Optimal sequence for AVL tree insertion (without any rotations)

Last Updated : 11 Jul, 2025

Given an array of integers, the task is to find the sequence in which these integers should be added to an AVL tree such that no rotations are required to balance the tree.

Examples :

Input : array = {1, 2, 3} Output : 2 1 3 Input : array = {2, 4, 1, 3, 5, 6, 7} Output : 4 2 6 1 3 5 7

Approach :

Sort the given array of integers.
Create the AVL tree from the sorted array by following the approach described here.
Now, find the level order traversal of the tree which is the required sequence.
Adding numbers in the sequence found in the previous step will always maintain the height balance property of all the nodes in the tree.

Below is the implementation of the above approach :

C++

// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; /* A Binary Tree node */ struct TNode {  int data;  struct TNode* left;  struct TNode* right; }; struct TNode* newNode(int data); /* Function to construct AVL tree   from a sorted array */ struct TNode* sortedArrayToBST(vector<int> arr, int start, int end) {  /* Base Case */  if (start > end)  return NULL;  /* Get the middle element   and make it root */  int mid = (start + end) / 2;  struct TNode* root = newNode(arr[mid]);  /* Recursively construct the   left subtree and make it   left child of root */  root->left = sortedArrayToBST(arr, start, mid - 1);  /* Recursively construct the   right subtree and make it   right child of root */  root->right = sortedArrayToBST(arr, mid + 1, end);  return root; } /* Helper function that allocates  a new node with the given data   and NULL to the left and   the right pointers. */ struct TNode* newNode(int data) {  struct TNode* node = new TNode();  node->data = data;  node->left = NULL;  node->right = NULL;  return node; } // This function is used for testing purpose void printLevelOrder(TNode *root)  {   if (root == NULL) return;   queue<TNode *> q;   q.push(root);     while (q.empty() == false)   {   TNode *node = q.front();   cout << node->data << " ";   q.pop();   if (node->left != NULL)   q.push(node->left);   if (node->right != NULL)   q.push(node->right);   }  }  /* Driver program to  test above functions */ int main() {  // Assuming the array is sorted  vector<int> arr = { 1, 2, 3, 4, 5, 6, 7 };  int n = arr.size();  /* Convert List to AVL tree */  struct TNode* root = sortedArrayToBST(arr, 0, n - 1);  printLevelOrder(root);  return 0; }

Java

  // Java implementation of the approach import java.util.*; class solution { /* A Binary Tree node */  static class TNode {  int data;  TNode left;  TNode right; } /* Function to con AVL tree   from a sorted array */  static TNode sortedArrayToBST(int arr[], int start, int end) {  /* Base Case */  if (start > end)  return null;  /* Get the middle element   and make it root */  int mid = (start + end) / 2;  TNode root = newNode(arr[mid]);  /* Recursively construct the   left subtree and make it   left child of root */  root.left = sortedArrayToBST(arr, start, mid - 1);  /* Recursively construct the   right subtree and make it   right child of root */  root.right = sortedArrayToBST(arr, mid + 1, end);  return root; } /* Helper function that allocates  a new node with the given data   and null to the left and   the right pointers. */ static TNode newNode(int data) {  TNode node = new TNode();  node.data = data;  node.left = null;  node.right = null;  return node; } // This function is used for testing purpose static void printLevelOrder(TNode root)  {   if (root == null) return;   Queue<TNode > q= new LinkedList<TNode>();   q.add(root);     while (q.size()>0)   {   TNode node = q.element();   System.out.print( node.data + " ");   q.remove();   if (node.left != null)   q.add(node.left);   if (node.right != null)   q.add(node.right);   }  }  /* Driver program to  test above functions */ public static void main(String args[]) {  // Assuming the array is sorted  int arr[] = { 1, 2, 3, 4, 5, 6, 7 };  int n = arr.length;  /* Convert List to AVL tree */  TNode root = sortedArrayToBST(arr, 0, n - 1);  printLevelOrder(root); } } //contributed by Arnab Kundu

