# Find the closest leaf in a Binary Tree

Given a Binary Tree and a key ‘k’, find distance of the closest leaf from ‘k’.

Examples:

```              A
/
B       C
/
E     F
/
G         H
/        /
I   J     K

Closest leaf to 'H' is 'K', so distance is 1 for 'H'
Closest leaf to 'C' is 'B', so distance is 2 for 'C'
Closest leaf to 'E' is either 'I' or 'J', so distance is 2 for 'E'
Closest leaf to 'B' is 'B' itself, so distance is 0 for 'B'
```

The main point to note here is that a closest key can either be a descendent of given key or can be reached through one of the ancestors.
The idea is to traverse the given tree in preorder and keep track of ancestors in an array. When we reach the given key, we evaluate distance of the closest leaf in subtree rooted with given key. We also traverse all ancestors one by one and find distance of the closest leaf in the subtree rooted with ancestor. We compare all distances and return minimum.

Below is the implementation of above approach.

## C++

 `// A C++ program to find the closesr leaf of a given key in Binary Tree ` `#include ` `#include ` `using` `namespace` `std; ` ` `  `/* A binary tree Node has key, pocharer to left and right children */` `struct` `Node ` `{ ` `    ``char` `key; ` `    ``struct` `Node* left, *right; ` `}; ` ` `  `/* Helper function that allocates a new node with the ` `   ``given data and NULL left and right pocharers. */` `Node *newNode(``char` `k) ` `{ ` `    ``Node *node = ``new` `Node; ` `    ``node->key = k; ` `    ``node->right = node->left = NULL; ` `    ``return` `node; ` `} ` ` `  `// A utility function to find minimum of x and y ` `int` `getMin(``int` `x, ``int` `y) ` `{ ` `    ``return` `(x < y)? x :y; ` `} ` ` `  `// A utility function to find distance of closest leaf of the tree ` `// rooted under given root ` `int` `closestDown(``struct` `Node *root) ` `{ ` `    ``// Base cases ` `    ``if` `(root == NULL) ` `        ``return` `INT_MAX; ` `    ``if` `(root->left == NULL && root->right == NULL) ` `        ``return` `0; ` ` `  `    ``// Return minimum of left and right, plus one ` `    ``return` `1 + getMin(closestDown(root->left), closestDown(root->right)); ` `} ` ` `  `// Returns distance of the cloest leaf to a given key 'k'.  The array ` `// ancestors is used to keep track of ancestors of current node and ` `// 'index' is used to keep track of curremt index in 'ancestors[]' ` `int` `findClosestUtil(``struct` `Node *root, ``char` `k, ``struct` `Node *ancestors[], ` `                                               ``int` `index) ` `{ ` `    ``// Base case ` `    ``if` `(root == NULL) ` `        ``return` `INT_MAX; ` ` `  `    ``// If key found ` `    ``if` `(root->key == k) ` `    ``{ ` `        ``//  Find the cloest leaf under the subtree rooted with given key ` `        ``int` `res = closestDown(root); ` ` `  `        ``// Traverse all ancestors and update result if any parent node ` `        ``// gives smaller distance ` `        ``for` `(``int` `i = index-1; i>=0; i--) ` `            ``res = getMin(res, index - i + closestDown(ancestors[i])); ` `        ``return` `res; ` `    ``} ` ` `  `    ``// If key node found, store current node and recur for left and ` `    ``// right childrens ` `    ``ancestors[index] = root; ` `    ``return` `getMin(findClosestUtil(root->left, k, ancestors, index+1), ` `                  ``findClosestUtil(root->right, k, ancestors, index+1)); ` ` `  `} ` ` `  `// The main function that returns distance of the closest key to 'k'. It ` `// mainly uses recursive function findClosestUtil() to find the closes ` `// distance. ` `int` `findClosest(``struct` `Node *root, ``char` `k) ` `{ ` `    ``// Create an array to store ancestors ` `    ``// Assumptiom: Maximum height of tree is 100 ` `    ``struct` `Node *ancestors; ` ` `  `    ``return` `findClosestUtil(root, k, ancestors, 0); ` `} ` ` `  `/* Driver program to test above functions*/` `int` `main() ` `{ ` `    ``// Let us construct the BST shown in the above figure ` `    ``struct` `Node *root        = newNode(``'A'``); ` `    ``root->left               = newNode(``'B'``); ` `    ``root->right              = newNode(``'C'``); ` `    ``root->right->left        = newNode(``'E'``); ` `    ``root->right->right       = newNode(``'F'``); ` `    ``root->right->left->left  = newNode(``'G'``); ` `    ``root->right->left->left->left  = newNode(``'I'``); ` `    ``root->right->left->left->right = newNode(``'J'``); ` `    ``root->right->right->right      = newNode(``'H'``); ` `    ``root->right->right->right->left = newNode(``'K'``); ` ` `  `    ``char` `k = ``'H'``; ` `    ``cout << ``"Distace of the closest key from "` `<< k << ``" is "` `         ``<< findClosest(root, k) << endl; ` `    ``k = ``'C'``; ` `    ``cout << ``"Distace of the closest key from "` `<< k << ``" is "` `         ``<< findClosest(root, k) << endl; ` `    ``k = ``'E'``; ` `    ``cout << ``"Distace of the closest key from "` `<< k << ``" is "` `         ``<< findClosest(root, k) << endl; ` `    ``k = ``'B'``; ` `    ``cout << ``"Distace of the closest key from "` `<< k << ``" is "` `         ``<< findClosest(root, k) << endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find closest leaf of a given key in Binary Tree ` `  `  `/* Class containing left and right child of current  ` `   ``node and key value*/` `class` `Node  ` `{ ` `    ``int` `data; ` `    ``Node left, right; ` `  `  `    ``public` `Node(``int` `item)  ` `    ``{ ` `        ``data = item; ` `        ``left = right = ``null``; ` `    ``} ` `} ` `  `  `class` `BinaryTree  ` `{ ` `    ``Node root; ` `      `  `    ``// A utility function to find minimum of x and y ` `    ``int` `getMin(``int` `x, ``int` `y)  ` `    ``{ ` `        ``return` `(x < y) ? x : y; ` `    ``} ` `  `  `    ``// A utility function to find distance of closest leaf of the tree ` `    ``// rooted under given root ` `    ``int` `closestDown(Node node)  ` `    ``{ ` `        ``// Base cases ` `        ``if` `(node == ``null``) ` `            ``return` `Integer.MAX_VALUE; ` `        ``if` `(node.left == ``null` `&& node.right == ``null``) ` `            ``return` `0``; ` `  `  `        ``// Return minimum of left and right, plus one ` `        ``return` `1` `+ getMin(closestDown(node.left), closestDown(node.right)); ` `    ``} ` `  `  `    ``// Returns distance of the cloest leaf to a given key 'k'.  