# Find the closest element in Binary Search Tree

Given a binary search tree and a target node K. The task is to find the node with minimum absolute difference with given target value K. Examples:

```// For above binary search tree
Input  :  k = 4
Output :  4

Input  :  k = 18
Output :  17

Input  :  k = 12
Output :  9
```

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

A simple solution for this problem is to store Inorder traversal of given binary search tree in an auxiliary array and then by taking absolute difference of each element find the node having minimum absolute difference with given target value K in linear time.

An efficient solution for this problem is to take advantage of characteristics of BST. Here is the algorithm to solve this problem :

• If target value K is present in given BST, then it’s the node having minimum absolute difference.
• If target value K is less than the value of current node then move to the left child.
• If target value K is greater than the value of current node then move to the right child.
• ## C++

 `// Recursive C++ program to find key closest to k ` `// in given Binary Search Tree. ` `#include ` `using` `namespace` `std; ` ` `  `/* A binary tree node has key, pointer to left child ` `and a pointer to right child */` `struct` `Node ` `{ ` `    ``int` `key; ` `    ``struct` `Node* left, *right; ` `}; ` ` `  `/* Utility that allocates a new node with the ` `  ``given key and NULL left and right pointers. */` `struct` `Node* newnode(``int` `key) ` `{ ` `    ``struct` `Node* node = ``new` `(``struct` `Node); ` `    ``node->key = key; ` `    ``node->left = node->right  = NULL; ` `    ``return` `(node); ` `} ` ` `  `// Function to find node with minimum absolute ` `// difference with given K ` `// min_diff   --> minimum difference till now ` `// min_diff_key  --> node having minimum absolute ` `//                   difference with K ` `void` `maxDiffUtil(``struct` `Node *ptr, ``int` `k, ``int` `&min_diff, ` `                                      ``int` `&min_diff_key) ` `{ ` `    ``if` `(ptr == NULL) ` `        ``return` `; ` ` `  `    ``// If k itself is present ` `    ``if` `(ptr->key == k) ` `    ``{ ` `        ``min_diff_key = k; ` `        ``return``; ` `    ``} ` ` `  `    ``// update min_diff and min_diff_key by checking ` `    ``// current node value ` `    ``if` `(min_diff > ``abs``(ptr->key - k)) ` `    ``{ ` `        ``min_diff = ``abs``(ptr->key - k); ` `        ``min_diff_key = ptr->key; ` `    ``} ` ` `  `    ``// if k is less than ptr->key then move in ` `    ``// left subtree else in right subtree ` `    ``if` `(k < ptr->key) ` `        ``maxDiffUtil(ptr->left, k, min_diff, min_diff_key); ` `    ``else` `        ``maxDiffUtil(ptr->right, k, min_diff, min_diff_key); ` `} ` ` `  `// Wrapper over maxDiffUtil() ` `int` `maxDiff(Node *root, ``int` `k) ` `{ ` `    ``// Initialize minimum difference ` `    ``int` `min_diff = INT_MAX, min_diff_key = -1; ` ` `  `    ``// Find value of min_diff_key (Closest key ` `    ``// in tree with k) ` `    ``maxDiffUtil(root, k, min_diff, min_diff_key); ` ` `  `    ``return` `min_diff_key; ` `} ` ` `  `// Driver program to run the case ` `int` `main() ` `{ ` `    ``struct` `Node *root = newnode(9); ` `    ``root->left    = newnode(4); ` `    ``root->right   = newnode(17); ` `    ``root->left->left = newnode(3); ` `    ``root->left->right = newnode(6); ` `    ``root->left->right->left = newnode(5); ` `    ``root->left->right->right = newnode(7); ` `    ``root->right->right = newnode(22); ` `    ``root->right->right->left = newnode(20); ` `    ``int` `k = 18; ` `    ``cout << maxDiff(root, k); ` `    ``return` `0; ` `} `