Python3

# Python3 code to print order of  # insertion into AVL tree to  # ensure no rotations # Tree Node class Node: def __init__(self, d): self.data = d self.left = None self.right = None # Function to convert sorted array  # to a balanced AVL Tree/BST # Input : sorted array of integers  # Output: root node of balanced AVL Tree/BST  def sortedArrayToBST(arr): if not arr: return None # Find middle and get its floor value mid = int((len(arr)) / 2) root = Node(arr[mid]) # Recursively construct the left  # and right subtree root.left = sortedArrayToBST(arr[:mid]) root.right = sortedArrayToBST(arr[mid + 1:]) # Return the root of the  # constructed tree return root # A utility function to print the # Level Order Traversal of AVL Tree # using a Queue def printLevelOrder(root): if not root: return q = [] q.append(root) # Keep printing the top element and # adding to queue while it is not empty while q != []: node = q.pop(0) print(node.data, end=" ") # If left node exists, enqueue it if node.left: q.append(node.left) # If right node exists, enqueue it  if node.right: q.append(node.right) # Driver Code arr = [1, 2, 3, 4, 5, 6, 7] root = sortedArrayToBST(arr) printLevelOrder(root) # This code is contributed  # by Adikar Bharath

// C# implementation of the approach using System; using System.Collections.Generic; class GFG { /* A Binary Tree node */ public class TNode {  public int data;  public TNode left;  public TNode right; } /* Function to con AVL tree  from a sorted array */ static TNode sortedArrayToBST(int []arr,  int start, int end) {  /* Base Case */  if (start > end)  return null;  /* Get the middle element   and make it root */  int mid = (start + end) / 2;  TNode root = newNode(arr[mid]);  /* Recursively construct the   left subtree and make it   left child of root */  root.left = sortedArrayToBST(arr, start, mid - 1);  /* Recursively construct the   right subtree and make it   right child of root */  root.right = sortedArrayToBST(arr, mid + 1, end);  return root; } /* Helper function that allocates a new node with the given data  and null to the left and  the right pointers. */ static TNode newNode(int data) {  TNode node = new TNode();  node.data = data;  node.left = null;  node.right = null;  return node; } // This function is used for testing purpose static void printLevelOrder(TNode root)  {   if (root == null) return;   Queue<TNode > q = new Queue<TNode>();   q.Enqueue(root);     while (q.Count > 0)   {   TNode node = q.Peek();   Console.Write( node.data + " ");   q.Dequeue();   if (node.left != null)   q.Enqueue(node.left);   if (node.right != null)   q.Enqueue(node.right);   }  }  /* Driver code */ public static void Main() {  // Assuming the array is sorted  int []arr = { 1, 2, 3, 4, 5, 6, 7 };  int n = arr.Length;  /* Convert List to AVL tree */  TNode root = sortedArrayToBST(arr, 0, n - 1);  printLevelOrder(root); } } /* This code contributed by PrinciRaj1992 */

JavaScript

<script> // Javascript implementation of the approach /* A Binary Tree node */ class TNode {  constructor()  {  this.data = 0;  this.left = null;  this.right = null;  } } /* Function to con AVL tree  from a sorted array */ function sortedArrayToBST(arr, start, end) {  /* Base Case */  if (start > end)  return null;  /* Get the middle element   and make it root */  var mid = parseInt((start + end) / 2);  var root = newNode(arr[mid]);  /* Recursively construct the   left subtree and make it   left child of root */  root.left = sortedArrayToBST(arr, start, mid - 1);  /* Recursively construct the   right subtree and make it   right child of root */  root.right = sortedArrayToBST(arr, mid + 1, end);  return root; } /* Helper function that allocates a new node with the given data  and null to the left and  the right pointers. */ function newNode(data) {  var node = new TNode();  node.data = data;  node.left = null;  node.right = null;  return node; } // This function is used for testing purpose function printLevelOrder(root)  {   if (root == null) return;   var q = [];   q.push(root);     while (q.length > 0)   {   var node = q[0];   document.write( node.data + " ");   q.shift();   if (node.left != null)   q.push(node.left);   if (node.right != null)   q.push(node.right);   }  }  /* Driver code */ // Assuming the array is sorted var arr = [1, 2, 3, 4, 5, 6, 7]; var n = arr.length; /* Convert List to AVL tree */ var root = sortedArrayToBST(arr, 0, n - 1); printLevelOrder(root); // This code is contributed by itsok. </script>