The array ` `    ``// ancestors is used to keep track of ancestors of current node and ` `    ``// 'index' is used to keep track of curremt index in 'ancestors[]' ` `    ``int` `findClosestUtil(Node node, ``char` `k, Node ancestors[], ``int` `index)  ` `    ``{ ` `        ``// Base case ` `        ``if` `(node == ``null``) ` `            ``return` `Integer.MAX_VALUE; ` `  `  `        ``// If key found ` `        ``if` `(node.data == k)  ` `        ``{ ` `            ``//  Find the cloest leaf under the subtree rooted with given key ` `            ``int` `res = closestDown(node); ` `  `  `            ``// Traverse all ancestors and update result if any parent node ` `            ``// gives smaller distance ` `            ``for` `(``int` `i = index - ``1``; i >= ``0``; i--) ` `                ``res = getMin(res, index - i + closestDown(ancestors[i])); ` `            ``return` `res; ` `        ``} ` `  `  `        ``// If key node found, store current node and recur for left and ` `        ``// right childrens ` `        ``ancestors[index] = node; ` `        ``return` `getMin(findClosestUtil(node.left, k, ancestors, index + ``1``), ` `                ``findClosestUtil(node.right, k, ancestors, index + ``1``)); ` `  `  `    ``} ` `  `  `    ``// The main function that returns distance of the closest key to 'k'. It ` `    ``// mainly uses recursive function findClosestUtil() to find the closes ` `    ``// distance. ` `    ``int` `findClosest(Node node, ``char` `k)  ` `    ``{ ` `        ``// Create an array to store ancestors ` `        ``// Assumptiom: Maximum height of tree is 100 ` `        ``Node ancestors[] = ``new` `Node[``100``]; ` `  `  `        ``return` `findClosestUtil(node, k, ancestors, ``0``); ` `    ``} ` `  `  `    ``// Driver program to test for above functions ` `    ``public` `static` `void` `main(String args[])  ` `    ``{ ` `        ``BinaryTree tree = ``new` `BinaryTree(); ` `        ``tree.root = ``new` `Node(``'A'``); ` `        ``tree.root.left = ``new` `Node(``'B'``); ` `        ``tree.root.right = ``new` `Node(``'C'``); ` `        ``tree.root.right.left = ``new` `Node(``'E'``); ` `        ``tree.root.right.right = ``new` `Node(``'F'``); ` `        ``tree.root.right.left.left = ``new` `Node(``'G'``); ` `        ``tree.root.right.left.left.left = ``new` `Node(``'I'``); ` `        ``tree.root.right.left.left.right = ``new` `Node(``'J'``); ` `        ``tree.root.right.right.right = ``new` `Node(``'H'``); ` `        ``tree.root.right.right.right.left = ``new` `Node(``'H'``); ` `  `  `        ``char` `k = ``'H'``; ` `        ``System.out.println(``"Distace of the closest key from "` `+ k + ``" is "` `                            ``+ tree.findClosest(tree.root, k)); ` `        ``k = ``'C'``; ` `        ``System.out.println(``"Distace of the closest key from "` `+ k + ``" is "` `                            ``+ tree.findClosest(tree.root, k)); ` `        ``k = ``'E'``; ` `        ``System.out.println(``"Distace of the closest key from "` `+ k + ``" is "` `                            ``+ tree.findClosest(tree.root, k)); ` `        ``k = ``'B'``; ` `        ``System.out.println(``"Distace of the closest key from "` `+ k + ``" is "` `                             ``+ tree.findClosest(tree.root, k)); ` `  `  `    ``} ` `} ` `  `  `// This code has been contributed by Mayank Jaiswal `

