Deletion in a Binary Tree

Given a binary tree, delete a node from it by making sure that the tree shrinks from the bottom (i.e. the deleted node is replaced by the bottom-most and rightmost node). This is different from BST deletion. Here we do not have any order among elements, so we replace them with the last element.

Examples :

Input : Delete 10 in below tree

       10
     /    \         
  20     30

Output:    
       30
     /             
 20     

Input : Delete 20 in below tree
       10
     /    \         
 20     30
            \
            40

Output:    
       10
   /      \             
40        30

Algorithm:

1. Starting at the root, find the deepest and rightmost node in the binary tree and the node which we want to delete. 
2. Replace the deepest rightmost node’s data with the node to be deleted. 
3. Then delete the deepest rightmost node.

Below is the implementation of the above approach:

C++

// C++ program to delete element in binary tree
#include <bits/stdc++.h>
using namespace std;

/* A binary tree node has key, pointer to left
child and a pointer to right child */
struct Node {
    int key;
    struct Node *left, *right;
};

/* function to create a new node of tree and
return pointer */
struct Node* newNode(int key)
{
    struct Node* temp = new Node;
    temp->key = key;
    temp->left = temp->right = NULL;
    return temp;
};

/* Inorder traversal of a binary tree*/
void inorder(struct Node* temp)
{
    if (!temp)
        return;
    inorder(temp->left);
    cout << temp->key << " ";
    inorder(temp->right);
}

/* function to delete the given deepest node
(d_node) in binary tree */
void deletDeepest(struct Node* root, struct Node* d_node)
{
    queue<struct Node*> q;
    q.push(root);

    // Do level order traversal until last node
    struct Node* temp;
    while (!q.empty()) {
        temp = q.front();
        q.pop();
        if (temp == d_node) {
            temp = NULL;
            delete (d_node);
            return;
        }
        if (temp->right) {
            if (temp->right == d_node) {
                temp->right = NULL;
                delete (d_node);
                return;
            }
            else
                q.push(temp->right);
        }

        if (temp->left) {
            if (temp->left == d_node) {
                temp->left = NULL;
                delete (d_node);
                return;
            }
            else
                q.push(temp->left);
        }
    }
}

/* function to delete element in binary tree */
Node* deletion(struct Node* root, int key)
{
    if (root == NULL)
        return NULL;

    if (root->left == NULL && root->right == NULL) {
        if (root->key == key)
            return NULL;
        else
            return root;
    }

    queue<struct Node*> q;
    q.push(root);

    struct Node* temp;
    struct Node* key_node = NULL;

    // Do level order traversal to find deepest
    // node(temp) and node to be deleted (key_node)
    while (!q.empty()) {
        temp = q.front();
        q.pop();

        if (temp->key == key)
            key_node = temp;

        if (temp->left)
            q.push(temp->left);

        if (temp->right)
            q.push(temp->right);
    }

    if (key_node != NULL) {
        int x = temp->key;
          key_node->key = x;
        deletDeepest(root, temp);
    }
    return root;
}

// Driver code
int main()
{
    struct Node* root = newNode(10);
    root->left = newNode(11);
    root->left->left = newNode(7);
    root->left->right = newNode(12);
    root->right = newNode(9);
    root->right->left = newNode(15);
    root->right->right = newNode(8);

    cout << "Inorder traversal before deletion: ";
    inorder(root);

    int key = 11;
    root = deletion(root, key);

    cout << endl;
    cout << "Inorder traversal after deletion: ";
    inorder(root);

    return 0;
}

Java

// Java program to delete element
// in binary tree
import java.util.LinkedList;
import java.util.Queue;

class GFG {

    // A binary tree node has key, pointer to
    // left child and a pointer to right child
    static class Node {
        int key;
        Node left, right;

        // Constructor
        Node(int key)
        {
            this.key = key;
            left = null;
            right = null;
        }
    }

    static Node root;
    static Node temp = root;

    // Inorder traversal of a binary tree
    static void inorder(Node temp)
    {
        if (temp == null)
            return;

        inorder(temp.left);
        System.out.print(temp.key + " ");
        inorder(temp.right);
    }

    // Function to delete deepest
    // element in binary tree
    static void deleteDeepest(Node root, Node delNode)
    {
        Queue<Node> q = new LinkedList<Node>();
        q.add(root);

        Node temp = null;

