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 30Output:
30
/
20Input : Delete 20 in below tree
10
/ \
20 30
\
40Output:
10
/ \
40 30
Algorithm:
- 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 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 leftchild and a pointer to right child */struct Node { int key; struct Node *left, *right;};/* function to create a new node of tree andreturn 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 codeint 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 treeimport 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; 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 treedef 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 treedef 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 treedef 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 deleteDeepest(root, temp) key_node.data = x return root# Driver codeif __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 |
C#
// C# program to delete element// in binary treeusing 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; 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); 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; deleteDeepest(root, temp); keyNode.key = x; } } 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> |
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.
Important Note: The above code will not work if the node to be deleted is the deepest node itself because after the function deletDeepest(root, temp) completes execution, the key_node gets deleted(as here key_node is equal to temp)and after which replacing key_node‘s data with the deepest node’s data(temp‘s data) throws a runtime error.
Output
To avoid the above error and also to avoid doing BFS twice (1st iteration while searching the rightmost deepest node, and 2nd while deleting the rightmost deepest node), we can store the parent node while first traversal and after setting the rightmost deepest node’s data to the node needed deletion, easily delete the rightmost deepest node.
Implementation:
C++
// C++ program to delete element in binary tree#include <bits/stdc++.h>using namespace std;/* A binary tree node has key, pointer to leftchild and a pointer to right child */struct Node { int data; struct Node *left, *right;};/* function to create a new node of tree andreturn pointer */struct Node* newNode(int key){ struct Node* temp = new Node; temp->data = 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->data << " "; inorder(temp->right);}struct Node* deletion(struct Node* root, int key){ if (root == NULL) return NULL; if (root->left == NULL && root->right == NULL) { if (root->data == key) return NULL; else return root; } Node* key_node = NULL; Node* temp; Node* last; queue<Node*> q; q.push(root); // Do level order traversal to find deepest // node(temp), node to be deleted (key_node) // and parent of deepest node(last) while (!q.empty()) { temp = q.front(); q.pop(); if (temp->data == key) key_node = temp; if (temp->left) { last = temp; // storing the parent node q.push(temp->left); } if (temp->right) { last = temp; // storing the parent node q.push(temp->right); } } if (key_node != NULL) { key_node->data = temp->data; // replacing key_node's data to // deepest node's data if (last->right == temp) last->right = NULL; else last->left = NULL; delete (temp); } return root;}// Driver codeint main(){ struct Node* root = newNode(9); root->left = newNode(2); root->left->left = newNode(4); root->left->right = newNode(7); root->right = newNode(8); cout << "Inorder traversal before deletion : "; inorder(root); int key = 7; root = deletion(root, key); cout << endl; cout << "Inorder traversal after deletion : "; inorder(root); return 0;} |
Java
// Java program to delete element in binary treeimport 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 data; Node left, right; public Node(int key) { this.data = key; } } // Inorder traversal of a binary tree static void inorder(Node root) { if (root == null) return; inorder(root.left); System.out.print(root.data + " "); inorder(root.right); } static Node deletion(Node root, int key) { if (root == null) return null; if (root.left == null && root.right == null) { return root.data == key ? root : null; } Node keyNode = null, temp = null, last = null; Queue<Node> q = new LinkedList<>(); q.offer(root); // Do level order traversal to find deepest // node(temp), node to be deleted (key_node) // and parent of deepest node(last) while (!q.isEmpty()) { temp = q.poll(); if (temp.data == key) keyNode = temp; if (temp.left != null) { last = temp; // storing the parent node q.offer(temp.left); } if (temp.right != null) { last = temp; // storing the parent node q.offer(temp.right); } } if (keyNode != null) { keyNode.data = temp.data; // replacing key_node's data to // deepest node's data if (last.right == temp) { last.right = null; } else { last.left = null; } } return root; } public static void main(String args[]) { Node root = new Node(9); root.left = new Node(2); root.left.left = new Node(4); root.left.right = new Node(7); root.right = new Node(8); System.out.print( "Inorder traversal before deletion : "); inorder(root); System.out.println(); int key = 7; root = deletion(root, key); System.out.print( "Inorder traversal after deletion : "); inorder(root); System.out.println(); }} |
