Deletion in a Binary Tree

Last Updated : 22 Oct, 2024

Given a binary tree, the task is to delete a given 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 : key = 10

Output:

Explanation: As the bottom & rightmost node in the above binary tree is 30 , replace the key node ie. 10 with 30 and remove the bottom & rightmost node.
Input : key = 20

Output:

Explanation: As the bottom & rightmost node in the above binary tree is 40, replace the key node ie. 20 with 40 and remove the bottom & rightmost node.

Approach:

The idea is to traverse the tree in level order manner. To perform the Deletion in a Binary Tree follow below:
Starting at the root, find the deepest and rightmost node in the binary tree and the node which we want to delete.
Replace the deepest rightmost node’s data with the node to be deleted.
Then delete the deepest rightmost node.

Below is the illustration of above approach:

Below is the implementation of the above approach:

C++

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

class Node {
public:    
  	int data;
    Node *left, *right;
	Node(int x){
    	data = x;
      	left = right = nullptr;
    }
};

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

    Node* curr;
    while (!q.empty()) {
        curr = q.front();
        q.pop();

        // If current node is the deepest
      	// node, delete it
        if (curr == dNode) {  
            curr = nullptr;
            delete (dNode);
            return;
        }

        // Check the right child first
        if (curr->right) {
          
            // If right child is the deepest
          	// node, delete it
            if (curr->right == dNode) {
                curr->right = nullptr;
                delete (dNode);
                return;
            } 
            q.push(curr->right);
        }

        // Check the left child
        if (curr->left) {
          
            // If left child is the deepest 
          	// node, delete it
            if (curr->left == dNode) {
                curr->left = nullptr;
                delete (dNode);
                return;
            } 
            q.push(curr->left);
        }
    }
}

// Function to delete the node with the given key
Node* deletion(Node* root, int key) {
  
    // If the tree is empty, return null
    if (root == nullptr)
        return nullptr;

    // If the tree has only one node
    if (root->left == nullptr && root->right == nullptr) {
      
        // If the root node is the key, delete it
        if (root->data == key)
            return nullptr;
        else
            return root;
    }

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

    Node* curr;
    Node* keyNode = nullptr;

    // Level order traversal to find the deepest
  	// node and the key node
    while (!q.empty()) {
        curr = q.front();
        q.pop();

        // If current node is the key node
        if (curr->data == key)
            keyNode = curr;

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

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

    // If key node is found, replace its data
  	// with the deepest node
    if (keyNode != nullptr) {
      
      	// Store the data of the deepest node
        int x = curr->data;  
      
      	// Replace key node data with deepest
      	// node's data
        keyNode->data = x;  
      
      	// Delete the deepest node
        deletDeepest(root, curr);  
    }
    return root;
}

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

int main() {
  
    // Construct the binary tree
    //       10         
  	//      /  \       
  	//    11    9
  	//   / \   / \     
  	//  7  12 15  8     

    Node* root = new Node(10);
    root->left = new Node(11);
    root->right = new Node(9);
    root->left->left = new Node(7);
    root->left->right = new Node(12);
    root->right->left = new Node(15);
    root->right->right = new Node(8);

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

    inorder(root);
    return 0;
}

Java

// Java program to delete a specific 
// element in a binary tree

import java.util.LinkedList;
import java.util.Queue;

class Node {
    int data;
    Node left, right;

    Node(int x) {
        data = x;
        left = right = null;
    }
}

class GfG {
    
    // Function to delete the deepest node in
  	// binary tree
    static void deletDeepest(Node root, Node dNode) {
        Queue<Node> q = new LinkedList<>();
        q.add(root);

        Node curr;
        while (!q.isEmpty()) {
            curr = q.poll();

            // If current node is the deepest 
          	// node, delete it
            if (curr == dNode) {
                curr = null;
                dNode = null;
                return;
            }

            // Check the right child first
            if (curr.right != null) {
              
                // If right child is the deepest node,
              	// delete it
                if (curr.right == dNode) {
                    curr.right = null;
                    dNode = null;
                    return;
                }
                q.add(curr.right);
            }

            // Check the left child
            if (curr.left != null) {
              
                // If left child is the deepest node,
              	// delete it
                if (curr.left == dNode) {
                    curr.left = null;
                    dNode = null;
                    return;
                }
                q.add(curr.left);
            }
        }
    }

