Invert the levels of binary tree
The problem at hand involves inverting the levels of a binary tree. In other words, the nodes at each level of the tree need to be reversed in their order. This means that the leftmost node of a level should become the rightmost, and vice versa, for each level.
Problem Statement
Given a binary tree, the task is to invert the order of nodes at each level of the tree.
Example Scenario
Consider the following binary tree:
7
/ \
/ \
3 4
/ / \
2 6 8
/ \ \ /
1 5 7 10
/ \ \
9 3 11
After inverting the levels, the tree should look like:
7
/ \
/ \
4 3
/ / \
8 6 2
/ \ \ /
10 7 5 1
/ \ \
11 3 9
Idea to Solve the Problem
To solve this problem, we can perform a level-order traversal of the binary tree while reversing the nodes at each level. We can use a queue to traverse the tree level by level. For each level, we can reverse the order of nodes in the queue and update the tree nodes accordingly.
Pseudocode
void invert_level_nodes(struct Node *root)
{
if (root is NULL)
{
return;
}
// Create a queue for level-order traversal
// Enqueue the root node
while (the queue is not empty)
{
// Get the number of nodes at the current level
// Create an array to store node values at the current level
// Dequeue nodes and store their values in the array
// Update nodes' values in reverse order
// Enqueue left and right children of nodes in the queue
}
}
Algorithm Explanation
- Implement the
invert_level_nodes
function that takes the root node of the binary tree as input. - Create a queue for level-order traversal using the provided
enqueue
function. - Enqueue the root node of the tree into the queue.
- Start a loop that continues as long as the queue is not empty.
- Inside the loop, get the number of nodes at the current level and create an array to store their values.
- Dequeue nodes from the queue, store their values in the array, and update their values in reverse order.
- Enqueue the left and right children of the nodes into the queue.
- After the loop ends, the tree's levels will be inverted.
Code Solution
// C program
// Invert the levels of binary tree
#include <stdio.h>
#include <stdlib.h>
//Node of binary tree
struct Node
{
int data;
struct Node *left, *right;
};
struct MyQueue
{
int level;
struct Node *element;
struct MyQueue *next;
};
//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 node value
new_node->data = data;
new_node->left = NULL;
new_node->right = NULL;
}
else
{
printf("Memory Overflow\n");
}
//return reference
return new_node;
}
//Create a queue node and returns this node
struct MyQueue *enqueue(struct Node *tree_node)
{
//Make a new Queue node
struct MyQueue *new_node = (struct MyQueue *) malloc(sizeof(struct MyQueue));
if (new_node != NULL)
{
//Set node values
new_node->element = tree_node;
new_node->next = NULL;
}
else
{
printf("Memory Overflow\n");
}
return new_node;
}
//Remove a queue elements
void dequeue(struct MyQueue **front)
{
if ( *front != NULL)
{
struct MyQueue *remove = *front;
//Visit to next node
*front = remove->next;
remove->element = NULL;
remove->next = NULL;
//free node
free(remove);
remove = NULL;
}
}
//Reverse level nodes
void reverse_level(struct MyQueue *front, int level)
{
if (front == NULL)
{
return;
}
int size = 0;
struct MyQueue *temp = front;
//Count number of nodes in given level
while (temp != NULL && temp->level == level)
{
size++;
temp = temp->next;
}
if (size == 1)
{
//When only one element in given level
return;
}
else
{
//Useful for storing level values
int collection[size];
int location = 0;
//Start to first node
temp = front;
//Get level nodes from left to right
while (temp != NULL && temp->level == level)
{
// Get node value
collection[location] = temp->element->data;
temp = temp->next;
// Change location
location++;
}
location = size - 1;
//Start to first node
temp = front;
// Update level node with its reverse order node value
while (location >= 0 && temp != NULL && temp->level == level)
{
temp->element->data = collection[location];
temp = temp->next;
location--;
}
}
}
// Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
void invert_level_nodes(struct Node *root)
{
if (root != NULL)
{
//make queue pointers
struct MyQueue *front = NULL, *tail = NULL;
struct MyQueue *temp = NULL;
//make a tree pointer
struct Node *node = NULL;
//Get first node of tree
front = enqueue(root);
//Start level of first node is one
front->level = 1;
//Set tail node to first node
tail = front;
// Start to first node
temp = front;
int level = 0;
// Get level elements into a queue
while (temp != NULL)
{
//Tree node
node = temp->element;
//Get node level
level = temp->level + 1;
if (node->left != NULL)
{
//Add new left child node
tail->next = enqueue(node->left);
tail->next->level = level;
tail = tail->next;
}
if (node->right != NULL)
{
//Add new right child node
tail->next = enqueue(node->right);
tail->next->level = level;
tail = tail->next;
}
//Visit to next node queue
temp = temp->next;
}
//Print level nodes, and reverse level elements
while (front != NULL)
{
// Get node level
level = front->level;
reverse_level(front, level);
printf(" [");
//Print and removing queue nodes
while (front != NULL && front->level == level)
{
printf(" %d ", front->element->data);
//remove a queue node
dequeue( &front);
}
printf("]\n");
}
tail = NULL;
}
else
{
printf("Empty Tree\n");
}
}
int main()
{
struct Node *root = NULL;
/*
Construct Binary Tree
-----------------------
7
/ \
/ \
3 4
/ / \
2 6 8
/ \ \ /
1 5 7 10
/ \ \
9 3 11
-----------------------
*/
//Add node
root = insert(7);
root->left = insert(3);
root->right = insert(4);
root->right->right = insert(8);
root->right->left = insert(6);
