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Binary Search Tree | Set 2 (Delete)
• Difficulty Level : Medium
• Last Updated : 01 Apr, 2021

We have discussed BST search and insert operations. In this post, the delete operation is discussed. When we delete a node, three possibilities arise.
1) Node to be deleted is the leaf: Simply remove from the tree.

```              50                            50
/     \         delete(20)      /   \
30      70       --------->    30     70
/  \    /  \                     \    /  \
20   40  60   80                   40  60   80```

2) Node to be deleted has only one child: Copy the child to the node and delete the child

```              50                            50
/     \         delete(30)      /   \
30      70       --------->    40     70
\    /  \                          /  \
40  60   80                       60   80```

3) Node to be deleted has two children: Find inorder successor of the node. Copy contents of the inorder successor to the node and delete the inorder successor. Note that inorder predecessor can also be used.

```              50                            60
/     \         delete(50)      /   \
40      70       --------->    40    70
/  \                            \
60   80                           80```

The important thing to note is, inorder successor is needed only when the right child is not empty. In this particular case, inorder successor can be obtained by finding the minimum value in the right child of the node.

## Python3

 `/``/` `C``+``+` `program to demonstrate``/``/` `delete operation ``in` `binary``/``/` `search tree``#include ``using namespace std;` `struct node {``    ``int` `key;``    ``struct node ``*``left, ``*``right;``};` `/``/` `A utility function to create a new BST node``struct node``*` `newNode(``int` `item)``{``    ``struct node``*` `temp``        ``=` `(struct node``*``)malloc(sizeof(struct node));``    ``temp``-``>key ``=` `item;``    ``temp``-``>left ``=` `temp``-``>right ``=` `NULL;``    ``return` `temp;``}` `/``/` `A utility function to do``/``/` `inorder traversal of BST``void inorder(struct node``*` `root)``{``    ``if` `(root !``=` `NULL) {``        ``inorder(root``-``>left);``        ``cout << root``-``>key;``        ``inorder(root``-``>right);``    ``}``}` `/``*` `A utility function to``insert a new node with given key ``in`` ``*` `BST ``*``/``struct node``*` `insert(struct node``*` `node, ``int` `key)``{``    ``/``*` `If the tree ``is` `empty, ``return` `a new node ``*``/``    ``if` `(node ``=``=` `NULL)``        ``return` `newNode(key);` `    ``/``*` `Otherwise, recur down the tree ``*``/``    ``if` `(key < node``-``>key)``        ``node``-``>left ``=` `insert(node``-``>left, key);``    ``else``        ``node``-``>right ``=` `insert(node``-``>right, key);` `    ``/``*` `return` `the (unchanged) node pointer ``*``/``    ``return` `node;``}` `/``*` `Given a non``-``empty binary search tree, ``return` `the node``with minimum key value found ``in` `that tree. Note that the``entire tree does ``not` `need to be searched. ``*``/``struct node``*` `minValueNode(struct node``*` `node)``{``    ``struct node``*` `current ``=` `node;` `    ``/``*` `loop down to find the leftmost leaf ``*``/``    ``while` `(current && current``-``>left !``=` `NULL)``        ``current ``=` `current``-``>left;` `    ``return` `current;``}` `/``*` `Given a binary search tree ``and` `a key, this function``deletes the key ``and` `returns the new root ``*``/``struct node``*` `deleteNode(struct node``*` `root, ``int` `key)``{``    ``/``/` `base case``    ``if` `(root ``=``=` `NULL)``        ``return` `root;` `    ``/``/` `If the key to be deleted ``is``    ``/``/` `smaller than the root's``    ``/``/` `key, then it lies ``in` `left subtree``    ``if` `(key < root``-``>key)``        ``root``-``>left ``=` `deleteNode(root``-``>left, key);` `    ``/``/` `If the key to be deleted ``is``    ``/``/` `greater than the root's``    ``/``/` `key, then it lies ``in` `right subtree``    ``else` `if` `(key > root``-``>key)``        ``root``-``>right ``=` `deleteNode(root``-``>right, key);` `    ``/``/` `if` `key ``is` `same as root's key, then This ``is` `the node``    ``/``/` `to be deleted``    ``else` `{``        ``/``/` `node has no child``        ``if` `(root.left``=``=``NULL ``and` `root.right``=``=``NULL):``            ``return` `NULL``      ` `        ``/``/` `node with only one child ``or` `no child``        ``elif` `(root``-``>left ``=``=` `NULL) {``            ``struct node``*` `temp ``=` `root``-``>right;``            ``free(root);``            ``return` `temp;``        ``}``        ``else` `if` `(root``-``>right ``=``=` `NULL) {``            ``struct node``*` `temp ``=` `root``-``>left;``            ``free(root);``            ``return` `temp;``        ``}` `        ``/``/` `node with two children: Get the inorder successor``        ``/``/` `(smallest ``in` `the right subtree)``        ``struct node``*` `temp ``=` `minValueNode(root``-``>right);` `        ``/``/` `Copy the inorder successor's content to this node``        ``root``-``>key ``=` `temp``-``>key;` `        ``/``/` `Delete the inorder successor``        ``root``-``>right ``=` `deleteNode(root``-``>right, temp``-``>key);``    ``}``    ``return` `root;``}` `/``/` `Driver Code``int` `main()``{``    ``/``*` `Let us create following BST``            ``50``        ``/`     `\``        ``30`     `70``        ``/` `\ ``/` `\``    ``20` `40` `60` `80` `*``/``    ``struct node``*` `root ``=` `NULL;``    ``root ``=` `insert(root, ``50``);``    ``root ``=` `insert(root, ``30``);``    ``root ``=` `insert(root, ``20``);``    ``root ``=` `insert(root, ``40``);``    ``root ``=` `insert(root, ``70``);``    ``root ``=` `insert(root, ``60``);``    ``root ``=` `insert(root, ``80``);` `    ``cout << ``"Inorder traversal of the given tree \n"``;``    ``inorder(root);` `    ``cout << ``"\nDelete 20\n"``;``    ``root ``=` `deleteNode(root, ``20``);``    ``cout << ``"Inorder traversal of the modified tree \n"``;``    ``inorder(root);` `    ``cout << ``"\nDelete 30\n"``;``    ``root ``=` `deleteNode(root, ``30``);``    ``cout << ``"Inorder traversal of the modified tree \n"``;``    ``inorder(root);` `    ``cout << ``"\nDelete 50\n"``;``    ``root ``=` `deleteNode(root, ``50``);``    ``cout << ``"Inorder traversal of the modified tree \n"``;``    ``inorder(root);` `    ``return` `0``;``}` `/``/` `This code ``is` `contributed by shivanisinghss2110`

## C

 `// C program to demonstrate``// delete operation in binary``// search tree``#include ``#include ` `struct` `node {``    ``int` `key;``    ``struct` `node *left, *right;``};` `// A utility function to create a new BST node``struct` `node* newNode(``int` `item)``{``    ``struct` `node* temp``        ``= (``struct` `node*)``malloc``(``sizeof``(``struct` `node));``    ``temp->key = item;``    ``temp->left = temp->right = NULL;``    ``return` `temp;``}` `// A utility function to do inorder traversal of BST``void` `inorder(``struct` `node* root)``{``    ``if` `(root != NULL) {``        ``inorder(root->left);``        ``printf``(``"%d "``, root->key);``        ``inorder(root->right);``    ``}``}` `/* A utility function to``   ``insert a new node with given key in`` ``* BST */``struct` `node* insert(``struct` `node* node, ``int` `key)``{``    ``/* If the tree is empty, return a new node */``    ``if` `(node == NULL)``        ``return` `newNode(key);` `    ``/* Otherwise, recur down the tree */``    ``if` `(key < node->key)``        ``node->left = insert(node->left, key);``    ``else``        ``node->right = insert(node->right, key);` `    ``/* return the (unchanged) node pointer */``    ``return` `node;``}` `/* Given a non-empty binary search``   ``tree, return the node``   ``with minimum key value found in``   ``that tree. Note that the``   ``entire tree does not need to be searched. */``struct` `node* minValueNode(``struct` `node* node)``{``    ``struct` `node* current = node;` `    ``/* loop down to find the leftmost leaf */``    ``while` `(current && current->left != NULL)``        ``current = current->left;` `    ``return` `current;``}` `/* Given a binary search tree``   ``and a key, this function``   ``deletes the key and``   ``returns the new root */``struct` `node* deleteNode(``struct` `node* root, ``int` `key)``{``    ``// base case``    ``if` `(root == NULL)``        ``return` `root;` `    ``// If the key to be deleted``    ``// is smaller than the root's``    ``// key, then it lies in left subtree``    ``if` `(key < root->key)``        ``root->left = deleteNode(root->left, key);` `    ``// If the key to be deleted``    ``// is greater than the root's``    ``// key, then it lies in right subtree``    ``else` `if` `(key > root->key)``        ``root->right = deleteNode(root->right, key);` `    ``// if key is same as root's key,``    ``// then This is the node``    ``// to be deleted``    ``else` `{``        ``// node with only one child or no child``        ``if` `(root->left == NULL) {``            ``struct` `node* temp = root->right;``            ``free``(root);``            ``return` `temp;``        ``}``        ``else` `if` `(root->right == NULL) {``            ``struct` `node* temp = root->left;``            ``free``(root);``            ``return` `temp;``        ``}` `        ``// node with two children:``        ``// Get the inorder successor``        ``// (smallest in the right subtree)``        ``struct` `node* temp = minValueNode(root->right);` `        ``// Copy the inorder``        ``// successor's content to this node``        ``root->key = temp->key;` `        ``// Delete the inorder successor``        ``root->right = deleteNode(root->right, temp->key);``    ``}``    ``return` `root;``}` `// Driver Code``int` `main()``{``    ``/* Let us create following BST``              ``50``           ``/     \``          ``30      70``         ``/  \    /  \``       ``20   40  60   80 */``    ``struct` `node* root = NULL;``    ``root = insert(root, 50);``    ``root = insert(root, 30);``    ``root = insert(root, 20);``    ``root = insert(root, 40);``    ``root = insert(root, 70);``    ``root = insert(root, 60);``    ``root = insert(root, 80);` `    ``printf``(``"Inorder traversal of the given tree \n"``);``    ``inorder(root);` `    ``printf``(``"\nDelete 20\n"``);``    ``root = deleteNode(root, 20);``    ``printf``(``"Inorder traversal of the modified tree \n"``);``    ``inorder(root);` `    ``printf``(``"\nDelete 30\n"``);``    ``root = deleteNode(root, 30);``    ``printf``(``"Inorder traversal of the modified tree \n"``);``    ``inorder(root);` `    ``printf``(``"\nDelete 50\n"``);``    ``root = deleteNode(root, 50);``    ``printf``(``"Inorder traversal of the modified tree \n"``);``    ``inorder(root);` `    ``return` `0;``}`

## Java

 `// Java program to demonstrate``// delete operation in binary``// search tree``class` `BinarySearchTree {``    ``/* Class containing left``    ``and right child of current node``     ``* and key value*/``    ``class` `Node {``        ``int` `key;``        ``Node left, right;` `        ``public` `Node(``int` `item)``        ``{``            ``key = item;``            ``left = right = ``null``;``        ``}``    ``}` `    ``// Root of BST``    ``Node root;` `    ``// Constructor``    ``BinarySearchTree() { root = ``null``; }` `    ``// This method mainly calls deleteRec()``    ``void` `deleteKey(``int` `key) { root = deleteRec(root, key); }` `    ``/* A recursive function to``      ``delete an existing key in BST``     ``*/``    ``Node deleteRec(Node root, ``int` `key)``    ``{``        ``/* Base Case: If the tree is empty */``        ``if` `(root == ``null``)``            ``return` `root;` `        ``/* Otherwise, recur down the tree */``        ``if` `(key < root.key)``            ``root.left = deleteRec(root.left, key);``        ``else` `if` `(key > root.key)``            ``root.right = deleteRec(root.right, key);` `        ``// if key is same as root's``        ``// key, then This is the``        ``// node to be deleted``        ``else` `{``            ``// node with only one child or no child``            ``if` `(root.left == ``null``)``                ``return` `root.right;``            ``else` `if` `(root.right == ``null``)``                ``return` `root.left;` `            ``// node with two children: Get the inorder``            ``// successor (smallest in the right subtree)``            ``root.key = minValue(root.right);` `            ``// Delete the inorder successor``            ``root.right = deleteRec(root.right, root.key);``        ``}` `        ``return` `root;``    ``}` `    ``int` `minValue(Node root)``    ``{``        ``int` `minv = root.key;``        ``while` `(root.left != ``null``)``        ``{``            ``minv = root.left.key;``            ``root = root.left;``        ``}``        ``return` `minv;``    ``}` `    ``// This method mainly calls insertRec()``    ``void` `insert(``int` `key) { root = insertRec(root, key); }` `    ``/* A recursive function to``       ``insert a new key in BST */``    ``Node insertRec(Node root, ``int` `key)``    ``{` `        ``/* If the tree is empty,``          ``return a new node */``        ``if` `(root == ``null``) {``            ``root = ``new` `Node(key);``            ``return` `root;``        ``}` `        ``/* Otherwise, recur down the tree */``        ``if` `(key < root.key)``            ``root.left = insertRec(root.left, key);``        ``else` `if` `(key > root.key)``            ``root.right = insertRec(root.right, key);` `        ``/* return the (unchanged) node pointer */``        ``return` `root;``    ``}` `    ``// This method mainly calls InorderRec()``    ``void` `inorder() { inorderRec(root); }` `    ``// A utility function to do inorder traversal of BST``    ``void` `inorderRec(Node root)``    ``{``        ``if` `(root != ``null``) {``            ``inorderRec(root.left);``            ``System.out.print(root.key + ``" "``);``            ``inorderRec(root.right);``        ``}``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``BinarySearchTree tree = ``new` `BinarySearchTree();` `        ``/* Let us create following BST``              ``50``           ``/     \``          ``30      70``         ``/  \    /  \``        ``20   40  60   80 */``        ``tree.insert(``50``);``        ``tree.insert(``30``);``        ``tree.insert(``20``);``        ``tree.insert(``40``);``        ``tree.insert(``70``);``        ``tree.insert(``60``);``        ``tree.insert(``80``);` `        ``System.out.println(``            ``"Inorder traversal of the given tree"``);``        ``tree.inorder();` `        ``System.out.println(``"\nDelete 20"``);``        ``tree.deleteKey(``20``);``        ``System.out.println(``            ``"Inorder traversal of the modified tree"``);``        ``tree.inorder();` `        ``System.out.println(``"\nDelete 30"``);``        ``tree.deleteKey(``30``);``        ``System.out.println(``            ``"Inorder traversal of the modified tree"``);``        ``tree.inorder();` `        ``System.out.println(``"\nDelete 50"``);``        ``tree.deleteKey(``50``);``        ``System.out.println(``            ``"Inorder traversal of the modified tree"``);``        ``tree.inorder();``    ``}``}`

## Python

 `# Python program to demonstrate delete operation``# in binary search tree` `# A Binary Tree Node`  `class` `Node:` `    ``# Constructor to create a new node``    ``def` `__init__(``self``, key):``        ``self``.key ``=` `key``        ``self``.left ``=` `None``        ``self``.right ``=` `None`  `# A utility function to do inorder traversal of BST``def` `inorder(root):``    ``if` `root ``is` `not` `None``:``        ``inorder(root.left)``        ``print` `root.key,``        ``inorder(root.right)`  `# A utility function to insert a``# new node with given key in BST``def` `insert(node, key):` `    ``# If the tree is empty, return a new node``    ``if` `node ``is` `None``:``        ``return` `Node(key)` `    ``# Otherwise recur down the tree``    ``if` `key < node.key:``        ``node.left ``=` `insert(node.left, key)``    ``else``:``        ``node.right ``=` `insert(node.right, key)` `    ``# return the (unchanged) node pointer``    ``return` `node` `# Given a non-empty binary``# search tree, return the node``# with minum key value``# found in that tree. Note that the``# entire tree does not need to be searched`  `def` `minValueNode(node):``    ``current ``=` `node` `    ``# loop down to find the leftmost leaf``    ``while``(current.left ``is` `not` `None``):``        ``current ``=` `current.left` `    ``return` `current` `# Given a binary search tree and a key, this function``# delete the key and returns the new root`  `def` `deleteNode(root, key):` `    ``# Base Case``    ``if` `root ``is` `None``:``        ``return` `root` `    ``# If the key to be deleted``    ``# is smaller than the root's``    ``# key then it lies in  left subtree``    ``if` `key < root.key:``        ``root.left ``=` `deleteNode(root.left, key)` `    ``# If the kye to be delete``    ``# is greater than the root's key``    ``# then it lies in right subtree``    ``elif``(key > root.key):``        ``root.right ``=` `deleteNode(root.right, key)` `    ``# If key is same as root's key, then this is the node``    ``# to be deleted``    ``else``:` `        ``# Node with only one child or no child``        ``if` `root.left ``is` `None``:``            ``temp ``=` `root.right``            ``root ``=` `None``            ``return` `temp` `        ``elif` `root.right ``is` `None``:``            ``temp ``=` `root.left``            ``root ``=` `None``            ``return` `temp` `        ``# Node with two children:``        ``# Get the inorder successor``        ``# (smallest in the right subtree)``        ``temp ``=` `minValueNode(root.right)` `        ``# Copy the inorder successor's``        ``# content to this node``        ``root.key ``=` `temp.key` `        ``# Delete the inorder successor``        ``root.right ``=` `deleteNode(root.right, temp.key)` `    ``return` `root`  `# Driver code``""" Let us create following BST``              ``50``           ``/     \``          ``30      70``         ``/  \    /  \``       ``20   40  60   80 """` `root ``=` `None``root ``=` `insert(root, ``50``)``root ``=` `insert(root, ``30``)``root ``=` `insert(root, ``20``)``root ``=` `insert(root, ``40``)``root ``=` `insert(root, ``70``)``root ``=` `insert(root, ``60``)``root ``=` `insert(root, ``80``)` `print` `"Inorder traversal of the given tree"``inorder(root)` `print` `"\nDelete 20"``root ``=` `deleteNode(root, ``20``)``print` `"Inorder traversal of the modified tree"``inorder(root)` `print` `"\nDelete 30"``root ``=` `deleteNode(root, ``30``)``print` `"Inorder traversal of the modified tree"``inorder(root)` `print` `"\nDelete 50"``root ``=` `deleteNode(root, ``50``)``print` `"Inorder traversal of the modified tree"``inorder(root)` `# This code is contributed by Nikhil Kumar Singh(nickzuck_007)`

## C#

 `// C# program to demonstrate delete``// operation in binary search tree``using` `System;` `public` `class` `BinarySearchTree {``    ``/* Class containing left and right``    ``child of current node and key value*/``    ``class` `Node {``        ``public` `int` `key;``        ``public` `Node left, right;` `        ``public` `Node(``int` `item)``        ``{``            ``key = item;``            ``left = right = ``null``;``        ``}``    ``}` `    ``// Root of BST``    ``Node root;` `    ``// Constructor``    ``BinarySearchTree() { root = ``null``; }` `    ``// This method mainly calls deleteRec()``    ``void` `deleteKey(``int` `key) { root = deleteRec(root, key); }` `    ``/* A recursive function to``      ``delete an existing key in BST``     ``*/``    ``Node deleteRec(Node root, ``int` `key)``    ``{``        ``/* Base Case: If the tree is empty */``        ``if` `(root == ``null``)``            ``return` `root;` `        ``/* Otherwise, recur down the tree */``        ``if` `(key < root.key)``            ``root.left = deleteRec(root.left, key);``        ``else` `if` `(key > root.key)``            ``root.right = deleteRec(root.right, key);` `        ``// if key is same as root's key, then This is the``        ``// node to be deleted``        ``else` `{``            ``// node with only one child or no child``            ``if` `(root.left == ``null``)``                ``return` `root.right;``            ``else` `if` `(root.right == ``null``)``                ``return` `root.left;` `            ``// node with two children: Get the``            ``// inorder successor (smallest``            ``// in the right subtree)``            ``root.key = minValue(root.right);` `            ``// Delete the inorder successor``            ``root.right = deleteRec(root.right, root.key);``        ``}``        ``return` `root;``    ``}` `    ``int` `minValue(Node root)``    ``{``        ``int` `minv = root.key;``        ``while` `(root.left != ``null``) {``            ``minv = root.left.key;``            ``root = root.left;``        ``}``        ``return` `minv;``    ``}` `    ``// This method mainly calls insertRec()``    ``void` `insert(``int` `key) { root = insertRec(root, key); }` `    ``/* A recursive function to insert a new key in BST */``    ``Node insertRec(Node root, ``int` `key)``    ``{` `        ``/* If the tree is empty, return a new node */``        ``if` `(root == ``null``) {``            ``root = ``new` `Node(key);``            ``return` `root;``        ``}` `        ``/* Otherwise, recur down the tree */``        ``if` `(key < root.key)``            ``root.left = insertRec(root.left, key);``        ``else` `if` `(key > root.key)``            ``root.right = insertRec(root.right, key);` `        ``/* return the (unchanged) node pointer */``        ``return` `root;``    ``}` `    ``// This method mainly calls InorderRec()``    ``void` `inorder() { inorderRec(root); }` `    ``// A utility function to do inorder traversal of BST``    ``void` `inorderRec(Node root)``    ``{``        ``if` `(root != ``null``) {``            ``inorderRec(root.left);``            ``Console.Write(root.key + ``" "``);``            ``inorderRec(root.right);``        ``}``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``BinarySearchTree tree = ``new` `BinarySearchTree();` `        ``/* Let us create following BST``            ``50``        ``/ \``        ``30 70``        ``/ \ / \``        ``20 40 60 80 */``        ``tree.insert(50);``        ``tree.insert(30);``        ``tree.insert(20);``        ``tree.insert(40);``        ``tree.insert(70);``        ``tree.insert(60);``        ``tree.insert(80);` `        ``Console.WriteLine(``            ``"Inorder traversal of the given tree"``);``        ``tree.inorder();` `        ``Console.WriteLine(``"\nDelete 20"``);``        ``tree.deleteKey(20);``        ``Console.WriteLine(``            ``"Inorder traversal of the modified tree"``);``        ``tree.inorder();` `        ``Console.WriteLine(``"\nDelete 30"``);``        ``tree.deleteKey(30);``        ``Console.WriteLine(``            ``"Inorder traversal of the modified tree"``);``        ``tree.inorder();` `        ``Console.WriteLine(``"\nDelete 50"``);``        ``tree.deleteKey(50);``        ``Console.WriteLine(``            ``"Inorder traversal of the modified tree"``);``        ``tree.inorder();``    ``}``}` `// This code has been contributed``// by PrinciRaj1992`

Output:

```Inorder traversal of the given tree
20 30 40 50 60 70 80
Delete 20
Inorder traversal of the modified tree
30 40 50 60 70 80
Delete 30
Inorder traversal of the modified tree
40 50 60 70 80
Delete 50
Inorder traversal of the modified tree
40 60 70 80```

Illustration:  Time Complexity: The worst case time complexity of delete operation is O(h) where h is the height of the Binary Search Tree. In worst case, we may have to travel from the root to the deepest leaf node. The height of a skewed tree may become n and the time complexity of delete operation may become O(n)

Optimization to above code for two children case :
In the above recursive code, we recursively call delete() for the successor. We can avoid recursive calls by keeping track of the parent node of the successor so that we can simply remove the successor by making the child of a parent NULL. We know that the successor would always be a leaf node.

