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.

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 <bits/stdc++.h>
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 <stdio.h>
#include <stdlib.h>

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

<script>
// Javascript program to demonstrate
// delete operation in binary
// search tree
class Node
{
    constructor(item)
    {
        this.key = item;
        this.left = this.right = null;
    }
}

// Root of BST
let root=null;

// This method mainly calls deleteRec()
function deleteKey(key)
{
    root = deleteRec(root, key);
}

/* A recursive function to
      delete an existing key in BST
     */
function deleteRec(root,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;
}

function minValue(root)
{
    let minv = root.key;
        while (root.left != null)
        {
            minv = root.left.key;
            root = root.left;
        }
        return minv;
}

// This method mainly calls insertRec()
function insert(key)
{
    root = insertRec(root, key);
}

/* A recursive function to
       insert a new key in BST */
function insertRec(root,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()
function inorder()
{
    inorderRec(root);
}

// A utility function to do inorder traversal of BST
function inorderRec(root)
{
    if (root != null) {
            inorderRec(root.left);
            document.write(root.key + " ");
            inorderRec(root.right);
        }
}

// Driver Code
/* Let us create following BST
              50
           /     \
          30      70
         /  \    /  \
        20   40  60   80 */
insert(50);
insert(30);
insert(20);
insert(40);
insert(70);
insert(60);
insert(80);

document.write(
"Inorder traversal of the given tree<br>");
inorder();

document.write("<br>Delete 20<br>");
deleteKey(20);
document.write(
"Inorder traversal of the modified tree<br>");
inorder();

document.write("<br>Delete 30<br>");
deleteKey(30);
document.write(
"Inorder traversal of the modified tree<br>");
inorder();

document.write("<br>Delete 50<br>");
deleteKey(50);
document.write(
"Inorder traversal of the modified tree<br>");
inorder();

// This code is contributed by avanitrachhadiya2155
</script>

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 <bits/stdc++.h>
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

<script>
// javascript program to implement optimized delete in BST.

class Node {
    constructor(val) {
        this.key = val;
        this.left = null;
        this.right = null;
    }
}
    // A utility function to create a new BST node
    function newNode(item) {
var temp = new Node();
        temp.key = item;
        temp.left = temp.right = null;
        return temp;
    }

    // A utility function to do inorder traversal of BST
    function inorder(root) {
        if (root != null) {
            inorder(root.left);
            document.write(root.key + " ");
            inorder(root.right);
        }
    }

    // A utility function to insert a new node
    // with given key in BST
    function insert(node , 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
    function deleteNode(root , 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) {
    var temp = root.right;
            return temp;
        } else if (root.right == null) {
    var temp = root.left;
            return temp;
        }

        // If both children exist
        else {
    var succParent = root;

            // Find successor
    var 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


        /*
         * Let us create following BST
         50
         / \
       30  70
      / \  / \
     20 40 60 80
         */
var 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);

        document.write("Inorder traversal of the " + "given tree<br/>");
        inorder(root);

        document.write("<br/>Delete 20<br/>");
        root = deleteNode(root, 20);
        document.write("Inorder traversal of the " + "modified tree<br/>");
        inorder(root);

        document.write("<br/>Delete 30<br/>");
        root = deleteNode(root, 30);
        document.write("Inorder traversal of the " + "modified tree<br/>");
        inorder(root);

        document.write("<br/>Delete 50<br/>");
        root = deleteNode(root, 50);
        document.write("Inorder traversal of the " + "modified tree<br/>");
        inorder(root);

// This code contributed by Rajput-Ji
</script>

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.

Related Links:

• Binary Search Tree Introduction, Search and Insert
• Quiz on Binary Search Tree
• Coding practice on BST
• All Articles on BST