## Python

 `# Python program to find closest leaf of a ` `# given key in binary tree ` ` `  `INT_MAX ``=` `2``*``*``32` ` `  `# A binary tree node ` `class` `Node: ` `    ``# Constructor to create a binary tree ` `    ``def` `__init__(``self` `,key): ` `        ``self``.key ``=` `key ` `        ``self``.left  ``=` `None` `        ``self``.right ``=` `None` ` `  `def` `closestDown(root): ` `    ``#Base Case ` `    ``if` `root ``is` `None``: ` `        ``return` `INT_MAX ` `    ``if` `root.left ``is` `None` `and` `root.right ``is` `None``: ` `        ``return` `0` `     `  `    ``# Return minum of left and right plus one ` `    ``return` `1` `+` `min``(closestDown(root.left), ` `                   ``closestDown(root.right)) ` ` `  `# Returns destance of the closes leaf to a given key k ` `# The array ancestors us used to keep track of ancestors ` `# of current node and 'index' is used to keep track of ` `# current index in 'ancestors[i]' ` `def` `findClosestUtil(root, k, ancestors, index): ` `    ``# Base Case  ` `    ``if` `root ``is` `None``: ` `        ``return` `INT_MAX ` `     `  `    ``# if key found ` `    ``if` `root.key ``=``=` `k: ` `        ``# Find closest leaf under the subtree rooted ` `        ``# with given key ` `        ``res ``=` `closestDown(root) ` `         `  `        ``# Traverse ll ancestors and update result if any ` `        ``# parent node gives smaller distance ` `        ``for` `i ``in` `reversed``(``range``(``0``,index)): ` `            ``res ``=` `min``(res, index``-``i``+``closestDown(ancestors[i])) ` `        ``return` `res ` ` `  `    ``# if key node found, store current node and recur for left ` `    ``# and right childrens ` `    ``ancestors[index] ``=` `root ` `    ``return` `min``( ` `        ``findClosestUtil(root.left, k,ancestors, index``+``1``), ` `        ``findClosestUtil(root.right, k, ancestors, index``+``1``)) ` ` `  `# The main function that return distance of the clses key to ` `# 'key'. It mainly uses recursive function findClosestUtil() ` `# to find the closes distance ` `def` `findClosest(root, k): ` `    ``# Create an arrray to store ancestors ` `    ``# Assumption: Maximum height of tree is 100 ` `    ``ancestors ``=` `[``None` `for` `i ``in` `range``(``100``)] ` ` `  `    ``return` `findClosestUtil(root, k, ancestors, ``0``) ` ` `  ` `  `# Driver program to test above function ` `root ``=` `Node(``'A'``) ` `root.left ``=` `Node(``'B'``) ` `root.right ``=` `Node(``'C'``); ` `root.right.left ``=` `Node(``'E'``); ` `root.right.right  ``=` `Node(``'F'``); ` `root.right.left.left ``=` `Node(``'G'``); ` `root.right.left.left.left  ``=` `Node(``'I'``); ` `root.right.left.left.right ``=` `Node(``'J'``); ` `root.right.right.right  ``=` `Node(``'H'``); ` `root.right.right.right.left ``=` `Node(``'K'``); ` ` `  `k ``=` `'H'``; ` `print` `"Distance of the closest key from "``+` `k ``+` `" is"``, ` `print` `findClosest(root, k) ` ` `  `k ``=` `'C'` `print` `"Distance of the closest key from "` `+` `k ``+` `" is"``, ` `print` `findClosest(root, k) ` ` `  `k ``=` `'E'` `print` `"Distance of the closest key from "` `+` `k ``+` `" is"``, ` `print` `findClosest(root, k) ` ` `  `k ``=` `'B'` `print` `"Distance of the closest key from "` `+` `k ``+` `" is"``, ` `print` `findClosest(root, k) ` ` `  `# This code is contributed by Nikhil Kumar Singh(nickzuck_007) `