## C++

 `// C++ program to implement optimized delete in BST.``#include ``using` `namespace` `std;` `struct` `Node {``    ``int` `key;``    ``struct` `Node *left, *right;``};` `// A utility function to create a new BST node``Node* newNode(``int` `item)``{``    ``Node* temp = ``new` `Node;``    ``temp->key = item;``    ``temp->left = temp->right = NULL;``    ``return` `temp;``}` `// A utility function to do inorder traversal of BST``void` `inorder(Node* root)``{``    ``if` `(root != NULL) {``        ``inorder(root->left);``        ``printf``(``"%d "``, root->key);``        ``inorder(root->right);``    ``}``}` `/* A utility function to insert a new node with given key in`` ``* BST */``Node* insert(Node* node, ``int` `key)``{``    ``/* If the tree is empty, return a new node */``    ``if` `(node == NULL)``        ``return` `newNode(key);` `    ``/* Otherwise, recur down the tree */``    ``if` `(key < node->key)``        ``node->left = insert(node->left, key);``    ``else``        ``node->right = insert(node->right, key);` `    ``/* return the (unchanged) node pointer */``    ``return` `node;``}` `/* Given a binary search tree and a key, this function``   ``deletes the key and returns the new root */``Node* deleteNode(Node* root, ``int` `k)``{``    ``// Base case``    ``if` `(root == NULL)``        ``return` `root;` `    ``// Recursive calls for ancestors of``    ``// node to be deleted``    ``if` `(root->key > k) {``        ``root->left = deleteNode(root->left, k);``        ``return` `root;``    ``}``    ``else` `if` `(root->key < k) {``        ``root->right = deleteNode(root->right, k);``        ``return` `root;``    ``}` `    ``// We reach here when root is the node``    ``// to be deleted.` `    ``// If one of the children is empty``    ``if` `(root->left == NULL) {``        ``Node* temp = root->right;``        ``delete` `root;``        ``return` `temp;``    ``}``    ``else` `if` `(root->right == NULL) {``        ``Node* temp = root->left;``        ``delete` `root;``        ``return` `temp;``    ``}` `    ``// If both children exist``    ``else` `{` `        ``Node* succParent = root;` `        ``// Find successor``        ``Node* succ = root->right;``        ``while` `(succ->left != NULL) {``            ``succParent = succ;``            ``succ = succ->left;``        ``}` `        ``// Delete successor.  Since successor``        ``// is always left child of its parent``        ``// we can safely make successor's right``        ``// right child as left of its parent.``        ``// If there is no succ, then assign``        ``// succ->right to succParent->right``        ``if` `(succParent != root)``            ``succParent->left = succ->right;``        ``else``            ``succParent->right = succ->right;` `        ``// Copy Successor Data to root``        ``root->key = succ->key;` `        ``// Delete Successor and return root``        ``delete` `succ;``        ``return` `root;``    ``}``}` `// Driver Code``int` `main()``{``    ``/* Let us create following BST``              ``50``           ``/     \``          ``30      70``         ``/  \    /  \``       ``20   40  60   80 */``    ``Node* root = NULL;``    ``root = insert(root, 50);``    ``root = insert(root, 30);``    ``root = insert(root, 20);``    ``root = insert(root, 40);``    ``root = insert(root, 70);``    ``root = insert(root, 60);``    ``root = insert(root, 80);` `    ``printf``(``"Inorder traversal of the given tree \n"``);``    ``inorder(root);` `    ``printf``(``"\nDelete 20\n"``);``    ``root = deleteNode(root, 20);``    ``printf``(``"Inorder traversal of the modified tree \n"``);``    ``inorder(root);` `    ``printf``(``"\nDelete 30\n"``);``    ``root = deleteNode(root, 30);``    ``printf``(``"Inorder traversal of the modified tree \n"``);``    ``inorder(root);` `    ``printf``(``"\nDelete 50\n"``);``    ``root = deleteNode(root, 50);``    ``printf``(``"Inorder traversal of the modified tree \n"``);``    ``inorder(root);` `    ``return` `0;``}`