## Java

 `// Recursive Java program to find key closest to k ` `// in given Binary Search Tree. ` ` `  ` ``class` `solution ` ` ``{ ` `      `  `     ``static` `int` `min_diff, min_diff_key; ` `       `  `/*  A binary tree node has key, pointer to left child ` `and a pointer to right child */` `static` `class` `Node ` `{ ` `    ``int` `key; ` `     `  `     ``Node  left,  right; ` `}; ` `  `  `/*  Utility that allocates a new node with the ` `  ``given key and null left and right pointers.  */` ` `  ` ``static` `Node  newnode(``int` `key) ` `{ ` `     `  `     ``Node  node = ``new` `Node(); ` `    ``node.key = key; ` `    ``node.left = node.right  = ``null``; ` `    ``return` `(node); ` `} ` `  `  `// Function to find node with minimum absolute ` `// difference with given K ` `// min_diff   -. minimum difference till now ` `// min_diff_key  -. node having minimum absolute ` `//                   difference with K ` `static` `void` `maxDiffUtil(Node  ptr, ``int` `k) ` `{ ` `    ``if` `(ptr == ``null``) ` `        ``return` `; ` `  `  `    ``// If k itself is present ` `    ``if` `(ptr.key == k) ` `    ``{ ` `        ``min_diff_key = k; ` `        ``return``; ` `    ``} ` `  `  `    ``// update min_diff and min_diff_key by checking ` `    ``// current node value ` `    ``if` `(min_diff > Math.abs(ptr.key - k)) ` `    ``{ ` `        ``min_diff = Math.abs(ptr.key - k); ` `        ``min_diff_key = ptr.key; ` `    ``} ` `  `  `    ``// if k is less than ptr.key then move in ` `    ``// left subtree else in right subtree ` `    ``if` `(k < ptr.key) ` `        ``maxDiffUtil(ptr.left, k); ` `    ``else` `        ``maxDiffUtil(ptr.right, k); ` `} ` `  `  `// Wrapper over maxDiffUtil() ` `static` `int` `maxDiff(Node  root, ``int` `k) ` `{ ` `    ``// Initialize minimum difference ` `    ``min_diff = ``999999999``; min_diff_key = -``1``; ` `  `  `    ``// Find value of min_diff_key (Closest key ` `    ``// in tree with k) ` `    ``maxDiffUtil(root, k); ` `  `  `    ``return` `min_diff_key; ` `} ` `  `  `// Driver program to run the case ` `public` `static` `void` `main(String args[]) ` `{ ` `     `  `     ``Node  root = newnode(``9``); ` `    ``root.left    = newnode(``4``); ` `    ``root.right   = newnode(``17``); ` `    ``root.left.left = newnode(``3``); ` `    ``root.left.right = newnode(``6``); ` `    ``root.left.right.left = newnode(``5``); ` `    ``root.left.right.right = newnode(``7``); ` `    ``root.right.right = newnode(``22``); ` `    ``root.right.right.left = newnode(``20``); ` `    ``int` `k = ``18``; ` `    ``System.out.println( maxDiff(root, k)); ` `     `  `} ` `} ` `//contributed by Arnab Kundu `

## Python3

 `# Recursive Python program to find key  ` `# closest to k in given Binary Search Tree.  ` ` `  `# Utility that allocates a new node with the  ` `# given key and NULL left and right pointers.  ` `class` `newnode:  ` ` `  `    ``# Constructor to create a new node  ` `    ``def` `__init__(``self``, data):  ` `        ``self``.key ``=` `data  ` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` ` `  `# Function to find node with minimum  ` `# absolute difference with given K  ` `# min_diff --> minimum difference till now  ` `# min_diff_key --> node having minimum absolute  ` `#                   difference with K  ` `def` `maxDiffUtil(ptr, k, min_diff, min_diff_key): ` `    ``if` `ptr ``=``=` `None``:  ` `        ``return` `         `  `    ``# If k itself is present  ` `    ``if` `ptr.key ``=``=` `k: ` `        ``min_diff_key[``0``] ``=` `k  ` `        ``return` ` `  `    ``# update min_diff and min_diff_key by   ` `    ``# checking current node value  ` `    ``if` `min_diff > ``abs``(ptr.key ``-` `k): ` `        ``min_diff ``=` `abs``(ptr.key ``-` `k)  ` `        ``min_diff_key[``0``] ``=` `ptr.key ` ` `  `    ``# if k is less than ptr->key then move  ` `    ``# in left subtree else in right subtree  ` `    ``if` `k < ptr.key: ` `        ``maxDiffUtil(ptr.left, k, min_diff,  ` `                                 ``min_diff_key) ` `    ``else``: ` `        ``maxDiffUtil(ptr.right, k, min_diff,  ` `                                  ``min_diff_key) ` ` `  `# Wrapper over maxDiffUtil()  ` `def` `maxDiff(root, k): ` `     `  `    ``# Initialize minimum difference  ` `    ``min_diff, min_diff_key ``=` `999999999999``, [``-``1``] ` ` `  `    ``# Find value of min_diff_key (Closest  ` `    ``# key in tree with k)  ` `    ``maxDiffUtil(root, k, min_diff, min_diff_key) ` ` `  `    ``return` `min_diff_key[``0``] ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``root ``=` `newnode(``9``)  ` `    ``root.left ``=` `newnode(``4``)  ` `    ``root.right ``=` `newnode(``17``) ` `    ``root.left.left ``=` `newnode(``3``)  ` `    ``root.left.right ``=` `newnode(``6``) ` `    ``root.left.right.left ``=` `newnode(``5``)  ` `    ``root.left.right.right ``=` `newnode(``7``)  ` `    ``root.right.right ``=` `newnode(``22``) ` `    ``root.right.right.left ``=` `newnode(``20``)  ` `    ``k ``=` `18` `    ``print``(maxDiff(root, k)) ` ` `  `# This code is contributed by PranchalK `