    // Function to delete the node with the given key
    static Node deletion(Node root, int key) {
      
        if (root == null)
            return null;

        // If the tree has only one node
        if (root.left == null && root.right == null) {
          
            // If the root node is the key, 
          	// delete it
            if (root.data == key)
                return null;
            else
                return root;
        }

        Queue<Node> q = new LinkedList<>();
        q.add(root);

        Node curr = null;
        Node keyNode = null;

        // Level order traversal to find the 
      	// deepest node and the key node
        while (!q.isEmpty()) {
            curr = q.poll();

            // If current node is the key node
            if (curr.data == key)
                keyNode = curr;

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

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

        // If key node is found, replace its
      	// data with the deepest node
        if (keyNode != null) {
          
          	 // Store the data of the
          	// deepest node
            int x = curr.data; 
          
          	 // Replace key node data with 
          	// deepest node's data
            keyNode.data = x; 
          
          	 // Delete the deepest node
            deletDeepest(root, curr); 
        }
        return root;
    }

    // Inorder traversal of a binary tree
    static void inorder(Node curr) {
        if (curr == null)
            return;
        inorder(curr.left);
        System.out.print(curr.data + " ");
        inorder(curr.right);
    }

    public static void main(String[] args) {
      
        // Construct the binary tree
        //       10         
        //      /  \       
        //    11    9
        //   / \   / \     
        //  7  12 15  8   
          Node root = new Node(10);
        root.left = new Node(11);
        root.right = new Node(9);
        root.left.left = new Node(7);
        root.left.right = new Node(12);
        root.right.left = new Node(15);
        root.right.right = new Node(8);


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

Python

# Python program to delete a specific 
# element in a binary tree

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

# Function to delete the deepest node
# in the binary tree
def delete_deepest(root, dNode):
    queue = [root]

    while queue:
        curr = queue.pop(0)

        # If current node is the deepest 
        # node, delete it
        if curr == dNode:
            curr = None
            del dNode
            return

        # Check the right child first
        if curr.right:
          
            # If right child is the deepest
            # node, delete it
            if curr.right == dNode:
                curr.right = None
                del dNode
                return
            queue.append(curr.right)

        # Check the left child
        if curr.left:
          
            # If left child is the deepest
            # node, delete it
            if curr.left == dNode:
                curr.left = None
                del dNode
                return
            queue.append(curr.left)

# Function to delete the node with the given key
def deletion(root, key):

    if root is None:
        return None

    # If the tree has only one node
    if root.left is None and root.right is None:
        if root.data == key:
            return None
        else:
            return root

    queue = [root]
    curr = None
    keyNode = None

    # Level order traversal to find the
    # deepest node and the key node
    while queue:
        curr = queue.pop(0)

        # If current node is the key node
        if curr.data == key:
            keyNode = curr

        if curr.left:
            queue.append(curr.left)

        if curr.right:
            queue.append(curr.right)

    # If key node is found, replace its
    # data with the deepest node
    if keyNode is not None:
      
        x = curr.data
        
        # Replace key node data with 
        # deepest node's data
        keyNode.data = x
        
        # Delete the deepest node
        delete_deepest(root, curr)

    return root

# Inorder traversal of a binary tree
def inorder(curr):
    if curr is None:
        return
    inorder(curr.left)
    print(curr.data, end=" ")
    inorder(curr.right)

if __name__ == "__main__":
  
    # Construct the binary tree
    #       10         
    #      /  \       
    #    11    9
    #   / \   / \     
    #  7  12 15  8     

    root = Node(10)
    root.left = Node(11)
    root.right = Node(9)
    root.left.left = Node(7)
    root.left.right = Node(12)
    root.right.left = Node(15)
    root.right.right = Node(8)

    key = 11
    root = deletion(root, key) 

    inorder(root)

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

using System;
using System.Collections.Generic;

class Node {
    public int data;
    public Node left, right;

    public Node(int x) {
        data = x;
        left = right = null;
    }
}

class GfG {
    
    // Function to delete the deepest node in binary tree
    static void deletDeepest(Node root, Node dNode) {
        Queue<Node> q = new Queue<Node>();
        q.Enqueue(root);

        Node curr;
        while (q.Count > 0) {
            curr = q.Dequeue();

            // If current node is the deepest
           // node, delete it
            if (curr == dNode) {
                curr = null;
                dNode = null;
                return;
            }

