Delete a node in binary tree
The problem at hand involves deleting a node from a binary tree. A binary tree is a hierarchical data structure in which each node has at most two children, referred to as the left child and the right child. Deleting a node from a binary tree requires reorganizing the tree while maintaining its structure and properties.
Problem Statement and Description
Given a binary tree and a value to be deleted, the task is to implement a function that removes the node with the specified value from the tree. The challenge lies in correctly handling the various cases that can arise during deletion, such as whether the node to be deleted has zero, one, or two children.
Example
Consider the following binary tree:
1
/ \
2 3
/ / \
6 5 4
\ /
8 7We want to delete nodes with values: 6, 1, 4, and 3.
After deleting 6:
1
/ \
2 3
/ / \
8 5 4
/
7
After deleting 1:
8
/ \
2 3
/ \
5 4
/
7
After deleting 4:
8
/ \
2 3
/ \
5 7
After deleting 3 :
8
/ \
2 5
\
7
Idea to Solve the Problem
To solve this problem, we need to follow these steps:
-
Search for the Node to Delete
Traverse the tree to locate the node with the value to be deleted.
-
Handle Different Cases
- If the node to be deleted has no children, simply remove the node.
- If the node to be deleted has one child, replace the node with its child.
- If the node to be deleted has two children, find the in-order successor (or predecessor) of the node, copy its value to the node to be deleted, and then recursively delete the in-order successor (or predecessor).
-
Update Parent Pointers
Adjust the parent pointers to reflect the changes in the tree structure after deletion.
Standard Pseudocode
Here's a high-level pseudocode representation of the algorithm to delete a node from a binary tree:
DeleteNode(root, value):
if root is NULL:
return NULL
if value is less than root's value:
root.left = DeleteNode(root.left, value)
else if value is greater than root's value:
root.right = DeleteNode(root.right, value)
else:
if root has no left child:
temp = root.right
free root
return temp
else if root has no right child:
temp = root.left
free root
return temp
temp = FindMinimumValueNode(root.right)
root.value = temp.value
root.right = DeleteNode(root.right, temp.value)
return root
Algorithm Explanation
- Start with the root of the tree.
- Recursively traverse the tree to locate the node to be deleted.
- If the node is found:
- Handle the case where the node has no children or only one child.
- For the case where the node has two children, find the in-order successor (minimum value node in the right subtree), copy its value to the current node, and recursively delete the in-order successor.
- After the deletion is complete, return the modified root of the tree.
Code Example
/*
C Program
+ Delete a node in binary tree
*/
#include<stdio.h>
#include<stdlib.h>
//structure of Binary Tree node
struct Node {
int data;
struct Node *left, *right;
};
//Create a binary tree nodes and node fields (data,pointer)
//And returning the reference of newly nodes
struct Node *insert(int data) {
//create dynamic memory to new binary tree node
struct Node *new_node = (struct Node *) malloc(sizeof(struct Node));
if (new_node != NULL) {
//set data and pointer values
new_node->data = data;
new_node->left = NULL; //Initially node left-pointer is NULL
new_node->right = NULL; //Initially node right-pointer is NULL
} else {
printf("Memory Overflow\n");
exit(0); //Terminate program execution
}
//return reference
return new_node;
}
//Find deleted node
void find(struct Node *root, struct Node *parent, int element, struct Node **result) {
if (root != NULL && *result == NULL) {
if (element == root->data) {
*result = parent;
return;
}
find(root->left, root, element, result);
find(root->right, root, element, result);
}
}
struct Node *getNode(struct Node *root) {
