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When you are ready to continue with the explanation of balanced BST (we use AVL Tree as our example), press [Esc] again or switch the mode back to 'e-Lecture Mode' from the top-right corner drop down menu. A tag already exists with the provided branch name. In this project, I have implemented custom events and event handlers, Hint: Go back to the previous 4 slides ago. Before running this project, first install bgi graphics in visual studio. In this project, I have implemented custom events and event handlers, I have used Binary Search tree and Red-Black tree, and also I have used drawing tools. This part is also clearly O(1) on top of the earlier O(h) search-like effort. Binary Search Tree This visualization is a Binary Search Tree I built using JavaScript. In a Microsoft Word document, write a Reflection for Part 1 and Part 2. Name. 0 forks Releases No releases published. This allows us to print the values in the tree in order. Root vertex does not have a parent. How to handle duplicates in Binary Search Tree? We illustrate the operations by a sequence of snapshots during the A tree can be represented by an array, can be transformed to the array or can be build from the array. run it with java Main This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. This software was written by Corey Sanders '04 in 2002, under the supervision of Bob Sedgewick and Kevin Wayne. As we do not allow duplicate integer in this visualization, the BST property is as follow: For every vertex X, all vertices on the left subtree of X are strictly smaller than X and all vertices on the right subtree of X are strictly greater than X. Part 1 Reflection In a Microsoft Word document, write your Part 1 Reflection. Answer 4.6.3 questions 1-4 again, but this time use the simulator to validate your answer. Removing v without doing anything else will disconnect the BST. About. Very often algorithms compare two nodes (their values). Array is indexed (1, 2, 3, 7) and has values (2, 5, 22, 39, 44). Download the Java source code. Such BST is called AVL Tree, like the example shown above. The (integer) key of each vertex is drawn inside the circle that represent that vertex. If you use research in your answer, be sure to cite your sources. Thus the parent of 6 (and 23) is 15. If v is found in the BST, we do not report that the existing integer v is found, but instead, we perform one of the three possible removal cases that will be elaborated in three separate slides (we suggest that you try each of them one by one). Selected node is highlighted with red stroke. At this point, we encourage you to press [Esc] or click the X button on the bottom right of this e-Lecture slide to enter the 'Exploration Mode' and try various BST operations yourself to strengthen your understanding about this versatile data structure. Label Part 1 and Part 2 of your reflection accordingly. Notice that only a few vertices along the insertion path: {41,20,29,32} increases their height by +1 and all other vertices will have their heights unchanged. Take a moment to pause here and try inserting a few new random vertices or deleting a few random existing vertices. 'https:' : 'http:') + Then you can start using the application to the full. gcse.async = true; This means the search time increases at the same rate that the size of the array increases. For the example BST shown in the background, we have: {{15}, {6, 4, 5, 7}, {23, 71, 50}}. In Postorder Traversal, we visit the left subtree and right subtree first, before visiting the current root. WebBinary Search Tree. The left and right subtree each must also be a binary search tree. What Should I Learn First: Data Structures or Algorithms? The binarysearch website currently does not support a binary tree visualization tool that exists in other sites like LeetCode. This tool helps to resolve that. You can either input the tree array given by binarysearch, or create your own tree and copy it to binarysearch as a test case. The resulting tree is both pannable and zoomable. We keep doing this until we either find the required vertex or we don't. If we call Remove(FindMax()), i.e. Selection Sort Visualization; Insertion Sort Visualization; AVL Tree Visualization; Binary Search Tree Visualization; Red Black Tree Visualization; Single Referenced node is called child of referring node. The height of such BST is h = N-1, so we have h < N. Discussion: Do you know how to get skewed left BST instead? [9] : 298 [10] : 287. Data Structure and Algorithms CoursePractice Problems on Binary Search Tree !Recent Articles on Binary Search Tree ! Search(v)/FindMin()/FindMax() operations run in O(h) where h is the height of the BST. of operations, a splay tree Screen capture each tree and paste into a Microsoft Word document. For Introducing AVL Tree, invented by two Russian (Soviet) inventors: Georgy Adelson-Velskii and Evgenii Landis, back in 1962. In AVL Tree, we will later see that its height h < 2 * log N (tighter analysis exist, but we will use easier analysis