root->left->left = insert(2);
root->left->left->left = insert(1);
root->left->left->right = insert(5);
root->right->left->right = insert(7);
root->right->right->left = insert(10);
root->left->left->right->left = insert(9);
root->left->left->right->right = insert(3);
root->right->left->right->right = insert(11);
/*
Converted Binary tree
-----------------------
7
/ \
/ \
4 3
/ / \
8 6 2
/ \ \ /
10 7 5 1
/ \ \
11 3 9
-----------------------
*/
invert_level_nodes(root);
return 0;
}
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
/*
Java program
Invert the levels of binary tree
*/
//Binary Tree node
class TreeNode
{
public int data;
public TreeNode left;
public TreeNode right;
public TreeNode(int data)
{
//set node value
this.data = data;
this.left = null;
this.right = null;
}
}
// Queue Node
class QueueNode
{
public TreeNode element;
public QueueNode next;
public int level;
public QueueNode(TreeNode element, int level)
{
this.element = element;
this.next = null;
this.level = level;
}
}
//Define custom queue class
class MyQueue
{
public QueueNode front;
public QueueNode tail;
public MyQueue()
{
this.front = null;
this.tail = null;
}
//Add a new node at last of queue
public void enqueue(TreeNode element, int level)
{
QueueNode new_node = new QueueNode(element, level);
if (this.front == null)
{
//When first node of queue
this.front = new_node;
}
else
{
//Add node at last position
this.tail.next = new_node;
}
this.tail = new_node;
}
//Delete first node of queue
public void dequeue()
{
if (this.front != null)
{
if (this.tail == this.front)
{
this.tail = null;
this.front = null;
}
else
{
this.front = this.front.next;
}
}
}
public boolean is_empty()
{
if (this.front == null)
{
return true;
}
else
{
return false;
}
}
}
class BinaryTree
{
public TreeNode root;
public BinaryTree()
{
// Set initial tree root to null
this.root = null;
}
//Reverse level nodes
public void reverse_level(MyQueue queue, int level)
{
if (queue.front == null)
{
return;
}
int size = 0;
QueueNode temp = queue.front;
//Count number of nodes in given level
while (temp != null && temp.level == level)
{
size++;
temp = temp.next;
}
if (size == 1)
{
//When only one element in given level
return;
}
else
{
//Useful for storing level values
int[] collection = new int[size];
int location = 0;
//Start to first node
temp = queue.front;
//Get level nodes from left to right
while (temp != null && temp.level == level)
{
// Get node value
collection[location] = temp.element.data;
temp = temp.next;
// Change location
location++;
}
location = size - 1;
//Start to first node
temp = queue.front;
// Update level node with its reverse order node value
while (location >= 0 && temp != null && temp.level == level)
{
temp.element.data = collection[location];
temp = temp.next;
location--;
}
}
}
// Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
public void invert_level_nodes()
{
if (this.root == null)
{
System.out.print("\n Empty Binary Tree \n");
}
else
{
//Get top node in tree
TreeNode node = this.root;
//Create a Queue
MyQueue queue = new MyQueue();
//Add first node at the level of one
queue.enqueue(node, 1);
QueueNode temp = queue.front;
int level = 0;
//Add tree level
while (temp != null)
{
node = temp.element;
level = temp.level;
if (node.left != null)
{
//Add left node
queue.enqueue(node.left, level + 1);
}
if (node.right != null)
{
//Add right node
queue.enqueue(node.right, level + 1);
}
temp = temp.next;
}
level = 0;
//Print level nodes, and reverse alternate level elements
while (queue.is_empty() == false)
{
level = queue.front.level;
System.out.print(" [");
//This reverse level
reverse_level(queue, level);
//Print and removing queue nodes
while (queue.is_empty() == false && queue.front.level == level)
{
//When sum exist
System.out.print(" " + queue.front.element.data);
//remove a queue node
queue.dequeue();
}
System.out.print(" ]\n");
}
}
}
public static void main(String[] args)
{
//Object of Binary Tree
BinaryTree tree = new BinaryTree();
/*
Construct Binary Tree
-----------------------
7
/ \
/ \
3 4
/ / \
2 6 8
/ \ \ /
1 5 7 10
/ \ \
9 3 11
--------------------------
*/
//Add node
tree.root = new TreeNode(7);
tree.root.left = new TreeNode(3);
tree.root.right = new TreeNode(4);
tree.root.right.right = new TreeNode(8);
tree.root.right.left = new TreeNode(6);
tree.root.left.left = new TreeNode(2);
tree.root.left.left.left = new TreeNode(1);
tree.root.left.left.right = new TreeNode(5);
tree.root.right.left.right = new TreeNode(7);
tree.root.right.right.left = new TreeNode(10);
tree.root.left.left.right.left = new TreeNode(9);
tree.root.left.left.right.right = new TreeNode(3);
tree.root.right.left.right.right = new TreeNode(11);
/*
Converted Binary tree
-----------------------
7
/ \
/ \
4 3
/ / \
2 6 8
/ \ \ /
10 7 5 1
/ \ \
9 3 11
-----------------------
*/
tree.invert_level_nodes();
}
}
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
//Include header file
#include <iostream>
using namespace std;
/*
C++ program
Invert the levels of binary tree
*/
//Binary Tree node
class TreeNode
{
public:
int data;
TreeNode *left;
TreeNode *right;
TreeNode(int data)
{
//set node value
this->data = data;
this->left = NULL;
this->right = NULL;
}
};
// Queue Node
class QueueNode
{
public:
TreeNode *element;
QueueNode *next;
int level;
QueueNode(TreeNode *element, int level)
{
this->element = element;
this->next = NULL;
this->level = level;
}
};
//Define custom queue class
class MyQueue
{
public:
QueueNode *front;
QueueNode *tail;
MyQueue()
{
this->front = NULL;
this->tail = NULL;
}
//Add a new node at last of queue
void enqueue(TreeNode *element, int level)
{