//Replace root with any node
//Either delete last node of tree
//Or delete any node which are zero or have one child node
struct Node *auxiliary = root, *temp = NULL;
while (auxiliary->left != NULL) {
temp = auxiliary;
auxiliary = auxiliary->left;
}
temp->left = auxiliary->right;
auxiliary->right = NULL;
//change data
(root)->data = auxiliary->data;
return auxiliary;
}
void deleteNode(struct Node **root, int element) {
if ( *root == NULL) return;
struct Node *auxiliary = NULL, *head = NULL;
if (( *root)->data == element) {
//Delete root
auxiliary = ( *root);
if (( *root)->left == NULL) {
//When no left sub tree
( *root) = ( *root)->right;
} else if (( *root)->right == NULL) {
//When no right sub tree
( *root) = ( *root)->left;
} else {
auxiliary = getNode( *root);
}
} else {
//Find parent of deleted node
find( *root, *root, element, & head);
if (head != NULL) {
//When deleted node are exist
if (head->left != NULL && head->left->data == element) {
auxiliary = head->left;
if (auxiliary->left == NULL) {
head->left = auxiliary->right;
} else if (auxiliary->right == NULL) {
head->left = auxiliary->left;
} else {
auxiliary = getNode(auxiliary);
}
} else if (head->right != NULL && head->right->data == element) {
auxiliary = head->right;
if (auxiliary->left == NULL) {
head->right = auxiliary->right;
} else if (auxiliary->right == NULL) {
head->right = auxiliary->left;
} else {
auxiliary = getNode(auxiliary);
}
}
}
}
if (auxiliary != NULL) {
printf("\n Delete : %d ", element);
free(auxiliary);
auxiliary = NULL;
} else {
printf("\n Delete node %d is not found", element);
}
printf("\n");
}
//Display tree element inorder form
void inorder(struct Node *node) {
if (node != NULL) {
inorder(node->left);
//Print node value
printf(" %d", node->data);
inorder(node->right);
}
}
int main() {
struct Node *root = NULL;
/* Make A Binary Tree
-----------------------
1
/ \
2 3
/ / \
6 5 4
\ /
8 7
*/
//Insertion of binary tree nodes
root = insert(1);
root->left = insert(2);
root->right = insert(3);
root->right->right = insert(4);
root->right->right->left = insert(7);
root->right->left = insert(5);
root->left->left = insert(6);
root->left->left->right = insert(8);
//Display Tree elements
inorder(root);
//Test case
deleteNode( & root, 6);
inorder(root);
deleteNode( & root, 1);
inorder(root);
deleteNode( & root, 4);
inorder(root);
deleteNode( & root, 3);
inorder(root);
deleteNode( & root, 3);
inorder(root);
return 0;
}
Output
6 8 2 1 5 3 7 4
Delete : 6
8 2 1 5 3 7 4
Delete : 1
2 8 5 3 7 4
Delete : 4
2 8 5 3 7
Delete : 3
2 8 5 7
Delete node 3 is not found
2 8 5 7/*
C++ Program
Delete a node in binary tree
*/
#include<iostream>
using namespace std;
class Node {
public:
int data;
Node *left, *right;
Node(int value) {
this->data = value;
this->left = this->right = NULL;
}
};
class BinaryTree {
public:
Node *root;
Node *parent;
BinaryTree() {
this->root = NULL;
this->parent = NULL;
}
void find_parent(Node *head, Node *result, int element) {
if (head != NULL && this->parent == NULL) {
if (element == head->data) {
this->parent = result;
return;
}
this->find_parent(head->left, head, element);
this->find_parent(head->right, head, element);
}
}
Node *getNode(Node *head) {
Node *auxiliary = head, *temp = NULL;
while (auxiliary->left != NULL) {
temp = auxiliary;
auxiliary = auxiliary->left;
}
temp->left = auxiliary->right;
auxiliary->right = NULL;
head->data = auxiliary->data;
return auxiliary;
}
void deleteNode(int element) {
Node *head = this->root;
if (head == NULL) {
return;
}
Node *auxiliary = NULL;
if (head->data == element) {
auxiliary = head;
if (head->left == NULL) {
this->root = head->right;
} else
if (head->right == NULL) {
this->root = head->left;
} else {
auxiliary = this->getNode(head);
}
} else {
this->parent = NULL;
this->find_parent(head, head, element);
if (this->parent != NULL) {