in VisuAlgo where c = 2). For the node with the maximum value, similarly follow the right child pointers repeatedly. This is data structure project in cpp. Dictionary of Algorithms and Data Structures. To make life easier in 'Exploration Mode', you can create a new BST using these options: We are midway through the explanation of this BST module. The height is the maximum number of edges between the root and a leaf node. Kevin Wayne. ), list currently animating (sub)algorithm. A BST with N nodes has at least log2N levels and at most N levels. These graphic elements will show you which node is next in line. This is data structure project in cpp. The easiest way to support this is to add one more attribute at each vertex: the frequency of occurrence of X (this visualization will be upgraded with this feature soon). Enter the data you see in the 4.6.1 Participation Activity tree (19, 14, 25) by inserting each node in the simulator. We allow for duplicate entries, as the contents of e.g. Binary-Search-Tree-Visualization. Removing v without doing anything else will disconnect the BST. Scrolling back Binary Search Tree and Balanced Binary Search Tree Visualization To facilitate AVL Tree implementation, we need to augment add more information/attribute to each BST vertex. You can try each of these cases by clicking to remove nodes above, and check whether the invariant is maintained after the operation. Quiz: What are the values of height(20), height(65), and height(41) on the BST above? To have efficient performance, we shall not maintain height(v) attribute via the O(N) recursive method every time there is an update (Insert(v)/Remove(v)) operation. Try Insert(60) on the example above. You can learn more about Binary Search Trees sequence of tree operations. WebBinary Search Tree (BST) Code. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Binary Search Tree and Balanced Binary Search Tree Visualization. WebBinary Search Tree. Screen capture each tree and paste it into a Microsoft Word document. 0 stars Watchers. the search tree. Learn more. But this time, instead of reporting that the new integer is not found, we create a new vertex in the insertion point and put the new integer there. Discussion: Is there other tree rotation cases for Insert(v) operation of AVL Tree? See that all vertices are height-balanced, an AVL Tree. Installation. Reflect on how you observed this behavior in the simulator. Part 2 Reflection In a Microsoft Word document, write your Part 2 Reflection. Consider the tree on 15 nodes in the form of a linear list. Working with large BSTs can become complicated and inefficient unless a programmer can visualize them. Take screen captures of your trees as indicated in the steps below. trees have the wonderful property to adjust optimally to any The simpler data structure that can be used to implement Table ADT is Linked List. Data structure that is only efficient if there is no (or rare) update, especially the insert and/or remove operation(s) is called static data structure. to use Codespaces. The visualizations here are the work of David Galles. For the BST it is defined per node: all values in the left subtree of a node have to be less than or equal to the value of the parent node, while the values in the right subtree of a node have to be larger than or equal to the value of the parent node. Take screen captures as indicated in the steps for Part 1 and Part 2. Because of the BST properties, we can find the Successor of an integer v (assume that we already know where integer v is located from earlier call of Search(v)) as follows: The operations for Predecessor of an integer v are defined similarly (just the mirror of Successor operations). An Adelson-Velskii Landis (AVL) tree is a self-balancing BST that maintains it's height to be O(log N) when having N vertices in the AVL tree. This visualization is a Binary Search Tree I built using JavaScript. If it has no children, being a so-called leaf node, we can simply remove it without further ado. Leave open. The second case is also not that hard: Vertex v is an (internal/root) vertex of the BST and it has exactly one child. Screen capture and paste into a Microsoft Word document. This will open in a separate window. The main difference compared to Insert(v) in AVL tree is that we may trigger one of the four possible rebalancing cases several times, but not more than h = O(log N) times :O, try Remove(7) on the example above to see two chain reactions rotateRight(6) and then rotateRight(16)+rotateLeft(8) combo. We improve by your feedback. Binary search trees are called search trees because they make searching for a certain value more efficient than in an unordered tree. In an ideal binary search tree, we do not have to visit every node when searching for a particular value. The case where the new key is already present in the tree is not a problem. Thus, only O(h) vertices may change its height(v) attribute and in AVL Tree, h < 2 * log N. Try Insert(37) on the example AVL Tree (ignore the resulting rotation for now, we