QueueNode *new_node = new QueueNode(element, level);
if (this->front == NULL)
{
//When first node of queue
this->front = new_node;
}
else
{
//Add node at last position
this->tail->next = new_node;
}
this->tail = new_node;
}
//Delete first node of queue
void dequeue()
{
if (this->front != NULL)
{
if (this->tail == this->front)
{
this->tail = NULL;
this->front = NULL;
}
else
{
this->front = this->front->next;
}
}
}
bool is_empty()
{
if (this->front == NULL)
{
return true;
}
else
{
return false;
}
}
};
class BinaryTree
{
public: TreeNode *root;
BinaryTree()
{
// Set initial tree root to null
this->root = NULL;
}
//Reverse level nodes
void reverse_level(MyQueue queue, int level)
{
if (queue.front == NULL)
{
return;
}
int size = 0;
QueueNode *temp = queue.front;
//Count number of nodes in given level
while (temp != NULL && temp->level == level)
{
size++;
temp = temp->next;
}
if (size == 1)
{
//When only one element in given level
return;
}
else
{
//Useful for storing level values
int collection[size];
int location = 0;
//Start to first node
temp = queue.front;
//Get level nodes from left to right
while (temp != NULL && temp->level == level)
{
// Get node value
collection[location] = temp->element->data;
temp = temp->next;
// Change location
location++;
}
location = size - 1;
//Start to first node
temp = queue.front;
// Update level node with its reverse order node value
while (location >= 0 && temp != NULL && temp->level == level)
{
temp->element->data = collection[location];
temp = temp->next;
location--;
}
}
}
// Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
void invert_level_nodes()
{
if (this->root == NULL)
{
cout << "\n Empty Binary Tree \n";
}
else
{
//Get top node in tree
TreeNode *node = this->root;
//Create a Queue
MyQueue queue = MyQueue();
//Add first node at the level of one
queue.enqueue(node, 1);
QueueNode *temp = queue.front;
int level = 0;
//Add tree level
while (temp != NULL)
{
node = temp->element;
level = temp->level;
if (node->left != NULL)
{
//Add left node
queue.enqueue(node->left, level + 1);
}
if (node->right != NULL)
{
//Add right node
queue.enqueue(node->right, level + 1);
}
temp = temp->next;
}
level = 0;
//Print level nodes, and reverse alternate level elements
while (queue.is_empty() == false)
{
level = queue.front->level;
cout << " [";
//This reverse level
this->reverse_level(queue, level);
//Print and removing queue nodes
while (queue.is_empty() == false && queue.front->level == level)
{
//When sum exist
cout << " " << queue.front->element->data;
//remove a queue node
queue.dequeue();
}
cout << " ]\n";
}
}
}
};
int main()
{
//Object of Binary Tree
BinaryTree tree = BinaryTree();
/*
Construct Binary Tree
-----------------------
7
/ \
/ \
3 4
/ / \
2 6 8
/ \ \ /
1 5 7 10
/ \ \
9 3 11
--------------------------
*/
tree.root = new TreeNode(7);
tree.root->left = new TreeNode(3);
tree.root->right = new TreeNode(4);
tree.root->right->right = new TreeNode(8);
tree.root->right->left = new TreeNode(6);
tree.root->left->left = new TreeNode(2);
tree.root->left->left->left = new TreeNode(1);
tree.root->left->left->right = new TreeNode(5);
tree.root->right->left->right = new TreeNode(7);
tree.root->right->right->left = new TreeNode(10);
tree.root->left->left->right->left = new TreeNode(9);
tree.root->left->left->right->right = new TreeNode(3);
tree.root->right->left->right->right = new TreeNode(11);
/*
Converted Binary tree
-----------------------
7
/ \
/ \
4 3
/ / \
2 6 8
/ \ \ /
10 7 5 1
/ \ \
9 3 11
-----------------------
*/
tree.invert_level_nodes();
return 0;
}
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
//Include namespace system
using System;
/*
C# program
Invert the levels of binary tree
*/
//Binary Tree node
class TreeNode
{
public int data;
public TreeNode left;
public TreeNode right;
public TreeNode(int data)
{
//set node value
this.data = data;
this.left = null;
this.right = null;
}
}
// Queue Node
class QueueNode
{
public TreeNode element;
public QueueNode next;
public int level;
public QueueNode(TreeNode element, int level)
{
this.element = element;
this.next = null;
this.level = level;
}
}
//Define custom queue class
class MyQueue
{
public QueueNode front;
public QueueNode tail;
public MyQueue()
{
this.front = null;
this.tail = null;
}
//Add a new node at last of queue
public void enqueue(TreeNode element, int level)
{
QueueNode new_node = new QueueNode(element, level);
if (this.front == null)
{
//When first node of queue
this.front = new_node;
}
else
{
//Add node at last position
this.tail.next = new_node;
}
this.tail = new_node;
}
//Delete first node of queue
public void dequeue()
{
if (this.front != null)
{
if (this.tail == this.front)
{
this.tail = null;
this.front = null;
}
else
{
this.front = this.front.next;
}
}
}
public Boolean is_empty()
{
if (this.front == null)
{
return true;
}
else
{
return false;
}
}
}
class BinaryTree
{
public TreeNode root;
public BinaryTree()
{
// Set initial tree root to null
this.root = null;
}
//Reverse level nodes
public void reverse_level(MyQueue queue, int level)
{
if (queue.front == null)
{
return;
}
int size = 0;
QueueNode temp = queue.front;
//Count number of nodes in given level
while (temp != null && temp.level == level)
{
size++;
temp = temp.next;
}
if (size == 1)
{
//When only one element in given level
return;
}
else
{
//Useful for storing level values
int[] collection = new int[size];
int location = 0;
//Start to first node
temp = queue.front;
//Get level nodes from left to right
while (temp != null && temp.level == level)
{
// Get node value
collection[location] = temp.element.data;
temp = temp.next;
// Change location
location++;
}