if (this->parent->left != NULL && this->parent->left->data == element) {
auxiliary = this->parent->left;
if (auxiliary->left == NULL) {
this->parent->left = auxiliary->right;
} else
if (auxiliary->right == NULL) {
this->parent->left = auxiliary->left;
} else {
auxiliary = this->getNode(auxiliary);
}
} else
if (this->parent->right != NULL && this->parent->right->data == element) {
auxiliary = this->parent->right;
if (auxiliary->left == NULL) {
this->parent->right = auxiliary->right;
} else
if (auxiliary->right == NULL) {
this->parent->right = auxiliary->left;
} else {
auxiliary = this->getNode(auxiliary);
}
}
}
}
if (auxiliary != NULL) {
cout << "\n Delete : "<< element;
auxiliary = NULL;
} else {
cout << "\n Delete node "<< element <<" is not found";
}
cout <<"\n";
}
void inorder(Node *head) {
if (head != NULL) {
this->inorder(head->left);
cout << " " << head->data;
this->inorder(head->right);
}
}
};
int main() {
BinaryTree obj;
/* Make A Binary Tree
-----------------------
1
/ \
2 3
/ / \
6 5 4
\ /
8 7
*/
obj.root = new Node(1);
obj.root->left = new Node(2);
obj.root->right = new Node(3);
obj.root->right->right = new Node(4);
obj.root->right->right->left = new Node(7);
obj.root->right->left = new Node(5);
obj.root->left->left = new Node(6);
obj.root->left->left->right = new Node(8);
obj.inorder(obj.root);
obj.deleteNode(6);
obj.inorder(obj.root);
obj.deleteNode(1);
obj.inorder(obj.root);
obj.deleteNode(4);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
return 0;
}
Output
6 8 2 1 5 3 7 4
Delete : 6
8 2 1 5 3 7 4
Delete : 1
2 8 5 3 7 4
Delete : 4
2 8 5 3 7
Delete : 3
2 8 5 7
Delete node 3 is not found
2 8 5 7/*
Java Program
Delete a node in binary tree
*/
//Class of Binary Tree node
class Node {
public int data;
public Node left, right;
//Make a tree node
public Node(int value) {
//Assign field values
data = value;
left = right = null;
}
}
public class BinaryTree {
public Node root;
public Node parent;
public BinaryTree() {
//Set initial initial values
root = null;
parent = null;
}
//Find deleted node
public void find_parent(Node head, Node result, int element) {
if (head != null && this.parent == null) {
if (element == head.data) {
this.parent = result;
return;
}
find_parent(head.left, head, element);
find_parent(head.right, head, element);
}
}
public Node getNode(Node head) {
//Replace head with any node
//Either delete last node of tree
//Or delete any node which are zero or have one child node
Node auxiliary = head, temp = null;
while (auxiliary.left != null) {
temp = auxiliary;
auxiliary = auxiliary.left;
}
temp.left = auxiliary.right;
auxiliary.right = null;
//change data
head.data = auxiliary.data;
return auxiliary;
}
public void deleteNode(int element) {
Node head = this.root;
if (head == null) {
return;
}
Node auxiliary = null;
if (head.data == element) {
//Delete head
auxiliary = head;
if (head.left == null) {
//When no left sub tree
this.root = head.right;
} else if (head.right == null) {
//When no right sub tree
this.root = head.left;
} else {
auxiliary = getNode(head);
}
} else {
this.parent = null;
//Find parent of deleted node
find_parent(head, head, element);
if (this.parent != null) {
//When deleted node are exist
if (this.parent.left != null && this.parent.left.data == element) {
auxiliary = this.parent.left;
if (auxiliary.left == null) {
this.parent.left = auxiliary.right;
} else if (auxiliary.right == null) {
this.parent.left = auxiliary.left;
} else {
auxiliary = getNode(auxiliary);
}
} else if (this.parent.right != null && this.parent.right.data == element) {
auxiliary = this.parent.right;
if (auxiliary.left == null) {
this.parent.right = auxiliary.right;
} else if (auxiliary.right == null) {
this.parent.right = auxiliary.left;
} else {
auxiliary = getNode(auxiliary);
}
}
}
}
if (auxiliary != null) {
System.out.print("\n Delete : " + element);