## C#

 `using` `System; ` ` `  `// C# program to find closest leaf of a given key in Binary Tree  ` ` `  `/* Class containing left and right child of current   ` `   ``node and key value*/` `public` `class` `Node ` `{ ` `    ``public` `int` `data; ` `    ``public` `Node left, right; ` ` `  `    ``public` `Node(``int` `item) ` `    ``{ ` `        ``data = item; ` `        ``left = right = ``null``; ` `    ``} ` `} ` ` `  `public` `class` `BinaryTree ` `{ ` `    ``public` `Node root; ` ` `  `    ``// A utility function to find minimum of x and y  ` `    ``public` `virtual` `int` `getMin(``int` `x, ``int` `y) ` `    ``{ ` `        ``return` `(x < y) ? x : y; ` `    ``} ` ` `  `    ``// A utility function to find distance of closest leaf of the tree  ` `    ``// rooted under given root  ` `    ``public` `virtual` `int` `closestDown(Node node) ` `    ``{ ` `        ``// Base cases  ` `        ``if` `(node == ``null``) ` `        ``{ ` `            ``return` `int``.MaxValue; ` `        ``} ` `        ``if` `(node.left == ``null` `&& node.right == ``null``) ` `        ``{ ` `            ``return` `0; ` `        ``} ` ` `  `        ``// Return minimum of left and right, plus one  ` `        ``return` `1 + getMin(closestDown(node.left), closestDown(node.right)); ` `    ``} ` ` `  `    ``// Returns distance of the cloest leaf to a given key 'k'.  The array  ` `    ``// ancestors is used to keep track of ancestors of current node and  ` `    ``// 'index' is used to keep track of curremt index in 'ancestors[]'  ` `    ``public` `virtual` `int` `findClosestUtil(Node node, ``char` `k, Node[] ancestors, ``int` `index) ` `    ``{ ` `        ``// Base case  ` `        ``if` `(node == ``null``) ` `        ``{ ` `            ``return` `int``.MaxValue; ` `        ``} ` ` `  `        ``// If key found  ` `        ``if` `((``char``)node.data == k) ` `        ``{ ` `            ``//  Find the cloest leaf under the subtree rooted with given key  ` `            ``int` `res = closestDown(node); ` ` `  `            ``// Traverse all ancestors and update result if any parent node  ` `            ``// gives smaller distance  ` `            ``for` `(``int` `i = index - 1; i >= 0; i--) ` `            ``{ ` `                ``res = getMin(res, index - i + closestDown(ancestors[i])); ` `            ``} ` `            ``return` `res; ` `        ``} ` ` `  `        ``// If key node found, store current node and recur for left and  ` `        ``// right childrens  ` `        ``ancestors[index] = node; ` `        ``return` `getMin(findClosestUtil(node.left, k, ancestors, index + 1), findClosestUtil(node.right, k, ancestors, index + 1)); ` ` `  `    ``} ` ` `  `    ``// The main function that returns distance of the closest key to 'k'. It  ` `    ``// mainly uses recursive function findClosestUtil() to find the closes  ` `    ``// distance.  ` `    ``public` `virtual` `int` `findClosest(Node node, ``char` `k) ` `    ``{ ` `        ``// Create an array to store ancestors  ` `        ``// Assumptiom: Maximum height of tree is 100  ` `        ``Node[] ancestors = ``new` `Node; ` ` `  `        ``return` `findClosestUtil(node, k, ancestors, 0); ` `    ``} ` ` `  `    ``// Driver program to test for above functions  ` `    ``public` `static` `void` `Main(``string``[] args) ` `    ``{ ` `        ``BinaryTree tree = ``new` `BinaryTree(); ` `        ``tree.root = ``new` `Node(``'A'``); ` `        ``tree.root.left = ``new` `Node(``'B'``); ` `        ``tree.root.right = ``new` `Node(``'C'``); ` `        ``tree.root.right.left = ``new` `Node(``'E'``); ` `        ``tree.root.right.right = ``new` `Node(``'F'``); ` `        ``tree.root.right.left.left = ``new` `Node(``'G'``); ` `        ``tree.root.right.left.left.left = ``new` `Node(``'I'``); ` `        ``tree.root.right.left.left.right = ``new` `Node(``'J'``); ` `        ``tree.root.right.right.right = ``new` `Node(``'H'``); ` `        ``tree.root.right.right.right.left = ``new` `Node(``'H'``); ` ` `  `        ``char` `k = ``'H'``; ` `        ``Console.WriteLine(``"Distace of the closest key from "` `+ k + ``" is "` `+ tree.findClosest(tree.root, k)); ` `        ``k = ``'C'``; ` `        ``Console.WriteLine(``"Distace of the closest key from "` `+ k + ``" is "` `+ tree.findClosest(tree.root, k)); ` `        ``k = ``'E'``; ` `        ``Console.WriteLine(``"Distace of the closest key from "` `+ k + ``" is "` `+ tree.findClosest(tree.root, k)); ` `        ``k = ``'B'``; ` `        ``Console.WriteLine(``"Distace of the closest key from "` `+ k + ``" is "` `+ tree.findClosest(tree.root, k)); ` ` `  `    ``} ` `} ` ` `  `  ``//  This code is contributed by Shrikant13 `

Output:

```Distace of the closest key from H is 1
Distace of the closest key from C is 2
Distace of the closest key from E is 2
Distace of the closest key from B is 0 ```

The above code can be optimized by storing the left/right information also in ancestor array. The idea is, if given key is in left subtree of an ancestors, then there is no point to call closestDown(). Also, the loop can that traverses ancestors array can be optimized to not traverse ancestors which are at more distance than current result.

Exercise:
Extend the above solution to print not only distance, but the key of closest leaf also.

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