Python3
# Python3 program to delete element in 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 treedef inorder(temp): if(not temp): return inorder(temp.left) print(temp.data, end=" ") inorder(temp.right)def deletion(root, key): if(root == None): return None if(root.left == None and root.right == None): if(root.data == key): return None else: return root key_node = None temp = None last = None q = [] q.append(root) # Do level order traversal to find deepest # node(temp), node to be deleted (key_node) # and parent of deepest node(last) while(len(q)): temp = q.pop(0) if(temp.data == key): key_node = temp if(temp.left): last = temp # storing the parent node q.append(temp.left) if(temp.right): last = temp # storing the parent node q.append(temp.right) if(key_node != None): key_node.data = temp.data # replacing key_node's data to deepest node's data if(last.right == temp): last.right = None else: last.left = None return root# Driver codeif __name__ == '__main__': root = Node(9) root.left = Node(2) root.left.left = Node(4) root.left.right = Node(7) root.right = Node(8) print("Inorder traversal before deletion : ", end="") inorder(root) key = 7 root = deletion(root, key) print() print("Inorder traversal after deletion : ", end="") inorder(root)# This code is contributed by Abhijeet Kumar(abhijeet19403) |
C#
// This code is designed to delete a node in a Binary Treeusing System;namespace BinaryTreeDeletion {public class TreeNode { public int Data; public TreeNode leftNode; public TreeNode rightNode;}public class BinaryTreeOperations { TreeNode rootNode; TreeNode parentNode; int NodeToDelete; int NodeToBeReplaceWith; bool NodeValueReplaced = false; // Driver code public static void Main() { BinaryTreeOperations obj = new BinaryTreeOperations(); obj.AddNode(7); obj.AddNode(2); obj.AddNode(3); obj.AddNode(1); obj.AddNode(10); obj.AddNode(5); obj.AddNode(8); Console.WriteLine( "Inorder Traversal before Deletion : "); obj.PrintInorderTraversalData(obj.rootNode); obj.DeleteNode(5); Console.WriteLine(""); Console.WriteLine( "Inorder Traversal after Deletion : "); obj.PrintInorderTraversalData(obj.rootNode); } void PrintInorderTraversalData(TreeNode Node) { if (Node != null) { PrintInorderTraversalData(Node.leftNode); Console.Write(Node.Data + " "); PrintInorderTraversalData(Node.rightNode); } } public void AddNode(int Value) { TreeNode beforeNode = null; TreeNode afterNode = this.rootNode; while (afterNode != null) { beforeNode = afterNode; if (Value < afterNode.Data) afterNode = afterNode.leftNode; else if (Value > afterNode.Data) afterNode = afterNode.rightNode; else return; } TreeNode newNode = new TreeNode(); newNode.Data = Value; if (this.rootNode == null) rootNode = newNode; else { if (Value < beforeNode.Data) { beforeNode.leftNode = newNode; } else { beforeNode.rightNode = newNode; } } } void DeleteNode(int Value) { if (rootNode == null) { return; } NodeToBeReplaceWith = FindDeepestNode(rootNode); NodeToDelete = Value; Search(rootNode); } int FindDeepestNode(TreeNode rootnode) { if (rootnode.leftNode == null && rootnode.rightNode == null) { int deepestVal = rootnode.Data; parentNode.leftNode = null; parentNode.rightNode = null; return deepestVal; } parentNode = rootnode; return FindDeepestNode(rootnode.rightNode != null ? rootnode.rightNode : rootnode.leftNode); } void Search(TreeNode node) { if (!NodeValueReplaced) { SearchAndReplace(node.leftNode); } if (!NodeValueReplaced) { SearchAndReplace(node.rightNode); } } void SearchAndReplace(TreeNode rootnode) { if (rootnode == null) { return; } if (rootnode.Data == NodeToDelete) { rootnode.Data = NodeToBeReplaceWith; NodeValueReplaced = true; return; } if (!NodeValueReplaced) { SearchAndReplace(rootnode.leftNode); } if (!NodeValueReplaced) { SearchAndReplace(rootnode.rightNode); } }}}// This code is contributed by Prakher Mehrotra |
Output
Inorder traversal before deletion : 4 2 7 9 8 Inorder traversal after deletion : 4 2 9 8
Time complexity: O(n) where n is no number of nodes
Auxiliary Space: O(n) size of queue
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