auxiliary = null;
} else {
System.out.print("\n Delete node " + element + " is not found");
}
System.out.print("\n");
}
//Display tree element inorder form
public void inorder(Node head) {
if (head != null) {
inorder(head.left);
//Print node value
System.out.print(" " + head.data);
inorder(head.right);
}
}
public static void main(String[] args) {
//Make object of Binary Tree
BinaryTree obj = new BinaryTree();
/* Make A Binary Tree
-----------------------
1
/ \
2 3
/ / \
6 5 4
\ /
8 7
*/
//Binary tree nodes
obj.root = new Node(1);
obj.root.left = new Node(2);
obj.root.right = new Node(3);
obj.root.right.right = new Node(4);
obj.root.right.right.left = new Node(7);
obj.root.right.left = new Node(5);
obj.root.left.left = new Node(6);
obj.root.left.left.right = new Node(8);
//Display Tree elements
obj.inorder(obj.root);
//Test case
obj.deleteNode(6);
obj.inorder(obj.root);
obj.deleteNode(1);
obj.inorder(obj.root);
obj.deleteNode(4);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
}
}
Output
6 8 2 1 5 3 7 4
Delete : 6
8 2 1 5 3 7 4
Delete : 1
2 8 5 3 7 4
Delete : 4
2 8 5 3 7
Delete : 3
2 8 5 7
Delete node 3 is not found
2 8 5 7/*
C# Program
Delete a node in binary tree
*/
using System;
//Class of Binary Tree node
public class Node {
public int data;
public Node left, right;
//Make a tree node
public Node(int value) {
//Assign field values
data = value;
left = right = null;
}
}
public class BinaryTree {
public Node root;
public Node parent;
public BinaryTree() {
//Set initial initial values
root = null;
parent = null;
}
//Find deleted node
public void find_parent(Node head, Node result, int element) {
if (head != null && this.parent == null) {
if (element == head.data) {
this.parent = result;
return;
}
find_parent(head.left, head, element);
find_parent(head.right, head, element);
}
}
public Node getNode(Node head) {
//Replace head with any node
//Either delete last node of tree
//Or delete any node which are zero or have one child node
Node auxiliary = head, temp = null;
while (auxiliary.left != null) {
temp = auxiliary;
auxiliary = auxiliary.left;
}
temp.left = auxiliary.right;
auxiliary.right = null;
//change data
head.data = auxiliary.data;
return auxiliary;
}
public void deleteNode(int element) {
Node head = this.root;
if (head == null) {
return;
}
Node auxiliary = null;
if (head.data == element) {
//Delete head
auxiliary = head;
if (head.left == null) {
//When no left sub tree
this.root = head.right;
} else if (head.right == null) {
//When no right sub tree
this.root = head.left;
} else {
auxiliary = getNode(head);
}
} else {
this.parent = null;
//Find parent of deleted node
find_parent(head, head, element);
if (this.parent != null) {
//When deleted node are exist
if (this.parent.left != null && this.parent.left.data == element) {
auxiliary = this.parent.left;
if (auxiliary.left == null) {
this.parent.left = auxiliary.right;
} else if (auxiliary.right == null) {
this.parent.left = auxiliary.left;
} else {
auxiliary = getNode(auxiliary);
}
} else if (this.parent.right != null && this.parent.right.data == element) {
auxiliary = this.parent.right;
if (auxiliary.left == null) {
this.parent.right = auxiliary.right;
} else if (auxiliary.right == null) {
this.parent.right = auxiliary.left;
} else {
auxiliary = getNode(auxiliary);
}
}
}
}
if (auxiliary != null) {
Console.Write("\n Delete : " + element);
auxiliary = null;
} else {
Console.Write("\n Delete node " + element + " is not found");
}
Console.Write("\n");
}
//Display tree element inorder form
public void inorder(Node head) {
if (head != null) {
inorder(head.left);
//Print node value
Console.Write(" " + head.data);
inorder(head.right);
}
}
public static void Main(String[] args) {
//Make object of Binary Tree
BinaryTree obj = new BinaryTree();
/* Make A Binary Tree
-----------------------
1
/ \
2 3
/ / \