will come back to it in the next few slides). Part 1Validate zyBook Participation Activities 4.5.2, 4.5.3, and 4.5.4 in the tree simulator. Please share the post as many times as you can. PS: If you want to study how these seemingly complex AVL Tree (rotation) operations are implemented in a real program, you can download this AVLDemo.cpp (must be used together with this BSTDemo.cpp). s.parentNode.insertBefore(gcse, s); Binary Search Tree Algorithm Visualization. You can download the whole web and use it offline. WebBinary Tree Visualization Tree Type: BST RBT Min Heap (Tree) Max Heap (Tree) Min Heap (Array) Max Heap (Array) Stats: 0 reads, 0 writes. See the example shown above for N = 15 (a perfect BST which is rarely achievable in real life try inserting any other integer and it will not be perfect anymore). bf(29) = -2 and bf(20) = -2 too. Binary Search Tree Visualization. A splay tree is a self-adjusting binary search tree. Answer 4.6.1 questions 1-4 again, but this time use the simulator to validate your answer. })(); This software was written by Corey Sanders '04 in 2002, under the supervision of So can we have BST that has height closer to log2 N, i.e. Hi, I'm Ben. The level of engagement is determined by aspects like organic clicks, active sign ups or even potential leads to your classmates who can pay for the specific paper. Now I will try to show you a binary search tree. Insert(v) runs in O(h) where h is the height of the BST. , : site . WebBinaryTreeVisualiser - Binary Search Tree Site description here Home Binary Heap Binary Search Tree Pseudocodes Instructions Binary Search Tree Graphic elements There are As values are added to the Binary Search Tree new nodes are created. We can remove an integer in BST by performing similar operation as Search(v). Validate 4.5.4 questions 1-4 again, but this time use the simulator to check your answer. Will the resulting BST still considered height-balanced? We illustrate the Leaf nodes from Preorder of a Binary Search Tree (Using Recursion), Construct all possible BSTs for keys 1 to N, Check given array of size n can represent BST of n levels or not, Kth Largest Element in BST when modification to BST is not allowed, Check if given sorted sub-sequence exists in binary search tree, Maximum Unique Element in every subarray of size K, Count pairs from two BSTs whose sum is equal to a given value x, Print BST keys in given Range | O(1) Space, Inorder predecessor and successor for a given key in BST, Find if there is a triplet in a Balanced BST that adds to zero, Replace every element with the least greater element on its right, Count inversions in an array | Set 2 (Using Self-Balancing BST), Leaf nodes from Preorder of a Binary Search Tree. But recall that this h can be as tall as O(N) in a normal BST as shown in the random 'skewed right' example above. The right subtree of a node contains only nodes with keys greater than the nodes key. This article incorporates public domain material from Paul E. Black. Let's define the following important AVL Tree invariant (property that will never change): A vertex v is said to be height-balanced if |v.left.height - v.right.height| 1. Then I will briefly explain it to you. Growing Tree: A Binary Search Tree Visualization Launch using Java Web Start. Click on green node (left) to insert it into the tree, Click on any node in the tree to remove it. A start/end visualisation of an algorithms that traverse a tree. Resources. Browse the Java Installation. ASSIGNMENT Its time to demonstrate your skills and perform a Binary Search Tree Algorithm Visualization. Is it the same as the tree in zyBooks? Then you can start using the application to the full. We will try to resolve your query as soon as possible. Instructors are welcome to use this application, but if you do so, please Not all attributes will be used for all vertices, e.g. These web pages are part of my Bachelors final project on CTU FIT. It was updated by Jeffrey Hodes '12 in 2010. Download the Java source code. In the example above, the vertices on the left subtree of the root 15: {4, 5, 6, 7} are all smaller than 15 and the vertices on the right subtree of the root 15: {23, 50, 71} are all greater than 15. Growing Tree: A Binary Search Tree Visualization. Each Instead, we compute O(1): x.height = max(x.left.height, x.right.height) + 1 at the back of our Insert(v)/Remove(v) operation as only the height of vertices along the insertion/removal path may be affected. A Binary Search Tree (BST) is a binary tree in which each vertex has only up to 2 children that satisfies BST property: All vertices in the left subtree of a vertex must hold a value smaller than its own and all vertices in the right subtree of a vertex must hold a value larger than its own (we have assumption that all values are distinct integers in this visualization and small tweak is needed to cater for duplicates/non integer). A binary search tree is a rooted binary tree in which the nodes are arranged in total order in which the nodes with keys greater than any particular node is