Deletion in a Binary Tree

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

Delete 10 in below tree
       10
     /    \         
    20     30
Output :    
       30
     /             
    20     


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

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

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; 
        deletDeepest(root, temp); 
        key_node->key = x; 
    } 
    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)  
            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;  
        deleteDeepest(root, temp);  
        keyNode.key = x;  
    }  
} 
  
// 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  

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) 
    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 
        deleteDeepest(root,temp) 
        key_node.data = x 
    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:") 
    inorder(root) 
    key = 11
    root = deletion(root, key) 
    print() 
    print("The tree after the deletion;") 
    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

Note: We can also replace 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.

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C++

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