6 5 4
\ /
8 7
*/
//Binary tree nodes
obj.root = new Node(1);
obj.root.left = new Node(2);
obj.root.right = new Node(3);
obj.root.right.right = new Node(4);
obj.root.right.right.left = new Node(7);
obj.root.right.left = new Node(5);
obj.root.left.left = new Node(6);
obj.root.left.left.right = new Node(8);
//Display Tree elements
obj.inorder(obj.root);
//Test case
obj.deleteNode(6);
obj.inorder(obj.root);
obj.deleteNode(1);
obj.inorder(obj.root);
obj.deleteNode(4);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
}
}
Output
6 8 2 1 5 3 7 4
Delete : 6
8 2 1 5 3 7 4
Delete : 1
2 8 5 3 7 4
Delete : 4
2 8 5 3 7
Delete : 3
2 8 5 7
Delete node 3 is not found
2 8 5 7# Python Program
# Delete a node in binary tree
class Node :
def __init__(self, value) :
self.data = value
self.left = self.right = None
class BinaryTree :
def __init__(self) :
self.root = None
self.parent = None
def find_parent(self, head, result, element) :
if (head != None and self.parent == None) :
if (element == head.data) :
self.parent = result
return
self.find_parent(head.left, head, element)
self.find_parent(head.right, head, element)
def getNode(self, head) :
auxiliary = head
temp = None
while (auxiliary.left != None) :
temp = auxiliary
auxiliary = auxiliary.left
temp.left = auxiliary.right
auxiliary.right = None
head.data = auxiliary.data
return auxiliary
def deleteNode(self, element) :
head = self.root
if (head == None) :
return
auxiliary = None
if (head.data == element) :
auxiliary = head
if (head.left == None) :
self.root = head.right
elif (head.right == None) :
self.root = head.left
else :
auxiliary = self.getNode(head)
else :
self.parent = None
self.find_parent(head, head, element)
if (self.parent != None) :
if (self.parent.left != None and self.parent.left.data == element) :
auxiliary = self.parent.left
if (auxiliary.left == None) :
self.parent.left = auxiliary.right
elif (auxiliary.right == None) :
self.parent.left = auxiliary.left
else :
auxiliary = self.getNode(auxiliary)
elif (self.parent.right != None and self.parent.right.data == element) :
auxiliary = self.parent.right
if (auxiliary.left == None) :
self.parent.right = auxiliary.right
elif (auxiliary.right == None) :
self.parent.right = auxiliary.left
else :
auxiliary = self.getNode(auxiliary)
if (auxiliary != None) :
print("\n Delete : ", element)
auxiliary = None
else :
print("\n Delete node ", element ," is not found")
def inorder(self, head) :
if (head != None) :
self.inorder(head.left)
print(head.data,end=" ")
self.inorder(head.right)
def main() :
obj = BinaryTree()
# Make A Binary Tree
#
# 1
# / \
# 2 3
# / / \
# 6 5 4
# \ /
# 8 7
#
obj.root = Node(1)
obj.root.left = Node(2)
obj.root.right = Node(3)
obj.root.right.right = Node(4)
obj.root.right.right.left = Node(7)
obj.root.right.left = Node(5)
obj.root.left.left = Node(6)
obj.root.left.left.right = Node(8)
obj.inorder(obj.root)
obj.deleteNode(6)
obj.inorder(obj.root)
obj.deleteNode(1)
obj.inorder(obj.root)
obj.deleteNode(4)
obj.inorder(obj.root)
obj.deleteNode(3)
obj.inorder(obj.root)
obj.deleteNode(3)
obj.inorder(obj.root)
if __name__ == "__main__":
main()
Output
6 8 2 1 5 3 7 4
Delete : 6
8 2 1 5 3 7 4
Delete : 1
2 8 5 3 7 4
Delete : 4
2 8 5 3 7
Delete : 3
2 8 5 7
Delete node 3 is not found
2 8 5 7# Ruby Program
# Delete a node in binary tree
class Node
attr_reader :data, :left, :right
attr_accessor :data, :left, :right
def initialize(value)
@data = value
@left = @right = nil
end
end
class BinaryTree
attr_reader :root, :parent
attr_accessor :root, :parent
def initialize()
@root = nil
@parent = nil
end
def find_parent(head, result, element)
if (head != nil and self.parent == nil)
if (element == head.data)
self.parent = result
return
end
self.find_parent(head.left, head, element)
self.find_parent(head.right, head, element)
end
end
def getNode(head)
auxiliary = head
temp = nil