location = size - 1;
//Start to first node
temp = queue.front;
// Update level node with its reverse order node value
while (location >= 0 && temp != null && temp.level == level)
{
temp.element.data = collection[location];
temp = temp.next;
location--;
}
}
}
// Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
public void invert_level_nodes()
{
if (this.root == null)
{
Console.Write("\n Empty Binary Tree \n");
}
else
{
//Get top node in tree
TreeNode node = this.root;
//Create a Queue
MyQueue queue = new MyQueue();
//Add first node at the level of one
queue.enqueue(node, 1);
QueueNode temp = queue.front;
int level = 0;
//Add tree level
while (temp != null)
{
node = temp.element;
level = temp.level;
if (node.left != null)
{
//Add left node
queue.enqueue(node.left, level + 1);
}
if (node.right != null)
{
//Add right node
queue.enqueue(node.right, level + 1);
}
temp = temp.next;
}
level = 0;
//Print level nodes, and reverse alternate level elements
while (queue.is_empty() == false)
{
level = queue.front.level;
Console.Write(" [");
//This reverse level
reverse_level(queue, level);
//Print and removing queue nodes
while (queue.is_empty() == false && queue.front.level == level)
{
//When sum exist
Console.Write(" " + queue.front.element.data);
//remove a queue node
queue.dequeue();
}
Console.Write(" ]\n");
}
}
}
public static void Main(String[] args)
{
//Object of Binary Tree
BinaryTree tree = new BinaryTree();
/*
Construct Binary Tree
-----------------------
7
/ \
/ \
3 4
/ / \
2 6 8
/ \ \ /
1 5 7 10
/ \ \
9 3 11
--------------------------
*/
tree.root = new TreeNode(7);
tree.root.left = new TreeNode(3);
tree.root.right = new TreeNode(4);
tree.root.right.right = new TreeNode(8);
tree.root.right.left = new TreeNode(6);
tree.root.left.left = new TreeNode(2);
tree.root.left.left.left = new TreeNode(1);
tree.root.left.left.right = new TreeNode(5);
tree.root.right.left.right = new TreeNode(7);
tree.root.right.right.left = new TreeNode(10);
tree.root.left.left.right.left = new TreeNode(9);
tree.root.left.left.right.right = new TreeNode(3);
tree.root.right.left.right.right = new TreeNode(11);
/*
Converted Binary tree
-----------------------
7
/ \
/ \
4 3
/ / \
2 6 8
/ \ \ /
10 7 5 1
/ \ \
9 3 11
-----------------------
*/
tree.invert_level_nodes();
}
}
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
<?php
/*
Php program
Invert the levels of binary tree
*/
//Binary Tree node
class TreeNode
{
public $data;
public $left;
public $right;
function __construct($data)
{
//set node value
$this->data = $data;
$this->left = null;
$this->right = null;
}
}
// Queue Node
class QueueNode
{
public $element;
public $next;
public $level;
function __construct($element, $level)
{
$this->element = $element;
$this->next = null;
$this->level = $level;
}
}
//Define custom queue class
class MyQueue
{
public $front;
public $tail;
function __construct()
{
$this->front = null;
$this->tail = null;
}
//Add a new node at last of queue
public function enqueue($element, $level)
{
$new_node = new QueueNode($element, $level);
if ($this->front == null)
{
//When first node of queue
$this->front = $new_node;
}
else
{
//Add node at last position
$this->tail->next = $new_node;
}
$this->tail = $new_node;
}
//Delete first node of queue
public function dequeue()
{
if ($this->front != null)
{
if ($this->tail == $this->front)
{
$this->tail = null;
$this->front = null;
}
else
{
$this->front = $this->front->next;
}
}
}
public function is_empty()
{
if ($this->front == null)
{
return true;
}
else
{
return false;
}
}
}
class BinaryTree
{
public $root;
function __construct()
{
// Set initial tree root to null
$this->root = null;
}
//Reverse level nodes
public function reverse_level($queue, $level)
{
if ($queue->front == null)
{
return;
}
$size = 0;
$temp = $queue->front;
//Count number of nodes in given level
while ($temp != null && $temp->level == $level)
{
$size++;
$temp = $temp->next;
}
if ($size == 1)
{
//When only one element in given level
return;
}
else
{
//Useful for storing level values
$collection = array_fill(0, $size, 0);
$location = 0;
//Start to first node
$temp = $queue->front;
//Get level nodes from left to right
while ($temp != null && $temp->level == $level)
{
// Get node value
$collection[$location] = $temp->element->data;
$temp = $temp->next;
// Change location
$location++;
}
$location = $size - 1;
//Start to first node
$temp = $queue->front;
// Update level node with its reverse order node value
while ($location >= 0 && $temp != null && $temp->level == $level)
{
$temp->element->data = $collection[$location];
$temp = $temp->next;
$location--;
}
}
}
// Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
public function invert_level_nodes()
{
if ($this->root == null)
{
echo "\n Empty Binary Tree \n";
}
else
{
//Get top node in tree
$node = $this->root;
//Create a Queue
$queue = new MyQueue();
//Add first node at the level of one
$queue->enqueue($node, 1);
$temp = $queue->front;
$level = 0;
//Add tree level
while ($temp != null)
{
$node = $temp->element;
$level = $temp->level;
if ($node->left != null)
{
//Add left node
$queue->enqueue($node->left, $level + 1);
}
if ($node->right != null)
{
//Add right node
$queue->enqueue($node->right, $level + 1);
}
$temp = $temp->next;
}
$level = 0;
//Print level nodes, and reverse alternate level elements
while ($queue->is_empty() == false)
{
$level = $queue->front->level;
echo " [";
//This reverse level
$this->reverse_level($queue, $level);
//Print and removing queue nodes
while ($queue->is_empty() == false && $queue->front->level == $level)
{
//When sum exist
echo " ". $queue->front->element->data;
//remove a queue node
