Binary Search Tree | Set 2 (Delete)

23 Jun, 2022
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.
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// 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 nodestruct 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 BSTvoid inorder(struct node* root){    if (root != NULL) {        inorder(root->left);        cout << root->key;        inorder(root->right);    }} /* A utility function toinsert 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 nodewith minimum key value found in that tree. Note that theentire 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 functiondeletes 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 Codeint 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 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 nodestruct 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 BSTvoid 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 Codeint 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 program to demonstrate// delete operation in binary// search treeclass 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 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 BSTdef 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 BSTdef 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 = Noneroot = 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# program to demonstrate delete// operation in binary search treeusing 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
<script>// Javascript program to demonstrate// delete operation in binary// search treeclass Node{    constructor(item)    {        this.key = item;        this.left = this.right = null;    }} // Root of BSTlet 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 BSTfunction 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>
Inorder traversal of the given tree 
20304050607080
Delete 20
Inorder traversal of the modified tree 
304050607080
Delete 30
Inorder traversal of the modified tree 
4050607080
Delete 50
Inorder traversal of the modified tree 
40607080
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.
Implementation:
C++
Java
C#
Python3
Javascript
// 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 nodeNode* 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 BSTvoid 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 Codeint 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;}
// 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 nodestatic 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 BSTstatic 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 BSTstatic 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 rootstatic 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 Codepublic 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
// 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 nodestatic 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 BSTstatic 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 BSTstatic 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 rootstatic 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 Codepublic 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
# 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 BSTdef 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 BSTdef 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 rootdef 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 = Noneroot = 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)
<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>
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.Related Links: 
Binary Search Tree Introduction, Search and Insert
Quiz on Binary Search Tree
Coding practice on BST
All Articles on BST
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