while (auxiliary.left != nil)
temp = auxiliary
auxiliary = auxiliary.left
end
temp.left = auxiliary.right
auxiliary.right = nil
head.data = auxiliary.data
return auxiliary
end
def deleteNode(element)
head = self.root
if (head == nil)
return
end
auxiliary = nil
if (head.data == element)
auxiliary = head
if (head.left == nil)
self.root = head.right
elsif (head.right == nil)
self.root = head.left
else
auxiliary = self.getNode(head)
end
else
self.parent = nil
self.find_parent(head, head, element)
if (self.parent != nil)
if (self.parent.left != nil and self.parent.left.data == element)
auxiliary = self.parent.left
if (auxiliary.left == nil)
self.parent.left = auxiliary.right
elsif (auxiliary.right == nil)
self.parent.left = auxiliary.left
else
auxiliary = self.getNode(auxiliary)
end
elsif (self.parent.right != nil and self.parent.right.data == element)
auxiliary = self.parent.right
if (auxiliary.left == nil)
self.parent.right = auxiliary.right
elsif (auxiliary.right == nil)
self.parent.right = auxiliary.left
else
auxiliary = self.getNode(auxiliary)
end
end
end
end
if (auxiliary != nil)
print("\n Delete : ", element)
auxiliary = nil
else
print("\n Delete node ", element ," is not found")
end
print("\n")
end
def inorder(head)
if (head != nil)
self.inorder(head.left)
print(" ", head.data)
self.inorder(head.right)
end
end
end
def main()
obj = BinaryTree.new()
# Make A Binary Tree
#
# 1
# / \
# 2 3
# / / \
# 6 5 4
# \ /
# 8 7
#
obj.root = Node.new(1)
obj.root.left = Node.new(2)
obj.root.right = Node.new(3)
obj.root.right.right = Node.new(4)
obj.root.right.right.left = Node.new(7)
obj.root.right.left = Node.new(5)
obj.root.left.left = Node.new(6)
obj.root.left.left.right = Node.new(8)
obj.inorder(obj.root)
obj.deleteNode(6)
obj.inorder(obj.root)
obj.deleteNode(1)
obj.inorder(obj.root)
obj.deleteNode(4)
obj.inorder(obj.root)
obj.deleteNode(3)
obj.inorder(obj.root)
obj.deleteNode(3)
obj.inorder(obj.root)
end
main()
Output
6 8 2 1 5 3 7 4
Delete : 6
8 2 1 5 3 7 4
Delete : 1
2 8 5 3 7 4
Delete : 4
2 8 5 3 7
Delete : 3
2 8 5 7
Delete node 3 is not found
2 8 5 7<?php
/*
Php Program
Delete a node in binary tree
*/
class Node {
public $data;
public $left;
public $right;
function __construct($value) {
$this->data = $value;
$this->left = $this->right = null;
}
}
class BinaryTree {
public $root;
public $parent;
function __construct() {
$this->root = null;
$this->parent = null;
}
public function find_parent($head, $result, $element) {
if ($head != null && $this->parent == null) {
if ($element == $head->data) {
$this->parent = $result;
return;
}
$this->find_parent($head->left, $head, $element);
$this->find_parent($head->right, $head, $element);
}
}
public function getNode($head) {
$auxiliary = $head;
$temp = null;
while ($auxiliary->left != null) {
$temp = $auxiliary;
$auxiliary = $auxiliary->left;
}
$temp->left = $auxiliary->right;
$auxiliary->right = null;
$head->data = $auxiliary->data;
return $auxiliary;
}
public function deleteNode($element) {
$head = $this->root;
if ($head == null) {
return;
}
$auxiliary = null;
if ($head->data == $element) {
$auxiliary = $head;
if ($head->left == null) {
$this->root = $head->right;
} else
if ($head->right == null) {
$this->root = $head->left;
} else {
$auxiliary = $this->getNode($head);
}
} else {
$this->parent = null;
$this->find_parent($head, $head, $element);
if ($this->parent != null) {
if ($this->parent->left != null && $this->parent->left->data == $element) {
$auxiliary = $this->parent->left;
if ($auxiliary->left == null) {
$this->parent->left = $auxiliary->right;
} else
if ($auxiliary->right == null) {
$this->parent->left = $auxiliary->left;
} else {
$auxiliary = $this->getNode($auxiliary);
}
} else
if ($this->parent->right != null && $this->parent->right->data == $element) {
$auxiliary = $this->parent->right;
if ($auxiliary->left == null) {