$queue->dequeue();
}
echo " ]\n";
}
}
}
}
function main()
{
//Object of Binary Tree
$tree = new BinaryTree();
/*
Construct Binary Tree
-----------------------
7
/ \
/ \
3 4
/ / \
2 6 8
/ \ \ /
1 5 7 10
/ \ \
9 3 11
--------------------------
*/
//Add node
$tree->root = new TreeNode(7);
$tree->root->left = new TreeNode(3);
$tree->root->right = new TreeNode(4);
$tree->root->right->right = new TreeNode(8);
$tree->root->right->left = new TreeNode(6);
$tree->root->left->left = new TreeNode(2);
$tree->root->left->left->left = new TreeNode(1);
$tree->root->left->left->right = new TreeNode(5);
$tree->root->right->left->right = new TreeNode(7);
$tree->root->right->right->left = new TreeNode(10);
$tree->root->left->left->right->left = new TreeNode(9);
$tree->root->left->left->right->right = new TreeNode(3);
$tree->root->right->left->right->right = new TreeNode(11);
/*
Converted Binary tree
-----------------------
7
/ \
/ \
4 3
/ / \
2 6 8
/ \ \ /
10 7 5 1
/ \ \
9 3 11
-----------------------
*/
$tree->invert_level_nodes();
}
main();
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
/*
Node Js program
Invert the levels of binary tree
*/
//Binary Tree node
class TreeNode
{
constructor(data)
{
//set node value
this.data = data;
this.left = null;
this.right = null;
}
}
// Queue Node
class QueueNode
{
constructor(element, level)
{
this.element = element;
this.next = null;
this.level = level;
}
}
//Define custom queue class
class MyQueue
{
constructor()
{
this.front = null;
this.tail = null;
}
//Add a new node at last of queue
enqueue(element, level)
{
var new_node = new QueueNode(element, level);
if (this.front == null)
{
//When first node of queue
this.front = new_node;
}
else
{
//Add node at last position
this.tail.next = new_node;
}
this.tail = new_node;
}
//Delete first node of queue
dequeue()
{
if (this.front != null)
{
if (this.tail == this.front)
{
this.tail = null;
this.front = null;
}
else
{
this.front = this.front.next;
}
}
}
is_empty()
{
if (this.front == null)
{
return true;
}
else
{
return false;
}
}
}
class BinaryTree
{
constructor()
{
// Set initial tree root to null
this.root = null;
}
//Reverse level nodes
reverse_level(queue, level)
{
if (queue.front == null)
{
return;
}
var size = 0;
var temp = queue.front;
//Count number of nodes in given level
while (temp != null && temp.level == level)
{
size++;
temp = temp.next;
}
if (size == 1)
{
//When only one element in given level
return;
}
else
{
//Useful for storing level values
var collection = Array(size).fill(0);
var location = 0;
//Start to first node
temp = queue.front;
//Get level nodes from left to right
while (temp != null && temp.level == level)
{
// Get node value
collection[location] = temp.element.data;
temp = temp.next;
// Change location
location++;
}
location = size - 1;
//Start to first node
temp = queue.front;
// Update level node with its reverse order node value
while (location >= 0 && temp != null && temp.level == level)
{
temp.element.data = collection[location];
temp = temp.next;
location--;
}
}
}
// Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
invert_level_nodes()
{
if (this.root == null)
{
process.stdout.write("\n Empty Binary Tree \n");
}
else
{
//Get top node in tree
var node = this.root;
//Create a Queue
var queue = new MyQueue();
//Add first node at the level of one
queue.enqueue(node, 1);
var temp = queue.front;
var level = 0;
//Add tree level
while (temp != null)
{
node = temp.element;
level = temp.level;
if (node.left != null)
{
//Add left node
queue.enqueue(node.left, level + 1);
}
if (node.right != null)
{
//Add right node
queue.enqueue(node.right, level + 1);
}
temp = temp.next;
}
level = 0;
//Print level nodes, and reverse alternate level elements
while (queue.is_empty() == false)
{
level = queue.front.level;
process.stdout.write(" [");
//This reverse level
this.reverse_level(queue, level);
//Print and removing queue nodes
while (queue.is_empty() == false && queue.front.level == level)
{
//When sum exist
process.stdout.write(" " + queue.front.element.data);
//remove a queue node
queue.dequeue();
}
process.stdout.write(" ]\n");
}
}
}
}
function main()
{
//Object of Binary Tree
var tree = new BinaryTree();
/*
Construct Binary Tree
-----------------------
7
/ \
/ \
3 4
/ / \
2 6 8
/ \ \ /
1 5 7 10
/ \ \
9 3 11
--------------------------
*/
//Add node
tree.root = new TreeNode(7);
tree.root.left = new TreeNode(3);
tree.root.right = new TreeNode(4);
tree.root.right.right = new TreeNode(8);
tree.root.right.left = new TreeNode(6);
tree.root.left.left = new TreeNode(2);
tree.root.left.left.left = new TreeNode(1);
tree.root.left.left.right = new TreeNode(5);
tree.root.right.left.right = new TreeNode(7);
tree.root.right.right.left = new TreeNode(10);
tree.root.left.left.right.left = new TreeNode(9);
tree.root.left.left.right.right = new TreeNode(3);
tree.root.right.left.right.right = new TreeNode(11);
/*
Converted Binary tree
-----------------------
7
/ \
/ \
4 3
/ / \
2 6 8
/ \ \ /
10 7 5 1
/ \ \
9 3 11
-----------------------
*/
tree.invert_level_nodes();
}
main();
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
# Python 3 program
# Invert the levels of binary tree
# Binary Tree node
class TreeNode :
def __init__(self, data) :
# set node value
self.data = data
self.left = None
self.right = None
# Queue Node
class QueueNode :
def __init__(self, element, level) :
self.element = element
self.next = None
self.level = level
# Define custom queue class
class MyQueue :
def __init__(self) :
self.front = None
self.tail = None
# Add a new node at last of queue
def enqueue(self, element, level) :
new_node = QueueNode(element, level)