## C#

 `using` `System; ` ` `  `// Recursive C# program to find key closest to k  ` `// in given Binary Search Tree.  ` ` `  ` ``public` `class` `solution ` ` ``{ ` ` `  `     ``public` `static` `int` `min_diff, min_diff_key; ` ` `  `/*  A binary tree node has key, pointer to left child  ` `and a pointer to right child */` `public` `class` `Node ` `{ ` `    ``public` `int` `key; ` ` `  `     ``public` `Node left, right; ` `} ` ` `  `/*  Utility that allocates a new node with the  ` `  ``given key and null left and right pointers.  */` ` `  `public` `static` `Node newnode(``int` `key) ` ` ``{ ` ` `  `     ``Node node = ``new` `Node(); ` `    ``node.key = key; ` `    ``node.left = node.right = ``null``; ` `    ``return` `(node); ` ` ``} ` ` `  `// Function to find node with minimum absolute  ` `// difference with given K  ` `// min_diff   -. minimum difference till now  ` `// min_diff_key  -. node having minimum absolute  ` `//                   difference with K  ` `public` `static` `void` `maxDiffUtil(Node ptr, ``int` `k) ` `{ ` `    ``if` `(ptr == ``null``) ` `    ``{ ` `        ``return``; ` `    ``} ` ` `  `    ``// If k itself is present  ` `    ``if` `(ptr.key == k) ` `    ``{ ` `        ``min_diff_key = k; ` `        ``return``; ` `    ``} ` ` `  `    ``// update min_diff and min_diff_key by checking  ` `    ``// current node value  ` `    ``if` `(min_diff > Math.Abs(ptr.key - k)) ` `    ``{ ` `        ``min_diff = Math.Abs(ptr.key - k); ` `        ``min_diff_key = ptr.key; ` `    ``} ` ` `  `    ``// if k is less than ptr.key then move in  ` `    ``// left subtree else in right subtree  ` `    ``if` `(k < ptr.key) ` `    ``{ ` `        ``maxDiffUtil(ptr.left, k); ` `    ``} ` `    ``else` `    ``{ ` `        ``maxDiffUtil(ptr.right, k); ` `    ``} ` `} ` ` `  `// Wrapper over maxDiffUtil()  ` `public` `static` `int` `maxDiff(Node root, ``int` `k) ` `{ ` `    ``// Initialize minimum difference  ` `    ``min_diff = 999999999; ` `    ``min_diff_key = -1; ` ` `  `    ``// Find value of min_diff_key (Closest key  ` `    ``// in tree with k)  ` `    ``maxDiffUtil(root, k); ` ` `  `    ``return` `min_diff_key; ` `} ` ` `  `// Driver program to run the case  ` `public` `static` `void` `Main(``string``[] args) ` `{ ` ` `  `     ``Node root = newnode(9); ` `    ``root.left = newnode(4); ` `    ``root.right = newnode(17); ` `    ``root.left.left = newnode(3); ` `    ``root.left.right = newnode(6); ` `    ``root.left.right.left = newnode(5); ` `    ``root.left.right.right = newnode(7); ` `    ``root.right.right = newnode(22); ` `    ``root.right.right.left = newnode(20); ` `    ``int` `k = 18; ` `    ``Console.WriteLine(maxDiff(root, k)); ` ` `  `} ` ` ``} ` ` `  `  ``// This code is contributed by Shrikant13 `

Output:

```17
```

Time complexity : O(h) where h is height of given Binary Search Tree.

This article is contributed by Shashank Mishra ( Gullu ). 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.