stored on the right sub-trees and the ones with equal to or less than are stored on the left sub-tree satisfying the binary search property. You can also display the elements in inorder, preorder, and postorder. The only rule of the Binary Search Tree is that the left node's value must be less than or equal to the parent node's value and the right node's value must be greater than or equal to the parent's value. In the background picture, we have N5 = 20 vertices but we know that we can squeeze 43 more vertices (up to N = 63) before we have a perfect binary tree of height h = 5. Please share your knowledge to improve code and content standard. Therefore, most AVL Tree operations run in O(log N) time efficient. Basically, there are only these four imbalance cases. The left and right properties are other nodes in the tree that are connected to the current node. There are definitions of used data structures and explanation of the algorithms. On the example BST above, height(11) = height(32) = height(50) = height(72) = height(99) = 0 (all are leaves). ; Bayer : Level-up|G4A, : , DEMO: , , : 3.262 2022, 14 Covid-19, Lelos Group: , AMGEN Hellas: , Viatris: leader . This has to be maintained for all nodes, subject only to exception for empty subtrees. Due to the way nodes in a binary search tree are ordered, an in-order traversal (left node, then root node, then right node) will always produce a sequence of values in increasing numerical order. Binary search trees are called search trees because they make searching for a certain value more efficient than in an unordered tree. This part is clearly O(1) on top of the earlier O(h) search-like effort. Binary Search Tree Visualization Searching. Algorithms usually traverse a tree or recursively call themselves on one child of just processing node. The left/right child of a vertex (except leaf) is drawn on the left/right and below of that vertex, respectively. Practice Problems on Binary Search Tree ! Each vertex has at least 4 attributes: parent, left, right, key/value/data (there are potential other attributes). here. Binary Search Tree and Balanced Binary Search Tree Visualization. We provide visualization for the following common BST/AVL Tree operations: There are a few other BST (Query) operations that have not been visualized in VisuAlgo: The details of these two operations are currently hidden for pedagogical purpose in a certain NUS module. So, is there a way to make our BSTs 'not that tall'? Find the Successor(v) 'next larger'/Predecessor(v) 'previous smaller' element. The first case is the easiest: Vertex v is currently one of the leaf vertex of the BST. rotateRight(T)/rotateLeft(T) can only be called if T has a left/right child, respectively. Part 2Validate the 4.6.1, 4.6.2, and 4.6.3 Participation Activities in the tree simulator. View the javadoc. By using our site, you Data structure that is efficient even if there are many update operations is called dynamic data structure. However, for registered users, you should login and then go to the Main Training Page to officially clear this module and such achievement will be recorded in your user account. Code Issues Pull requests Implement Data structure using java. We also have URL shortcut to quickly access the AVL Tree mode, which is https://visualgo.net/en/avl (you can change the 'en' to your two characters preferred language - if available). As values are added to the Binary Search Tree new nodes are created. In this regard, adding images, Social media tags and mentions are likely to boost the visibility of your posts to the targeted audience and enable you to get a higher discount code. After rotation, notice that subtree rooted at B (if it exists) changes parent, but P B Q does not change. Update operations (the BST structure may likely change): Walk up the AVL Tree from the insertion point back to the root and at every step, we update the height and balance factor of the affected vertices: Walk up the AVL Tree from the deletion point back to the root and at every step, we update the height and balance factor of the affected vertices. In the example above, (key) 15 has 6 as its left child and 23 as its right child. Look at the Reflect on what you see. Try them to consolidate and improve your understanding about this data structure. The procedure for that case is as follows: swap the positions of the removal node with it's predecessor according to the order of the BST. Comment. Is it possible that the depth of a tree increases during a, Consider the complete tree on 15 nodes. Calling rotateRight(Q) on the left picture will produce the right picture. Our implementation supports the following tree operations: Splay Trees were invented by Sleator and Tarjan in 1985. here. In binary trees there are maximum two children of any node - left child and right child. The left and right properties are other nodes in the tree that are connected to the current node. New Comment. In my free time I enjoy cycling and rock climbing. Copyright 20002019 ", , Science: 85 , ELPEN: 6 . WebBinary Search