## Python3

 `# Python3 program to implement``# optimized delete in BST.` `class` `Node:` `    ``# Constructor to create a new node``    ``def` `__init__(``self``, key):``        ``self``.key ``=` `key``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `# A utility function to do``# inorder traversal of BST``def` `inorder(root):``    ``if` `root ``is` `not` `None``:``        ``inorder(root.left)``        ``print``(root.key, end``=``" "``)``        ``inorder(root.right)` `# A utility function to insert a``# new node with given key in BST``def` `insert(node, key):` `    ``# If the tree is empty,``    ``# return a new node``    ``if` `node ``is` `None``:``        ``return` `Node(key)` `    ``# Otherwise recur down the tree``    ``if` `key < node.key:``        ``node.left ``=` `insert(node.left, key)``    ``else``:``        ``node.right ``=` `insert(node.right, key)` `    ``# return the (unchanged) node pointer``    ``return` `node`  `# Given a binary search tree``# and a key, this function``# delete the key and returns the new root``def` `deleteNode(root, key):` `    ``# Base Case``    ``if` `root ``is` `None``:``        ``return` `root` `    ``# Recursive calls for ancestors of``    ``# node to be deleted``    ``if` `key < root.key:``        ``root.left ``=` `deleteNode(root.left, key)``        ``return` `root` `    ``elif``(key > root.key):``        ``root.right ``=` `deleteNode(root.right, key)``        ``return` `root` `    ``# We reach here when root is the node``    ``# to be deleted.``    ` `    ``# If root node is a leaf node``    ` `    ``if` `root.left ``is` `None` `and` `root.right ``is` `None``:``          ``return` `None` `    ``# If one of the children is empty` `    ``if` `root.left ``is` `None``:``        ``temp ``=` `root.right``        ``root ``=` `None``        ``return` `temp` `    ``elif` `root.right ``is` `None``:``        ``temp ``=` `root.left``        ``root ``=` `None``        ``return` `temp` `    ``# If both children exist` `    ``succParent ``=` `root` `    ``# Find Successor` `    ``succ ``=` `root.right` `    ``while` `succ.left !``=` `None``:``        ``succParent ``=` `succ``        ``succ ``=` `succ.left` `    ``# Delete successor.Since successor``    ``# is always left child of its parent``    ``# we can safely make successor's right``    ``# right child as left of its parent.``    ``# If there is no succ, then assign``    ``# succ->right to succParent->right``    ``if` `succParent !``=` `root:``        ``succParent.left ``=` `succ.right``    ``else``:``        ``succParent.right ``=` `succ.right` `    ``# Copy Successor Data to root` `    ``root.key ``=` `succ.key` `    ``return` `root`  `# Driver code``""" Let us create following BST``              ``50``           ``/     \``          ``30      70``         ``/  \    /  \``       ``20   40  60   80 """` `root ``=` `None``root ``=` `insert(root, ``50``)``root ``=` `insert(root, ``30``)``root ``=` `insert(root, ``20``)``root ``=` `insert(root, ``40``)``root ``=` `insert(root, ``70``)``root ``=` `insert(root, ``60``)``root ``=` `insert(root, ``80``)` `print``(``"Inorder traversal of the given tree"``)``inorder(root)` `print``(``"\nDelete 20"``)``root ``=` `deleteNode(root, ``20``)``print``(``"Inorder traversal of the modified tree"``)``inorder(root)` `print``(``"\nDelete 30"``)``root ``=` `deleteNode(root, ``30``)``print``(``"Inorder traversal of the modified tree"``)``inorder(root)` `print``(``"\nDelete 50"``)``root ``=` `deleteNode(root, ``50``)``print``(``"Inorder traversal of the modified tree"``)``inorder(root)` `# This code is contributed by Shivam Bhat (shivambhat45)`
Output
```Inorder traversal of the given tree
20 30 40 50 60 70 80
Delete 20
Inorder traversal of the modified tree
30 40 50 60 70 80
Delete 30
Inorder traversal of the modified tree
40 50 60 70 80
Delete 50
Inorder traversal of the modified tree
40 60 70 80 ```

Thanks to wolffgang010 for suggesting the above optimization.
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