Sorted Data Structure Based on Hierarchical Nodes with Two Subtrees
Balanced Binary Search Trees (BSTs) are a type of binary tree data structure that maintain an ordered arrangement of data for efficient search, insertion, and deletion operations. This concept has led to the creation of structurally related balanced tree algorithms like AVL trees and Red-Black trees.
At its core, a BST has a hierarchical structure composed of nodes, each having up to two children. The ordering property of a BST ensures that for every node, all values in the left subtree are smaller, and all values in the right subtree are larger than the node's value. This property makes BSTs ideal for maintaining sorted data and performing search operations quickly.
One of the key advantages of BSTs is that they allow for efficient operations like search, insertion, and deletion to be performed in O(log n) time, degrading to O(n) in the worst-case. With self-balancing BSTs like AVL and Red Black Trees, the worst case can be ensured as O(Log n).
There are numerous problems that can be solved using BSTs. For example, finding if there is a triplet in a Balanced BST that adds to zero, or maximizing unique elements in every subarray of size K, or even solving the 2 Sum problem in a BST. In-place conversion of a BST to a Min-Heap, counting pairs from two BSTs whose sum is equal to a given value x, and correcting a swapped pair of nodes in BST are some other problems that can be addressed using BSTs.
Moreover, BSTs can be used to solve problems like finding the k-th smallest element in a BST, finding the maximum between two nodes of a BST, or finding the largest BST subtree. Solving 2 Sum problems in a Balanced BST, merging two Balanced Binary Search Trees, and finding the maximum sum with no two adjacent nodes in a BST are some other interesting problems that can be tackled using BSTs.
Basic operations on a BST include insertion, searching, deletion, finding minimum and maximum, floor, ceil, inorder successor, inorder predecessor, handling duplicates, and more. Medium standard problems on BSTs include finding the common ancestor, finding the lowest common ancestor, finding the height of the tree, finding the diameter of the tree, and more.
Constructing a BST from Level Order, computing LCA in a BST, transforming a Preorder into a Binary Search Tree, and identifying special two-digit numbers in a Binary Search Tree are some other problems that can be solved using BSTs.
Lastly, it's important to note that BSTs can also be used to convert a Sorted Linked List into a Balanced BST, and to check if a given array can represent a BST of n levels or not. Furthermore, one can practice problems on Binary Search Trees to enhance their understanding and problem-solving skills.
In conclusion, Balanced Binary Search Trees offer a powerful tool for solving a variety of problems efficiently. With their ability to maintain an ordered arrangement of data and their logarithmic time complexity for key operations, BSTs are an essential data structure in computer science.
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