Tree (BST) Visualizer using Python by Tkinter. As you might have noticed by now, sometimes a binary tree becomes lopsided over time, like the one shown above, with all the nodes in the left or right subtree of the root. For the example BST shown in the background, we have: {{5, 4, 7, 6}, {50, 71, 23}, {15}}. var gcse = document.createElement('script'); 1 watching Forks. For a few more interesting questions about this data structure, please practice on BST/AVL training module (no login is required). - YouTube 0:00 / 5:52 If the desired key is less than the value of the current node, move to the left child node. Inorder Traversal runs in O(N), regardless of the height of the BST. You will have 6 images to submit for your Part II Reflection. WebUsage: Enter an integer key and click the Search button to search the key in the tree. Occasionally a rebalancing of the tree is necessary, more about this later. Try clicking FindMin() and FindMax() on the example BST shown above. var s = document.getElementsByTagName('script')[0]; Deletion of a leaf vertex is very easy: We just remove that leaf vertex try Remove(5) on the example BST above (second click onwards after the first removal will do nothing please refresh this page or go to another slide and return to this slide instead). At the moment there are implemented these data structures: binary search treeand binary heap + priority queue. Because of the way data (distinct integers for this visualization) is organised inside a BST, we can binary search for an integer v efficiently (hence the name of Binary Search Tree). Launch using Java Web Start. The predecessor will not have two children, so the removal node can be deleted from its new position using one of the two other cases above. Download as an executable jar. Aspirin Express icroctive, success story NUTRAMINS. Also, it can be shown that for any particular sequence Binary Search Tree Visualization. All rights reserved. in 2011 by Josh Israel '11. Work fast with our official CLI. We use Tree Rotation(s) to deal with each of them. A BST is called height-balanced according to the invariant above if every vertex in the BST is height-balanced. WebBinary search tree visualization. At this point, stop and ponder these three Successor(v)/Predecessor(v) cases to ensure that you understand these concepts. operations by a sequence of snapshots during the operation. Compilers; C Parser; We also have URL shortcut to quickly access the AVL Tree mode, which is https://visualgo.net/en/avl (you can change the 'en' to your two characters preferred language - if available). The third case is the most complex among the three: Vertex v is an (internal/root) vertex of the BST and it has exactly two children. For the best display, use integers between 0 and 99. More precisely, a sequence of m operations This visualization is a Binary Search Tree I built using JavaScript. Binary search trees (BSTs) are the typical tree data structure, and are used for fast access to data for a range of operations. https://kalkicode.com/data-structure/binary-search-tree New nodes can be inserted continuously and removed while maintaining good performance properties for all operations. A little of a theory you can get from pseudocode section. Post Comment. An edge is a reference from one node to another. We focus on AVL Tree (Adelson-Velskii & Landis, 1962) that is named after its inventor: Adelson-Velskii and Landis. If nothing happens, download GitHub Desktop and try again. Submit your Reflection for Part 1 and Part 2 as a single Microsoft Word document. Binary-Search-Tree-Visualization. We also have a few programming problems that somewhat requires the usage of this balanced BST (like AVL Tree) data structure: Kattis - compoundwords and Kattis - baconeggsandspam. First, we set the current vertex = root and then check if the current vertex is smaller/equal/larger than integer v that we are searching for. '//www.google.com/cse/cse.js?cx=' + cx; The hard part is the case where the node we want to remove has two child nodes. If the search ends at a node without an appropriate child node, the search terminates, failing to find the key. Robert Sedgewick Minimum Possible value of |ai + aj k| for given array and k. Special two digit numbers in a Binary Search Tree, Practice Problems on Binary Search Tree, Quizzes on Balanced Binary Search Trees, Learn Data Structure and Algorithms | DSA Tutorial. We will end this module with a few more interesting things about BST and balanced BST (especially AVL Tree). Algorithm Visualizations. (function() { We have now see how AVL Tree defines the height-balance invariant, maintain it for all vertices during Insert(v) and Remove(v) update operations, and a proof that AVL Tree has h < 2 * log N. Therefore, all BST operations (both update and query operations except Inorder Traversal) that we have learned so far, if they have time complexity of O(h), they have time complexity of O(log N) if we use AVL Tree version of BST. On the example BST above, try clicking Search(23) (found after 2 