$this->parent->right = $auxiliary->right;
} else
if ($auxiliary->right == null) {
$this->parent->right = $auxiliary->left;
} else {
$auxiliary = $this->getNode($auxiliary);
}
}
}
}
if ($auxiliary != null) {
echo("\n Delete : ". $element);
$auxiliary = null;
} else {
echo("\n Delete node ". $element ." is not found");
}
echo("\n");
}
public function inorder($head) {
if ($head != null) {
$this->inorder($head->left);
echo(" ". $head->data);
$this->inorder($head->right);
}
}
}
function main() {
$obj = new BinaryTree();
/* Make A Binary Tree
-----------------------
1
/ \
2 3
/ / \
6 5 4
\ /
8 7
*/
$obj->root = new Node(1);
$obj->root->left = new Node(2);
$obj->root->right = new Node(3);
$obj->root->right->right = new Node(4);
$obj->root->right->right->left = new Node(7);
$obj->root->right->left = new Node(5);
$obj->root->left->left = new Node(6);
$obj->root->left->left->right = new Node(8);
$obj->inorder($obj->root);
$obj->deleteNode(6);
$obj->inorder($obj->root);
$obj->deleteNode(1);
$obj->inorder($obj->root);
$obj->deleteNode(4);
$obj->inorder($obj->root);
$obj->deleteNode(3);
$obj->inorder($obj->root);
$obj->deleteNode(3);
$obj->inorder($obj->root);
}
main();
Output
6 8 2 1 5 3 7 4
Delete : 6
8 2 1 5 3 7 4
Delete : 1
2 8 5 3 7 4
Delete : 4
2 8 5 3 7
Delete : 3
2 8 5 7
Delete node 3 is not found
2 8 5 7/*
Node JS Program
Delete a node in binary tree
*/
class Node {
constructor(value) {
this.data = value;
this.left = this.right = null;
}
}
class BinaryTree {
constructor() {
this.root = null;
this.parent = null;
}
find_parent(head, result, element) {
if (head != null && this.parent == null) {
if (element == head.data) {
this.parent = result;
return;
}
this.find_parent(head.left, head, element);
this.find_parent(head.right, head, element);
}
}
getNode(head) {
var auxiliary = head;
var temp = null;
while (auxiliary.left != null) {
temp = auxiliary;
auxiliary = auxiliary.left;
}
temp.left = auxiliary.right;
auxiliary.right = null;
head.data = auxiliary.data;
return auxiliary;
}
deleteNode(element) {
var head = this.root;
if (head == null) {
return;
}
var auxiliary = null;
if (head.data == element) {
auxiliary = head;
if (head.left == null) {
this.root = head.right;
} else
if (head.right == null) {
this.root = head.left;
} else {
auxiliary = this.getNode(head);
}
} else {
this.parent = null;
this.find_parent(head, head, element);
if (this.parent != null) {
if (this.parent.left != null && this.parent.left.data == element) {
auxiliary = this.parent.left;
if (auxiliary.left == null) {
this.parent.left = auxiliary.right;
} else
if (auxiliary.right == null) {
this.parent.left = auxiliary.left;
} else {
auxiliary = this.getNode(auxiliary);
}
} else
if (this.parent.right != null && this.parent.right.data == element) {
auxiliary = this.parent.right;
if (auxiliary.left == null) {
this.parent.right = auxiliary.right;
} else
if (auxiliary.right == null) {
this.parent.right = auxiliary.left;
} else {
auxiliary = this.getNode(auxiliary);
}
}
}
}
if (auxiliary != null) {
process.stdout.write("\n Delete : " + element);
auxiliary = null;
} else {
process.stdout.write("\n Delete node " + element + " is not found");
}
process.stdout.write("\n");
}
inorder(head) {
if (head != null) {
this.inorder(head.left);
process.stdout.write(" " + head.data);
this.inorder(head.right);
}
}
}
function main() {
var obj = new BinaryTree();
/* Make A Binary Tree
-----------------------
1
/ \
2 3
/ / \
6 5 4
\ /
8 7
*/
obj.root = new Node(1);
obj.root.left = new Node(2);
obj.root.right = new Node(3);
obj.root.right.right = new Node(4);
obj.root.right.right.left = new Node(7);
obj.root.right.left = new Node(5);
obj.root.left.left = new Node(6);
obj.root.left.left.right = new Node(8);
obj.inorder(obj.root);
obj.deleteNode(6);
obj.inorder(obj.root);
obj.deleteNode(1);
obj.inorder(obj.root);