        // Do level order traversal until last node
        while (!q.isEmpty()) {
            temp = q.peek();
            q.remove();

            if (temp == delNode) {
                temp = null;
                return;
            }
            if (temp.right != null) {
                if (temp.right == delNode) {
                    temp.right = null;
                    return;
                }
                else
                    q.add(temp.right);
            }

            if (temp.left != null) {
                if (temp.left == delNode) {
                    temp.left = null;
                    return;
                }
                else
                    q.add(temp.left);
            }
        }
    }

    // Function to delete given element
    // in binary tree
    static void delete(Node root, int key)
    {
        if (root == null)
            return;

        if (root.left == null && root.right == null) {
            if (root.key == key) {
                root = null;
                return;
            }
            else
                return;
        }

        Queue<Node> q = new LinkedList<Node>();
        q.add(root);
        Node temp = null, keyNode = null;

        // Do level order traversal until
        // we find key and last node.
        while (!q.isEmpty()) {
            temp = q.peek();
            q.remove();

            if (temp.key == key)
                keyNode = temp;

            if (temp.left != null)
                q.add(temp.left);

            if (temp.right != null)
                q.add(temp.right);
        }

        if (keyNode != null) {
            int x = temp.key;
              keyNode.key = x;
            deleteDeepest(root, temp);
        }
    }

    // Driver code
    public static void main(String args[])
    {
        root = new Node(10);
        root.left = new Node(11);
        root.left.left = new Node(7);
        root.left.right = new Node(12);
        root.right = new Node(9);
        root.right.left = new Node(15);
        root.right.right = new Node(8);

        System.out.print("Inorder traversal "
                         + "before deletion:");
        inorder(root);

        int key = 11;
        delete(root, key);

        System.out.print("\nInorder traversal "
                         + "after deletion:");
        inorder(root);
    }
}

// This code is contributed by Ravi Kant Verma

C#

// C# program to delete element
// in binary tree

using System;
using System.Collections.Generic;

class GFG {

    // A binary tree node has key, pointer to
    // left child and a pointer to right child
    public class Node {
        public int key;
        public Node left, right;

        // Constructor
        public Node(int key)
        {
            this.key = key;
            left = null;
            right = null;
        }
    }

    static Node root;

    // Inorder traversal of a binary tree
    static void inorder(Node temp)
    {
        if (temp == null)
            return;

        inorder(temp.left);
        Console.Write(temp.key + " ");
        inorder(temp.right);
    }

    // Function to delete deepest
    // element in binary tree
    static void deleteDeepest(Node root, Node delNode)
    {
        Queue<Node> q = new Queue<Node>();
        q.Enqueue(root);

        Node temp = null;

        // Do level order traversal until last node
        while (q.Count != 0) {
            temp = q.Peek();
            q.Dequeue();

            if (temp == delNode) {
                temp = null;
                return;
            }
            if (temp.right != null) {
                if (temp.right == delNode) {
                    temp.right = null;
                    return;
                }

                else
                    q.Enqueue(temp.right);
            }

            if (temp.left != null) {
                if (temp.left == delNode) {
                    temp.left = null;
                    return;
                }
                else
                    q.Enqueue(temp.left);
            }
        }
    }

    // Function to delete given element
    // in binary tree
    static void delete(Node root, int key)
    {
        if (root == null)
            return;

        if (root.left == null && root.right == null) {
            if (root.key == key) {
                root = null;
                return;
            }
            else
                return;
        }

        Queue<Node> q = new Queue<Node>();
        q.Enqueue(root);
        Node temp = null, keyNode = null;

        // Do level order traversal until
        // we find key and last node.
        while (q.Count != 0) {
            temp = q.Peek();
            q.Dequeue();

            if (temp.key == key)
                keyNode = temp;

            if (temp.left != null)
                q.Enqueue(temp.left);

            if (temp.right != null)
                q.Enqueue(temp.right);
        }

        if (keyNode != null) {
            int x = temp.key;
            keyNode.key = x;
            deleteDeepest(root, temp);
        }
    }

    // Driver code
    public static void Main(String[] args)
    {
        root = new Node(10);
        root.left = new Node(11);
        root.left.left = new Node(7);
        root.left.right = new Node(12);
        root.right = new Node(9);
        root.right.left = new Node(15);
        root.right.right = new Node(8);

        Console.Write("Inorder traversal "
                      + "before deletion: ");
        inorder(root);

        int key = 11;
        delete(root, key);

        Console.Write("\nInorder traversal "
                      + "after deletion: ");
        inorder(root);
    }
}

// This code is contributed by Abhijeet Kumar(abhijeet19403)

