Optimal Sequence for AVL Tree Insertion

Algorithm -

Step 1. Create a “Node” class for constructing the trees.

Step 2. Create a function “findOptimalSequence()” which takes two inputs - sorted array of integers and size of the array, and returns the optimal sequence for AVL tree insertion. Inside this function, call a function to create an AVL tree from the sorted array and then call a function to find its level order traversal. This vector formed by level order traversal will be the optimal sequence for AVL tree insertion, so return this.

Step 3. Next, create a function “sortedArrayToAVLTree()” to construct an AVL tree from a sorted array. Inside the function, create the root of the tree with the value of the middle element and then call the function recursively to construct the left and right subtree using the first and last half of array integers, respectively.  

Step 4. Finally, create a function “levelOrderTraversal()”, which will take the root of the binary tree and return its level order traversal.

C++ code:

// C++ program to find optimal sequence for AVL tree insertion #include <bits/stdc++.h> using namespace std; // Node class to create tree class Node { public: int data; Node* left; Node* right; Node(int val) { data = val; left = NULL; right = NULL; } }; //Function to construct AVL tree from a sorted array Node* sortedArrayToAVLTree(int arr[], int start, int end) { // Base Case if (start > end) { return NULL; } // Get the middle element and make it root int middle = (start + end) / 2; Node* root = new Node(arr[middle]); // Call the function recursively to construct the left subtree root->left = sortedArrayToAVLTree(arr, start, middle - 1);      // Call the function recursively to construct the right subtree root->right = sortedArrayToAVLTree(arr, middle + 1, end);    // Return the root of the tree return root; } // Function to find the level order traversal vector<int> levelOrderTraversal(Node *root) { vector<int> levelOrder; queue<Node*> q; if(root!=NULL) { q.push(root); } while (!q.empty()) { Node* curr_node = q.front(); q.pop(); levelOrder.push_back(curr_node->data); if (curr_node->left) { q.push(curr_node->left); } if (curr_node->right) { q.push(curr_node->right); } }    return levelOrder; } // Function to find the optimal sequence for AVL tree insertion vector<int> findOptimalSequence(int arr[], int n) { // Calling a function to construct an AVL tree using the sorted array Node* root = sortedArrayToAVLTree(arr, 0, n-1); // Calling a function to find the level order traversal of the AVL tree vector<int> optimalSequence = levelOrderTraversal(root); return optimalSequence; } // Main function int main() {    // Given size of the array    int n = 5;       // Given array int arr[5] = {4, 3, 2, 5, 1};    // sort the given array    sort(arr, arr+n);       // Call the function to find the optimal sequence for AVL tree insertion    vector<int> optimalSequence = findOptimalSequence(arr, n);    // Print the optimal sequence    for(int i=0; i<n; i++)    { cout<<optimalSequence[i]<<" ";    } return 0; } You can also try this code with Online C++ Compiler Run Code

Output: 3 1 4 2 5 You can also try this code with Online C++ Compiler Run Code

Algorithm Complexity: 

Time Complexity: O(N * log(N))

In the above approach to find an optimal sequence for AVL tree insertion, first, we have sorted the array which takes O(N * log(N)) time and then constructed the AVL tree, which takes O(N) time, and finally, the level order traversal which takes O(N) time. So, the overall time complexity is O(N * log(N)), where ‘N’ is the number of integers in the given array.

Space Complexity: O(N) 

In the above approach to find an optimal sequence for AVL tree insertion, we have constructed an AVL tree that takes O(N) space, and the vector to store the level order traversal also takes O(N) space. So, the overall space complexity is O(N), where ‘N’ is the number of integers in the given array.

Frequently asked questions-

1. What is a Binary Search Tree?

BST (Binary Search Tree) is a special binary tree in which there is a condition that all the nodes in the left subtree of any node will have a value less than that of the node, and all the nodes in the right subtree of the node will have a value greater than the value of the node.

2. What is an AVL Tree?

AVL trees, also known as self-balancing binary search trees, are a special type of binary search trees that adjust their height such that the difference of heights of left and right subtree of any node is either 0 or 1

Key takeaways-

IThis article discussed the problem “Optimal sequence for AVL tree construction”, the solution approach to this problem, its C++ implementation, and its time and space complexity. If you want to solve more problems on tree data structure for practice, you can visit Coding Ninjas Studio.

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Check out this problem - Largest BST In Binary Tree

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