obj.deleteNode(4);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
}
main();
Output
6 8 2 1 5 3 7 4
Delete : 6
8 2 1 5 3 7 4
Delete : 1
2 8 5 3 7 4
Delete : 4
2 8 5 3 7
Delete : 3
2 8 5 7
Delete node 3 is not found
2 8 5 7/*
Swift 4 Program
Delete a node in binary tree
*/
class Node {
var data: Int;
var left: Node? ;
var right: Node? ;
init(_ value: Int) {
self.data = value;
self.left = nil;
self.right = nil;
}
}
class BinaryTree {
var root: Node? ;
var parent: Node? ;
init() {
self.root = nil;
self.parent = nil;
}
func find_parent(_ head: Node? , _ result : Node? , _ element : Int) {
if (head != nil && self.parent == nil) {
if (element == head!.data) {
self.parent = result;
return;
}
self.find_parent(head!.left, head, element);
self.find_parent(head!.right, head, element);
}
}
func getNode(_ head: Node? ) -> Node? {
var auxiliary: Node? = head;
var temp: Node? = nil;
while (auxiliary!.left != nil) {
temp = auxiliary;
auxiliary = auxiliary!.left;
}
temp!.left = auxiliary!.right;
auxiliary!.right = nil;
head!.data = auxiliary!.data;
return auxiliary;
}
func deleteNode(_ element: Int) {
let head: Node? = self.root;
if (head == nil) {
return;
}
var auxiliary: Node? = nil;
if (head!.data == element) {
auxiliary = head;
if (head!.left == nil) {
self.root = head!.right;
} else
if (head!.right == nil) {
self.root = head!.left;
} else {
auxiliary = self.getNode(head);
}
} else {
self.parent = nil;
self.find_parent(head, head, element);
if (self.parent != nil) {
if (self.parent!.left != nil && self.parent!.left!.data == element) {
auxiliary = self.parent!.left;
if (auxiliary!.left == nil) {
self.parent!.left = auxiliary!.right;
} else
if (auxiliary!.right == nil) {
self.parent!.left = auxiliary!.left;
} else {
auxiliary = self.getNode(auxiliary);
}
} else
if (self.parent!.right != nil && self.parent!.right!.data == element) {
auxiliary = self.parent!.right;
if (auxiliary!.left == nil) {
self.parent!.right = auxiliary!.right;
} else
if (auxiliary!.right == nil) {
self.parent!.right = auxiliary!.left;
} else {
auxiliary = self.getNode(auxiliary);
}
}
}
}
if (auxiliary != nil) {
print("\n Delete : ", element);
auxiliary = nil;
} else {
print("\n Delete node ", element , " is not found");
}
}
func inorder(_ head: Node? ) {
if (head != nil) {
self.inorder(head!.left);
print(head!.data,terminator : " ");
self.inorder(head!.right);
}
}
}
func main() {
let obj: BinaryTree = BinaryTree();
/* Make A Binary Tree
-----------------------
1
/ \
2 3
/ / \
6 5 4
\ /
8 7
*/
obj.root = Node(1);
obj.root!.left = Node(2);
obj.root!.right = Node(3);
obj.root!.right!.right = Node(4);
obj.root!.right!.right!.left = Node(7);
obj.root!.right!.left = Node(5);
obj.root!.left!.left = Node(6);
obj.root!.left!.left!.right = Node(8);
obj.inorder(obj.root);
obj.deleteNode(6);
obj.inorder(obj.root);
obj.deleteNode(1);
obj.inorder(obj.root);
obj.deleteNode(4);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
obj.deleteNode(3);
obj.inorder(obj.root);
}
main();
Output
6 8 2 1 5 3 7 4
Delete : 6
8 2 1 5 3 7 4
Delete : 1
2 8 5 3 7 4
Delete : 4
2 8 5 3 7
Delete : 3
2 8 5 7
Delete node 3 is not found
2 8 5 7Time Complexity
The time complexity of the mentioned code is primarily determined by the tree traversal during the deletion operation, which is O(h), where 'h' is the height of the tree. In the worst case, when the tree is unbalanced and resembles a linked list, the time complexity becomes O(n), where 'n' is the number of nodes in the tree. However, in a balanced binary tree, the time complexity is closer to O(log n), where 'n' is the number of nodes.
This complexity arises because in the worst case, the algorithm may need to traverse the height of the tree twice: once during the search for the node to be deleted and again during the recursive deletion process.
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