Javascript

<script>
    // Javascript program to delete element in binary tree
    
    class Node
    {
        constructor(key) {
           this.left = null;
           this.right = null;
           this.key = key;
        }
    }
    
    let root;
    let temp = root;

    // Inorder traversal of a binary tree
    function inorder(temp)
    {
        if (temp == null)
            return;

        inorder(temp.left);
        document.write(temp.key + " ");
        inorder(temp.right);
    }

    // Function to delete deepest
    // element in binary tree
    function deleteDeepest(root, delNode)
    {
        let q = [];
        q.push(root);

        let temp = null;

        // Do level order traversal until last node
        while (q.length > 0)
        {
            temp = q[0];
            q.shift();

            if (temp == delNode)
            {
                temp = null;
                return;

            }
            if (temp.right!=null)
            {
                if (temp.right == delNode)
                {
                    temp.right = null;
                    return;
            }
            else
                q.push(temp.right);
        }

        if (temp.left != null)
        {
            if (temp.left == delNode)
            {
                temp.left = null;
                return;
            }
            else
                q.push(temp.left);
        }
    }
    }

    // Function to delete given element
    // in binary tree
    function Delete(root, key)
    {
        if (root == null)
            return;

        if (root.left == null &&
           root.right == null)
        {
            if (root.key == key)
            {
                  root=null;
                  return;
            }
            else
                return;
        }

        let q = [];
        q.push(root);
        let temp = null, keyNode = null;

        // Do level order traversal until
        // we find key and last node.
        while (q.length > 0)
        {
            temp = q[0];
            q.shift();

            if (temp.key == key)
                keyNode = temp;

            if (temp.left != null)
                q.push(temp.left);

            if (temp.right != null)
                q.push(temp.right);
        }

        if (keyNode != null)
        {
            let x = temp.key;
            keyNode.key = x;
            deleteDeepest(root, temp);
        }
    }
    
    root = new Node(10);
    root.left = new Node(11);
    root.left.left = new Node(7);
    root.left.right = new Node(12);
    root.right = new Node(9);
    root.right.left = new Node(15);
    root.right.right = new Node(8);
 
    document.write("Inorder traversal " +
                     "before deletion: ");
    inorder(root);
 
    let key = 11;
    Delete(root, key);
 
    document.write("</br>" + "Inorder traversal " +
                     "after deletion: ");
    inorder(root);

</script>

Python3

# Python3 program to illustrate deletion in a Binary Tree

# class to create a node with data, left child and right child.


class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

# Inorder traversal of a binary tree


def inorder(temp):
    if(not temp):
        return
    inorder(temp.left)
    print(temp.data, end=" ")
    inorder(temp.right)

# function to delete the given deepest node (d_node) in binary tree


def deleteDeepest(root, d_node):
    q = []
    q.append(root)
    while(len(q)):
        temp = q.pop(0)
        if temp is d_node:
            temp = None
            return
        if temp.right:
            if temp.right is d_node:
                temp.right = None
                return
            else:
                q.append(temp.right)
        if temp.left:
            if temp.left is d_node:
                temp.left = None
                return
            else:
                q.append(temp.left)

# function to delete element in binary tree


def deletion(root, key):
    if root == None:
        return None
    if root.left == None and root.right == None:
        if root.key == key:
            return None
        else:
            return root
    key_node = None
    q = []
    q.append(root)
    temp = None
    while(len(q)):
        temp = q.pop(0)
        if temp.data == key:
            key_node = temp
        if temp.left:
            q.append(temp.left)
        if temp.right:
            q.append(temp.right)
    if key_node:
        x = temp.data
        key_node.data = x
        deleteDeepest(root, temp)
    return root


# Driver code
if __name__ == '__main__':
    root = Node(10)
    root.left = Node(11)
    root.left.left = Node(7)
    root.left.right = Node(12)
    root.right = Node(9)
    root.right.left = Node(15)
    root.right.right = Node(8)
    print("The tree before the deletion: ", end = "")
    inorder(root)
    key = 11
    root = deletion(root, key)
    print();
    print("The tree after the deletion: ", end = "")
    inorder(root)

# This code is contributed by Monika Anandan

Output

Inorder traversal before deletion : 7 11 12 10 15 9 8 
Inorder traversal after deletion : 7 8 12 10 15 9 

Time complexity: O(n) where n is no number of nodes
Auxiliary Space: O(n) size of queue

Note: We can also replace the node’s data that is to be deleted with any node whose left and right child points to NULL but we only use deepest node in order to maintain the Balance of a binary tree.