if (self.front == None) :
# When first node of queue
self.front = new_node
else :
# Add node at last position
self.tail.next = new_node
self.tail = new_node
# Delete first node of queue
def dequeue(self) :
if (self.front != None) :
if (self.tail == self.front) :
self.tail = None
self.front = None
else :
self.front = self.front.next
def is_empty(self) :
if (self.front == None) :
return True
else :
return False
class BinaryTree :
def __init__(self) :
# Set initial tree root to null
self.root = None
# Reverse level nodes
def reverse_level(self, queue, level) :
if (queue.front == None) :
return
size = 0
temp = queue.front
# Count number of nodes in given level
while (temp != None and temp.level == level) :
size += 1
temp = temp.next
if (size == 1) :
# When only one element in given level
return
else :
# Useful for storing level values
collection = [0] * (size)
location = 0
# Start to first node
temp = queue.front
# Get level nodes from left to right
while (temp != None and temp.level == level) :
# Get node value
collection[location] = temp.element.data
temp = temp.next
# Change location
location += 1
location = size - 1
# Start to first node
temp = queue.front
# Update level node with its reverse order node value
while (location >= 0 and temp != None and temp.level == level) :
temp.element.data = collection[location]
temp = temp.next
location -= 1
# Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
def invert_level_nodes(self) :
if (self.root == None) :
print("\n Empty Binary Tree \n", end = "")
else :
# Get top node in tree
node = self.root
# Create a Queue
queue = MyQueue()
# Add first node at the level of one
queue.enqueue(node, 1)
temp = queue.front
level = 0
# Add tree level
while (temp != None) :
node = temp.element
level = temp.level
if (node.left != None) :
# Add left node
queue.enqueue(node.left, level + 1)
if (node.right != None) :
# Add right node
queue.enqueue(node.right, level + 1)
temp = temp.next
level = 0
# Print level nodes, and reverse alternate level elements
while (queue.is_empty() == False) :
level = queue.front.level
print(" [", end = "")
# This reverse level
self.reverse_level(queue, level)
# Print and removing queue nodes
while (queue.is_empty() == False and queue.front.level == level) :
# When sum exist
print(" ", queue.front.element.data, end = "")
# remove a queue node
queue.dequeue()
print(" ]\n", end = "")
def main() :
# Object of Binary Tree
tree = BinaryTree()
#
# Construct Binary Tree
# -----------------------
# 7
# / \
# / \
# 3 4
# / / \
# 2 6 8
# / \ \ /
# 1 5 7 10
# / \ \
# 9 3 11
# --------------------------
#
# Add node
tree.root = TreeNode(7)
tree.root.left = TreeNode(3)
tree.root.right = TreeNode(4)
tree.root.right.right = TreeNode(8)
tree.root.right.left = TreeNode(6)
tree.root.left.left = TreeNode(2)
tree.root.left.left.left = TreeNode(1)
tree.root.left.left.right = TreeNode(5)
tree.root.right.left.right = TreeNode(7)
tree.root.right.right.left = TreeNode(10)
tree.root.left.left.right.left = TreeNode(9)
tree.root.left.left.right.right = TreeNode(3)
tree.root.right.left.right.right = TreeNode(11)
#
# Converted Binary tree
# -----------------------
# 7
# / \
# / \
# 4 3
# / / \
# 2 6 8
# / \ \ /
# 10 7 5 1
# / \ \
# 9 3 11
# -----------------------
#
tree.invert_level_nodes()
if __name__ == "__main__": main()
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
# Ruby program
# Invert the levels of binary tree
# Binary Tree node
class TreeNode
# Define the accessor and reader of class TreeNode
attr_reader :data, :left, :right
attr_accessor :data, :left, :right
def initialize(data)
# set node value
self.data = data
self.left = nil
self.right = nil
end
end
# Queue Node
class QueueNode
# Define the accessor and reader of class QueueNode
attr_reader :element, :next, :level
attr_accessor :element, :next, :level
def initialize(element, level)
self.element = element
self.next = nil
self.level = level
end
end
# Define custom queue class
class MyQueue
# Define the accessor and reader of class MyQueue
attr_reader :front, :tail
attr_accessor :front, :tail
def initialize()
self.front = nil
self.tail = nil
end
# Add a new node at last of queue
def enqueue(element, level)
new_node = QueueNode.new(element, level)
if (self.front == nil)
# When first node of queue
self.front = new_node
else
# Add node at last position
self.tail.next = new_node
end
self.tail = new_node
end
# Delete first node of queue
def dequeue()
if (self.front != nil)
if (self.tail == self.front)
self.tail = nil
self.front = nil
else
self.front = self.front.next
end
end
end
def is_empty()
if (self.front == nil)
return true
else
return false
end
end
end
class BinaryTree
# Define the accessor and reader of class BinaryTree
attr_reader :root
attr_accessor :root
def initialize()
# Set initial tree root to null
self.root = nil
end
# Reverse level nodes
def reverse_level(queue, level)
if (queue.front == nil)
return
end
size = 0
temp = queue.front
# Count number of nodes in given level
while (temp != nil && temp.level == level)
size += 1
temp = temp.next
end
if (size == 1)
# When only one element in given level
return
else
# Useful for storing level values
collection = Array.new(size) {0}
location = 0
# Start to first node
temp = queue.front
# Get level nodes from left to right
while (temp != nil && temp.level == level)
# Get node value
collection[location] = temp.element.data
temp = temp.next
# Change location
location += 1
end
location = size - 1
# Start to first node
temp = queue.front
# Update level node with its reverse order node value
while (location >= 0 && temp != nil && temp.level == level)
temp.element.data = collection[location]
