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# Deletion in Binary Search Tree

We have discussed BST search and insert operations. In this post, the delete operation is discussed. When we delete a node, three possibilities arise.

### Node to be deleted is the leaf:

Simply remove it from the tree.

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

### Node to be deleted has only one child:

Copy the child to the node and delete the node.

Deletion of node with only one child

### Node to be deleted has two children:

Find the inorder successor of the node. Copy contents of the inorder successor to the node and delete the inorder successor.

Note: Inorder predecessor can also be used.

Deletion of node with two children

Note: Inorder successor is needed only when the right child is not empty. In this particular case, the inorder successor can be obtained by finding the minimum value in the right child of the node.

Recommended Practice

### Steps to delete a node from BST:

Follow the below steps to solve the problem:

• Create a recursive function (say deleteNode) which returns the correct node that will be in the position.
• If the root is NULL, then return root (Base case)
• If the key is less than the root’s value, then set root->left = deleteNode(root->left, key)
• If the key is greater than the root’s value, then set root->right = deleteNode(root->right, key)
• Else check
• If the root is a leaf node then return null
• Else if it has only the left child, then return the left child
• Else if it has only the right child, then return the right child
• Otherwise, set the value of root as of its inorder successor and recur to delete the node with the value of the inorder successor.

Below is the implementation of the above approach:

## C++

 `// 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` `        ``else` `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);`   `    ``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`   `import` `java.io.*;`   `public` `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();` `    ``}` `}`

## Python3

 `# 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, 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 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`     `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`

## Javascript

 ``

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 ```

Time Complexity: O(logN), where N is the number of nodes of the BST
Auxiliary Space: O(h), h is the height of the BST and O(N), in the worst case

### Optimized approach for two children case:

We recursively call delete() for the successor in the above recursive code. 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.

Below is the implementation of the above approach:

## 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``(``"\n\nDelete 20\n"``);` `    ``root = deleteNode(root, 20);` `    ``printf``(``"Inorder traversal of the modified tree \n"``);` `    ``inorder(root);`   `    ``printf``(``"\n\nDelete 30\n"``);` `    ``root = deleteNode(root, 30);` `    ``printf``(``"Inorder traversal of the modified tree \n"``);` `    ``inorder(root);`   `    ``printf``(``"\n\nDelete 50\n"``);` `    ``root = deleteNode(root, 50);` `    ``printf``(``"Inorder traversal of the modified tree \n"``);` `    ``inorder(root);`   `    ``return` `0;` `}`

## Java

 `// Java program to implement optimized delete in BST.` `import` `java.util.*;`   `class` `GFG {`   `    ``static` `class` `Node {` `        ``int` `key;` `        ``Node left, right;` `    ``}`   `    ``// A utility function to create a new BST node` `    ``static` `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` `    ``static` `void` `inorder(Node root)` `    ``{` `        ``if` `(root != ``null``) {` `            ``inorder(root.left);` `            ``System.out.print(root.key + ``" "``);` `            ``inorder(root.right);` `        ``}` `    ``}`   `    ``// A utility function to insert a new node` `    ``// with given key in BST` `    ``static` `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` `    ``static` `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;` `            ``return` `temp;` `        ``}` `        ``else` `if` `(root.right == ``null``) {` `            ``Node temp = root.left;` `            ``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;`   `            ``return` `root;` `        ``}` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String args[])` `    ``{`   `        ``/* 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``);`   `        ``System.out.println(``"Inorder traversal of the "` `                           ``+ ``"given tree"``);` `        ``inorder(root);`   `        ``System.out.println(``"\nDelete 20\n"``);` `        ``root = deleteNode(root, ``20``);` `        ``System.out.println(``"Inorder traversal of the "` `                           ``+ ``"modified tree"``);` `        ``inorder(root);`   `        ``System.out.println(``"\nDelete 30\n"``);` `        ``root = deleteNode(root, ``30``);` `        ``System.out.println(``"Inorder traversal of the "` `                           ``+ ``"modified tree"``);` `        ``inorder(root);`   `        ``System.out.println(``"\nDelete 50\n"``);` `        ``root = deleteNode(root, ``50``);` `        ``System.out.println(``"Inorder traversal of the "` `                           ``+ ``"modified tree"``);` `        ``inorder(root);` `    ``}` `}`   `// This code is contributed by adityapande88`

## 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``(``"\n\nDelete 20"``)` `root ``=` `deleteNode(root, ``20``)` `print``(``"Inorder traversal of the modified tree"``)` `inorder(root)`   `print``(``"\n\nDelete 30"``)` `root ``=` `deleteNode(root, ``30``)` `print``(``"Inorder traversal of the modified tree"``)` `inorder(root)`   `print``(``"\n\nDelete 50"``)` `root ``=` `deleteNode(root, ``50``)` `print``(``"Inorder traversal of the modified tree"``)` `inorder(root)`   `# This code is contributed by Shivam Bhat (shivambhat45)`

## C#

 `// C# program to implement optimized delete in BST.` `using` `System;`   `class` `GFG {`   `    ``class` `Node {` `        ``public` `int` `key;` `        ``public` `Node left, right;` `    ``}`   `    ``// A utility function to create a new BST node` `    ``static` `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` `    ``static` `void` `inorder(Node root)` `    ``{` `        ``if` `(root != ``null``) {` `            ``inorder(root.left);` `            ``Console.Write(root.key + ``" "``);` `            ``inorder(root.right);` `        ``}` `    ``}`   `    ``// A utility function to insert a new node` `    ``// with given key in BST` `    ``static` `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` `    ``static` `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;` `            ``return` `temp;` `        ``}` `        ``else` `if` `(root.right == ``null``) {` `            ``Node temp = root.left;` `            ``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;`   `            ``return` `root;` `        ``}` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main(String[] args)` `    ``{`   `        ``/* 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);`   `        ``Console.WriteLine(``"Inorder traversal of the "` `                          ``+ ``"given tree"``);` `        ``inorder(root);`   `        ``Console.WriteLine(``"\nDelete 20\n"``);` `        ``root = deleteNode(root, 20);` `        ``Console.WriteLine(``"Inorder traversal of the "` `                          ``+ ``"modified tree"``);` `        ``inorder(root);`   `        ``Console.WriteLine(``"\nDelete 30\n"``);` `        ``root = deleteNode(root, 30);` `        ``Console.WriteLine(``"Inorder traversal of the "` `                          ``+ ``"modified tree"``);` `        ``inorder(root);`   `        ``Console.WriteLine(``"\nDelete 50\n"``);` `        ``root = deleteNode(root, 50);` `        ``Console.WriteLine(``"Inorder traversal of the "` `                          ``+ ``"modified tree"``);` `        ``inorder(root);` `    ``}` `}`   `// This code is contributed by shivanisinghss2110`

## Javascript

 ``

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 ```

Time Complexity: O(h), where h is the height of the BST.
Auxiliary Space: O(n).

Thanks to wolffgang010 for suggesting the above optimization.