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++

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// 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;
}

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Python3

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# 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

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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.

This article is contributed by Yash Singla. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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