temp = temp.next
location -= 1
end
end
end
# Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
def invert_level_nodes()
if (self.root == nil)
print("\n Empty Binary Tree \n")
else
# Get top node in tree
node = self.root
# Create a Queue
queue = MyQueue.new()
# Add first node at the level of one
queue.enqueue(node, 1)
temp = queue.front
level = 0
# Add tree level
while (temp != nil)
node = temp.element
level = temp.level
if (node.left != nil)
# Add left node
queue.enqueue(node.left, level + 1)
end
if (node.right != nil)
# Add right node
queue.enqueue(node.right, level + 1)
end
temp = temp.next
end
level = 0
# Print level nodes, and reverse alternate level elements
while (queue.is_empty() == false)
level = queue.front.level
print(" [")
# This reverse level
self.reverse_level(queue, level)
# Print and removing queue nodes
while (queue.is_empty() == false && queue.front.level == level)
# When sum exist
print(" ", queue.front.element.data)
# remove a queue node
queue.dequeue()
end
print(" ]\n")
end
end
end
end
def main()
# Object of Binary Tree
tree = BinaryTree.new()
#
# Construct Binary Tree
# -----------------------
# 7
# / \
# / \
# 3 4
# / / \
# 2 6 8
# / \ \ /
# 1 5 7 10
# / \ \
# 9 3 11
# --------------------------
#
# Add node
tree.root = TreeNode.new(7)
tree.root.left = TreeNode.new(3)
tree.root.right = TreeNode.new(4)
tree.root.right.right = TreeNode.new(8)
tree.root.right.left = TreeNode.new(6)
tree.root.left.left = TreeNode.new(2)
tree.root.left.left.left = TreeNode.new(1)
tree.root.left.left.right = TreeNode.new(5)
tree.root.right.left.right = TreeNode.new(7)
tree.root.right.right.left = TreeNode.new(10)
tree.root.left.left.right.left = TreeNode.new(9)
tree.root.left.left.right.right = TreeNode.new(3)
tree.root.right.left.right.right = TreeNode.new(11)
#
# Converted Binary tree
# -----------------------
# 7
# / \
# / \
# 4 3
# / / \
# 2 6 8
# / \ \ /
# 10 7 5 1
# / \ \
# 9 3 11
# -----------------------
#
tree.invert_level_nodes()
end
main()
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
/*
Scala program
Invert the levels of binary tree
*/
//Binary Tree node
class TreeNode(var data: Int,
var left: TreeNode,
var right: TreeNode)
{
def this(data: Int)
{
this(data, null, null);
}
}
// Queue Node
class QueueNode(var element: TreeNode,
var next: QueueNode,
var level: Int)
{
def this(element: TreeNode, level: Int)
{
this(element, null, level);
}
}
//Define custom queue class
class MyQueue(var front: QueueNode,
var tail: QueueNode)
{
def this()
{
this(null, null);
}
//Add a new node at last of queue
def enqueue(element: TreeNode, level: Int): Unit = {
var new_node: QueueNode = new QueueNode(element, level);
if (this.front == null)
{
//When first node of queue
this.front = new_node;
}
else
{
//Add node at last position
this.tail.next = new_node;
}
this.tail = new_node;
}
//Delete first node of queue
def dequeue(): Unit = {
if (this.front != null)
{
if (this.tail == this.front)
{
this.tail = null;
this.front = null;
}
else
{
this.front = this.front.next;
}
}
}
def is_empty(): Boolean = {
if (this.front == null)
{
return true;
}
else
{
return false;
}
}
}
class BinaryTree(var root: TreeNode)
{
def this()
{
this(null);
}
//Reverse level nodes
def reverse_level(queue: MyQueue, level: Int): Unit = {
if (queue.front == null)
{
return;
}
var size: Int = 0;
var temp: QueueNode = queue.front;
//Count number of nodes in given level
while (temp != null && temp.level == level)
{
size += 1;
temp = temp.next;
}
if (size == 1)
{
//When only one element in given level
return;
}
else
{
//Useful for storing level values
var collection: Array[Int] = Array.fill[Int](size)(0);
var location: Int = 0;
//Start to first node
temp = queue.front;
//Get level nodes from left to right
while (temp != null && temp.level == level)
{
// Get node value
collection(location) = temp.element.data;
temp = temp.next;
// Change location
location += 1;
}
location = size - 1;
//Start to first node
temp = queue.front;
// Update level node with its reverse order node value
while (location >= 0 && temp != null && temp.level == level)
{
temp.element.data = collection(location);
temp = temp.next;
location -= 1;
}
}
}
// Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
def invert_level_nodes(): Unit = {
if (this.root == null)
{
print("\n Empty Binary Tree \n");
}
else
{
//Get top node in tree
var node: TreeNode = this.root;
//Create a Queue
var queue: MyQueue = new MyQueue();
//Add first node at the level of one
queue.enqueue(node, 1);
var temp: QueueNode = queue.front;
var level: Int = 0;
//Add tree level
while (temp != null)
{
node = temp.element;
level = temp.level;
if (node.left != null)
{
//Add left node
queue.enqueue(node.left, level + 1);
}
if (node.right != null)
{
//Add right node
queue.enqueue(node.right, level + 1);
}
temp = temp.next;
}
level = 0;
//Print level nodes, and reverse alternate level elements
while (queue.is_empty() == false)
{
level = queue.front.level;
print(" [");
//This reverse level
reverse_level(queue, level);
//Print and removing queue nodes
while (queue.is_empty() == false && queue.front.level == level)
{
//When sum exist
print(" " + queue.front.element.data);
//remove a queue node
queue.dequeue();
}
print(" ]\n");
}
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
//Object of Binary Tree
var tree: BinaryTree = new BinaryTree();
/*
Construct Binary Tree
-----------------------
7
/ \
/ \
3 4
/ / \
2 6 8
/ \ \ /
1 5 7 10
/ \ \
9 3 11
--------------------------
*/
//Add node
tree.root = new TreeNode(7);
tree.root.left = new TreeNode(3);
tree.root.right = new TreeNode(4);
tree.root.right.right = new TreeNode(8);
