(``10``);``    ``root.left = newNode(``48``);``    ``root.right = newNode(``12``);`` ` `    ``root.right.left = newNode(``18``);``    ``root.right.right = newNode(``35``);`` ` `    ``root.right.left.left = newNode(``21``);``    ``root.right.left.right = newNode(``29``);``    ``root.right.right.left = newNode(``43``);``    ``root.right.right.right = newNode(``16``);``    ``root.right.right.right.left = newNode(``7``);`` ` `    ``// Print all nodes``    ``// with Co-Prime children``    ``System.out.print(getCount(root) +``"\n"``);``}``static` `int` `__gcd(``int` `a, ``int` `b) ``{ ``    ``return` `b == ``0``? a:__gcd(b, a % b);    ``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``// Function Call``    ``findCount();`` ` `}``}` `// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 program for counting nodes``# whose immediate children``# are co-prime``from` `collections ``import` `deque as queue``from` `math ``import` `gcd as __gcd` `# A Binary Tree Node``class` `Node:``    ` `    ``def` `__init__(``self``, key):``        ` `        ``self``.data ``=` `key``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `# Function to check and print if``# two nodes are co-prime or not``def` `coprime(a, b):``    ` `    ``if` `(__gcd(a.data, b.data) ``=``=` `1``):``        ``return` `True``    ``else``:``        ``return` `False` `# Function to get the count of``# Nodes whose immediate children``# are co-prime in a binary tree``def` `getCount(node):` `    ``# Base Case``    ``if` `(``not` `node):``        ``return` `0` `    ``q ``=` `queue()` `    ``# Do level order traversal``    ``# starting from root``    ``count ``=` `0``    ``q.append(node)` `    ``while` `(``len``(q) > ``0``):``        ``temp ``=` `q.popleft()``        ``#q.pop()` `        ``if` `(temp.left ``and` `temp.right):``            ``if` `(coprime(temp.left, temp.right)):``                ``count ``+``=` `1` `        ``if` `(temp.left !``=` `None``):``            ``q.append(temp.left)``        ``if` `(temp.right !``=` `None``):``            ``q.append(temp.right)` `    ``return` `count` `# Function to find total``# number of nodes``# In a given binary tree``def` `findSize(node):` `    ``# Base condition``    ``if` `(node ``=``=` `None``):``        ``return` `0` `    ``return` `(``1` `+` `findSize(node.left) ``+``                ``findSize(node.right))` `# Function to create Tree``# and find the count of nodes``# whose immediate children``# are co-prime``def` `findCount():``    ` `    ``#          10``    ``#         /  \``    ``#       48   12``    ``#           /  \``    ``#         18    35``    ``#        / \    / \``    ``#       21 29  43 16``    ``#              /``    ``#             7``    ``#` `    ``# Create Binary Tree``    ``root ``=` `Node(``10``)``    ``root.left ``=` `Node(``48``)``    ``root.right ``=` `Node(``12``)` `    ``root.right.left ``=` `Node(``18``)``    ``root.right.right ``=` `Node(``35``)` `    ``root.right.left.left ``=` `Node(``21``)``    ``root.right.left.right ``=` `Node(``29``)``    ``root.right.right.left ``=` `Node(``43``)``    ``root.right.right.right ``=` `Node(``16``)``    ``root.right.right.right.left ``=` `Node(``7``)` `    ``# Print all nodes``    ``# with Co-Prime children``    ``print``(getCount(root))` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``# Function Call``    ``findCount()` `# This code is contributed by mohit kumar 29`

## C#

 `// C# program for Counting nodes``// whose immediate children``// are co-prime``using` `System;``using` `System.Collections.Generic;` `class` `GFG{``  ` `// Structure of node``class` `Node {``    ``public` `int` `key;``    ``public` `Node left, right;``};``  ` `// Utility function to``// create a new node``static` `Node newNode(``int` `key)``{``    ``Node temp = ``new` `Node();``    ``temp.key = key;``    ``temp.left = temp.right = ``null``;``    ``return` `(temp);``}``  ` `// Function to check and print if``// two nodes are co-prime or not``static` `bool` `coprime(Node a,``             ``Node b)``{``  ` `    ``if` `(__gcd(a.key, b.key) == 1)``        ``return` `true``;``    ``else``        ``return` `false``;``}``  ` `// Function to get the count of``// Nodes whose immediate children``// are co-prime in a binary tree``static` `int` `getCount(Node node)``{``    ``// Base Case``    ``if` `(node == ``null``)``        ``return` `0;``  ` `    ``List q = ``new` `List();``  ` `    ``// Do level order traversal``    ``// starting from root``    ``int` `count = 0;``    ``q.Add(node);``  ` `    ``while` `(q.Count != 0) {``        ``Node temp = q[0];``        ``q.RemoveAt(0);``  ` `        ``if` `(temp.left != ``null` `&& temp.right != ``null``) {``            ``if` `(coprime(temp.left,``                        ``temp.right))``                ``count++;``        ``}``  ` `        ``if` `(temp.left != ``null``)``            ``q.Add(temp.left);``        ``if` `(temp.right != ``null``)``            ``q.Add(temp.right);``    ``}``    ``return` `count;``}``  ` `// Function to find total``// number of nodes``// In a given binary tree``static` `int` `findSize(Node node)``{``    ``// Base condition``    ``if` `(node == ``null``)``        ``return` `0;``  ` `    ``return` `1``           ``+ findSize(node.left)``           ``+ findSize(node.right);``}``  ` `// Function to create Tree``// and find the count of nodes``// whose immediate children``// are co-prime``static` `void` `findCount()``{``    ``/*         10``            ``/  \``          ``48   12``              ``/  \``            ``18    35``           ``/ \    / \``          ``21 29  43 16``                 ``/``                ``7``    ``*/``  ` `    ``// Create Binary Tree``    ``Node root = newNode(10);``    ``root.left = newNode(48);``    ``root.right = newNode(12);``  ` `    ``root.right.left = newNode(18);``    ``root.right.right = newNode(35);``  ` `    ``root.right.left.left = newNode(21);``    ``root.right.left.right = newNode(29);``    ``root.right.right.left = newNode(43);``    ``root.right.right.right = newNode(16);``    ``root.right.right.right.left = newNode(7);``  ` `    ``// Print all nodes``    ``// with Co-Prime children``    ``Console.Write(getCount(root) +``"\n"``);``}``static` `int` `__gcd(``int` `a, ``int` `b) ``{ ``    ``return` `b == 0? a:__gcd(b, a % b);    ``}`` ` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``// Function Call``    ``findCount();``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`3`

Complexity Analysis:

Time Complexity: O(N*logV) where V is the weight of a node in the tree.

In bfs, every node of the tree is processed once and hence the complexity due to the bfs is O(N) if there are total N nodes in the tree. Also, while processing every node, in order to check if the node values are co-prime or not, the inbuilt __gcd(A, B) function where A, B are the weight of the nodes is being called and this function has a complexity of O(log(min(A, B))), hence for every node there is an added complexity of O(logV). Therefore, the time complexity is O(N*logV).

Auxiliary Space : O(w) where w is the maximum width of the tree.