comparisons), Search(7) (found after 3 comparisons), Search(21) (not found after 2 comparisons at this point we will realize that we cannot find 21). Quiz: So what is the point of learning this BST module if Hash Table can do the crucial Table ADT operations in unlikely-to-be-beaten expected O(1) time? Vertices that are not leaf are called the internal vertices. A Table ADT must support at least the following three operations as efficient as possible: Reference: See similar slide in Hash Table e-Lecture. Binary Search Tree is a node-based binary tree data structure which has the following properties: A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. and forth in this sequence helps the user to understand the evolution of We are referring to Table ADT where the keys need to be ordered (as opposed to Table ADT where the keys do not need to be unordered). As above, to delete a node, we first find it in the tree, by search. Binary Search Tree is a node-based binary tree data structure which has the following properties: The left subtree of a node contains only nodes with keys lesser than This marks the end of this e-Lecture, but please switch to 'Exploration Mode' and try making various calls to Insert(v) and Remove(v) in AVL Tree mode to strengthen your understanding of this data structure. You will have 6 images to submit for your Part 1 Reflection. gcse.src = (document.location.protocol == 'https:' ? We can perform an Inorder Traversal of this BST to obtain a list of sorted integers inside this BST (in fact, if we 'flatten' the BST into one line, we will see that the vertices are ordered from smallest/leftmost to largest/rightmost). Rather than answering the question in the participation activity again, use the simulator to answer and validate your answers. We need to restore the balance. Validate 4.5.3 questions 1-5 again, but this time use the simulator to check your answer. They consist of nodes with zero to two To quickly detect if a vertex v is height balanced or not, we modify the AVL Tree invariant (that has absolute function inside) into: bf(v) = v.left.height - v.right.height. Use Git or checkout with SVN using the web URL. Before rotation, P B Q. When you get a discount code, you use it to place an order through this link, and a waiver applies based on the code you get via email, for example, a 100% discount means no charges will apply. Validate 4.5.2 questions 1-4 again by using the simulator to check your answer. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Full Stack Development with React & Node JS (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, What is Data Structure: Types, Classifications and Applications, Introduction to Hierarchical Data Structure, Overview of Graph, Trie, Segment Tree and Suffix Tree Data Structures. WebThe BinaryTreeVisualiseris a JavaScript application for visualising algorithms on binary trees. D3 Visualization | Bubble Chart - LADC Sample Sales, eCommerce Stories | Automating Order Placement & Data Entry, How To Build A Flip Card Component With React, How To Optimize Your Next.js Production Build, Build An eCommerce Color Search Tool With NodeJS + React | Part 2, Build An eCommerce Color Search Tool With NodeJS + React | Part 1. , . A copy resides here that may be modified from the original to be used for lectures and students. Inorder Traversal is a recursive method whereby we visit the left subtree first, exhausts all items in the left subtree, visit the current root, before exploring the right subtree and all items in the right subtree. Algorithm Visualizations. The trees shown here are used to store integers up to 200. Take screen captures of your trees as indicated in the steps below. Tree Rotation preserves BST property. First look at instructions where you find how to use this application. There are listed all graphic elements used in this application and their meanings. Also submit your doubts, and test case. A few vertices along the insertion path: {41,20,29,32} increases their height by +1. Browse the Java source code. They consist of nodes with zero to two children each, and a designated root node, shown at the top, above. Check for Identical BSTs without building the trees, Add all greater values to every node in a given BST, Check if two BSTs contain same set of elements, Construct BST from given preorder traversal | Set 1, BST to a Tree with sum of all smaller keys, Construct BST from its given level order traversal, Check if the given array can represent Level Order Traversal of Binary Search Tree, Lowest Common Ancestor in a Binary Search Tree, Find k-th smallest element in BST (Order Statistics in BST), Kth Largest element in BST using constant extra space, Largest number in BST which is less than or equal to N, Find distance between two nodes of a Binary Search Tree, Remove all leaf nodes from the binary search tree, Find the largest BST subtree in a given Binary Tree, Find a pair with given sum in a Balanced BST, Two nodes of a BST are swapped, correct the BST. 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