            // Check the right child first
            if (curr.right != null) {
                if (curr.right == dNode) {
                    curr.right = null;
                    dNode = null;
                    return;
                }
                q.Enqueue(curr.right);
            }

            // Check the left child
            if (curr.left != null) {
                if (curr.left == dNode) {
                    curr.left = null;
                    dNode = null;
                    return;
                }
                q.Enqueue(curr.left);
            }
        }
    }

    // Function to delete the node with the given key
    static Node deletion(Node root, int key) {
      
        if (root == null)
            return null;

        // If the tree has only one node
        if (root.left == null && root.right == null) {
            if (root.data == key)
                return null;
            else
                return root;
        }

        Queue<Node> q = new Queue<Node>();
        q.Enqueue(root);

        Node curr = null;
        Node key_node = null;

        // Level order traversal to find the
      	// deepest node and the key node
        while (q.Count > 0) {
            curr = q.Dequeue();

            // If current node is the key node
            if (curr.data == key)
                key_node = curr;

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

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

        // If key node is found, replace 
      	// its data with the deepest node
        if (key_node != null) {
          
          	// Store the data of the deepest node
            int x = curr.data;  
          
          	// Replace key node data with deepest 
          	// node's data
            key_node.data = x;  
          
          	 // Delete the deepest node
            deletDeepest(root, curr); 
        }
        return root;
    }

    // Inorder traversal of a binary tree
    static void inorder(Node curr) {
        if (curr == null)
            return;
        inorder(curr.left);
        Console.Write(curr.data + " ");
        inorder(curr.right);
    }

    static void Main(string[] args) {
      
        // Construct the binary tree
        //       10         
        //      /  \       
        //    11    9
        //   / \   / \     
        //  7  12 15  8   
        Node root = new Node(10);
        root.left = new Node(11);
        root.right = new Node(9);
        root.left.left = new Node(7);
        root.left.right = new Node(12);
        root.right.left = new Node(15);
        root.right.right = new Node(8);

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

JavaScript

// JavaScript program to delete a specific 
// element in a binary tree

class Node {
    constructor(data) {
        this.data = data;
        this.left = null;
        this.right = null;
    }
}

// Function to delete the deepest node in 
// a binary tree
function deleteDeepest(root, dNode) {
    let queue = [];
    queue.push(root);

    while (queue.length !== 0) {
        let curr = queue.shift();

        // If current node is the deepest
        // node, delete it
        if (curr === dNode) {
            curr = null;
            return;
        }

        // Check the right child first
        if (curr.right) {
            if (curr.right === dNode) {
                curr.right = null;
                return;
            } else {
                queue.push(curr.right);
            }
        }

        // Check the left child
        if (curr.left) {
            if (curr.left === dNode) {
                curr.left = null;
                return;
            } else {
                queue.push(curr.left);
            }
        }
    }
}

// Function to delete the node with the given key
function deletion(root, key) {

    if (root === null) return null;

    // If the tree has only one node
    if (root.left === null && root.right === null) {
        if (root.data === key) return null;
        else return root;
    }

    let queue = [];
    queue.push(root);

    let keyNode = null;
    let curr = null;

    // Level order traversal to find the 
    // deepest node and the key node
    while (queue.length !== 0) {
        curr = queue.shift();

        // If current node is the key node
        if (curr.data === key) keyNode = curr;

        if (curr.left) queue.push(curr.left);
        if (curr.right) queue.push(curr.right);
    }

    // If the key node is found, replace its data
    // with the deepest node's data
    if (keyNode !== null) {
    
    	// Store the deepest node's data
        let x = curr.data;
        
        // Replace the key node's data with the
        // deepest node's data
        keyNode.data = x;
        
         // Delete the deepest node
        deleteDeepest(root, curr);
    }

    return root;
}

// Inorder traversal of a binary tree
function inorder(curr) {
    if (curr === null) return;
    inorder(curr.left);
    console.log(curr.data + " ");
    inorder(curr.right);
}

// Construct the binary tree
let root = new Node(10);
root.left = new Node(11);
root.right = new Node(9);
root.left.left = new Node(7);
root.left.right = new Node(12);
root.right.left = new Node(15);
root.right.right = new Node(8);

let key = 11;
root = deletion(root, key);
inorder(root);

Output

7 8 12 10 15 9

Time complexity: O(n), where n is number of nodes.
Auxiliary Space: O(n)

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.

Enumeration of Binary Trees

Yash Singla

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