tree.root.right.left = new TreeNode(6);
tree.root.left.left = new TreeNode(2);
tree.root.left.left.left = new TreeNode(1);
tree.root.left.left.right = new TreeNode(5);
tree.root.right.left.right = new TreeNode(7);
tree.root.right.right.left = new TreeNode(10);
tree.root.left.left.right.left = new TreeNode(9);
tree.root.left.left.right.right = new TreeNode(3);
tree.root.right.left.right.right = new TreeNode(11);
/*
Converted Binary tree
-----------------------
7
/ \
/ \
4 3
/ / \
2 6 8
/ \ \ /
10 7 5 1
/ \ \
9 3 11
-----------------------
*/
tree.invert_level_nodes();
}
}
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
/*
Swift 4 program
Invert the levels of binary tree
*/
//Binary Tree node
class TreeNode
{
var data: Int;
var left: TreeNode? ;
var right: TreeNode? ;
init(_ data: Int)
{
//set node value
self.data = data;
self.left = nil;
self.right = nil;
}
}
// Queue Node
class QueueNode
{
var element: TreeNode? ;
var next: QueueNode? ;
var level: Int;
init(_ element: TreeNode? , _ level : Int)
{
self.element = element;
self.next = nil;
self.level = level;
}
}
//Define custom queue class
class MyQueue
{
var front: QueueNode? ;
var tail: QueueNode? ;
init()
{
self.front = nil;
self.tail = nil;
}
//Add a new node at last of queue
func enqueue(_ element: TreeNode? , _ level : Int)
{
let new_node: QueueNode? = QueueNode(element, level);
if (self.front == nil)
{
//When first node of queue
self.front = new_node;
}
else
{
//Add node at last position
self.tail!.next = new_node;
}
self.tail = new_node;
}
//Delete first node of queue
func dequeue()
{
if (self.front != nil)
{
if (self.tail === self.front)
{
self.tail = nil;
self.front = nil;
}
else
{
self.front = self.front!.next;
}
}
}
func is_empty() -> Bool
{
if (self.front == nil)
{
return true;
}
else
{
return false;
}
}
}
class BinaryTree
{
var root: TreeNode? ;
init()
{
// Set initial tree root to null
self.root = nil;
}
//Reverse level nodes
func reverse_level(_ queue: MyQueue , _ level : Int)
{
if (queue.front == nil)
{
return;
}
var size: Int = 0;
var temp: QueueNode? = queue.front;
//Count number of nodes in given level
while (temp != nil && temp!.level == level)
{
size += 1;
temp = temp!.next;
}
if (size == 1)
{
//When only one element in given level
return;
}
else
{
//Useful for storing level values
var collection: [Int] = Array(repeating: 0, count: size);
var location: Int = 0;
//Start to first node
temp = queue.front;
//Get level nodes from left to right
while (temp != nil && temp!.level == level)
{
// Get node value
collection[location] = temp!.element!.data;
temp = temp!.next;
// Change location
location += 1;
}
location = size - 1;
//Start to first node
temp = queue.front;
// Update level node with its reverse order node value
while (location >= 0 && temp != nil && temp!.level == level)
{
temp!.element!.data = collection[location];
temp = temp!.next;
location -= 1;
}
}
}
// Traverses the level order nodes in the binary tree , // And reversing the level nodes of the tree
func invert_level_nodes()
{
if (self.root == nil)
{
print("\n Empty Binary Tree \n", terminator: "");
}
else
{
//Get top node in tree
var node: TreeNode? = self.root;
//Create a Queue
let queue: MyQueue = MyQueue();
//Add first node at the level of one
queue.enqueue(node, 1);
var temp: QueueNode? = queue.front;
var level: Int = 0;
//Add tree level
while (temp != nil)
{
node = temp!.element;
level = temp!.level;
if (node!.left != nil)
{
//Add left node
queue.enqueue(node!.left, level + 1);
}
if (node!.right != nil)
{
//Add right node
queue.enqueue(node!.right, level + 1);
}
temp = temp!.next;
}
level = 0;
//Print level nodes, and reverse alternate level elements
while (queue.is_empty() == false)
{
level = queue.front!.level;
print(" [", terminator: "");
//This reverse level
self.reverse_level(queue, level);
//Print and removing queue nodes
while (queue.is_empty() == false && queue.front!.level == level)
{
//When sum exist
print(" ", queue.front!.element!.data, terminator: "");
//remove a queue node
queue.dequeue();
}
print(" ]\n", terminator: "");
}
}
}
}
func main()
{
//Object of Binary Tree
let tree: BinaryTree = BinaryTree();
/*
Construct Binary Tree
-----------------------
7
/ \
/ \
3 4
/ / \
2 6 8
/ \ \ /
1 5 7 10
/ \ \
9 3 11
--------------------------
*/
tree.root = TreeNode(7);
tree.root!.left = TreeNode(3);
tree.root!.right = TreeNode(4);
tree.root!.right!.right = TreeNode(8);
tree.root!.right!.left = TreeNode(6);
tree.root!.left!.left = TreeNode(2);
tree.root!.left!.left!.left = TreeNode(1);
tree.root!.left!.left!.right = TreeNode(5);
tree.root!.right!.left!.right = TreeNode(7);
tree.root!.right!.right!.left = TreeNode(10);
tree.root!.left!.left!.right!.left = TreeNode(9);
tree.root!.left!.left!.right!.right = TreeNode(3);
tree.root!.right!.left!.right!.right = TreeNode(11);
/*
Converted Binary tree
-----------------------
7
/ \
/ \
4 3
/ / \
2 6 8
/ \ \ /
10 7 5 1
/ \ \
9 3 11
-----------------------
*/
tree.invert_level_nodes();
}
main();
Output
[ 7 ]
[ 4 3 ]
[ 8 6 2 ]
[ 10 7 5 1 ]
[ 11 3 9 ]
Output Explanation
The code implements the algorithm and inverts the levels of the given binary tree. It constructs the binary tree, performs the level-order traversal while reversing the nodes' values at each level, and then prints the resulting inverted levels.
Time Complexity
The time complexity of this algorithm depends on the level-order traversal of the tree. If there are N nodes in the tree, the time complexity is O(N) as each node is processed once. The space complexity is also O(N) due to the queue used for traversal.
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