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In Binary Tree, Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal.In Binary Search Tree, Inorder Successor of an input node can also be defined as the node with the smallest key greater than the key of the input node. So, it is sometimes important to find next node in sorted order.Inorder Successor in Binary Search Tree: <a href="https://www.geeksforgeeks.org/inorder-successor-in-binary-search-tree/">https://www.geeksforgeeks.org/inorder-successor-in-binary-search-tree/</a>

Inorder Successor in Binary Search Tree

Given values of two values n1 and n2 in a Binary Search Tree, find the Lowest Common Ancestor (LCA). You may assume that both the values exist in the tree.&nbsp; Input: LCA of 10 and 14 Output: &nbsp;12 Explanation: 12 is the closest node to both 10 and 14&nbsp; Algorithm: &nbsp;Create a recursive function that takes a node and the two values n1 and n2. If the value of the current node is less than both n1 and n2, then LCA lies in the right subtree. Call the recursive function for the right subtree. If the value of the current node is greater than both n1 and n2, then LCA lies in the left subtree. Call the recursive function for the left subtree. If both the above cases are false then return the current node as LCA.&nbsp;Lowest Common Ancestor in a Binary Search Tree &nbsp;: <a href="https://www.geeksforgeeks.org/lowest-common-ancestor-in-a-binary-search-tree/">https://www.geeksforgeeks.org/lowest-common-ancestor-in-a-binary-search-tree/</a>

Lowest Common Ancestor in a Binary Search Tree

Given two values k1 and k2 (where k1 &lt; k2) and a root pointer to a Binary Search Tree. Print all the keys of the tree in range k1 to k2. i.e. print all x such that k1&lt;=x&lt;=k2 and x is a key of given BST. Print all the keys in increasing order.&nbsp; Example:Graph: Input: k1 = 10 and k2 = 22 Output: 12, 20 and 22. Explanation: The keys are 4, 8, 12, 20, and 22. So keys in range 10 to 22 is 12, 20 and 22.Print BST keys in the given range: <a href="https://www.geeksforgeeks.org/print-bst-keys-in-the-given-range/">https://www.geeksforgeeks.org/print-bst-keys-in-the-given-range/</a>

Print BST keys in the given range

AVL Tree is a self-balancing Binary Search Tree where the height difference between left and right subtrees is at most one. Named after its inventors, it ensures O(Log n) time complexity for search, insertion, and deletion. AVL Trees perform rotations to maintain balance and allow efficient operations. They are commonly used in scenarios requiring predictable and consistent performance. AVL Trees are simpler to understand compared to Red-Black Trees. For more details, visit the GeeksforGeeks article: <a href="https://www.geeksforgeeks.org/introduction-to-avl-tree/">AVL Tree Data Structure</a>.

AVL Tree Data Structure

Given a Binary Search Tree (BST) and a range [min, max], remove all keys which are outside the given range. The modified tree should also be BST. For example, consider the following BST and range [-10, 13].&nbsp; There are two possible cases for every node.Node’s key is outside the given range. This case has two sub-cases.&nbsp; Node’s key is smaller than the min value.&nbsp; Node’s key is greater than the max value.Remove BST keys outside the given range &nbsp;: <a href="https://www.geeksforgeeks.org/remove-bst-keys-outside-the-given-range/">https://www.geeksforgeeks.org/remove-bst-keys-outside-the-given-range/</a>

Remove BST keys outside the given range

A simple method for solving this is to find the sum of all greater values for every node. This method would take O(n^2) time. The method discussed in this article uses the technique of reverse in-order tree traversal of BST which optimizes the problem to be solved in a single traversal.Approach: In this problem as we could notice that the largest node would remain the same. The value of 2nd largest node = value of largest + value of second largest node. Similarly, the value of nth largest node will be the sum of the n-th node and value of (n-1)th largest node after modification. So if we traverse the tree in descending order and simultaneously update the sum value at every step while adding the value to the root node, the problem would be solved.Add all greater values to every node in a given BST: <a href="https://www.geeksforgeeks.org/add-greater-values-every-node-given-bst/">https://www.geeksforgeeks.org/add-greater-values-every-node-given-bst/</a>

Add all greater values to every node in a given BST

Given a Binary Search Tree (BST) and a positive integer k, find the k’th largest element in the Binary Search Tree. For example, in the following BST, if k = 3, then output should be 14, and if k = 5, then output should be 10.&nbsp;K’th Largest Element in BST when modification to BST is not allowed : https://www.geeksforgeeks.org/kth-largest-element-in-bst-when-modification-to-bst-is-not-allowed/given a Binary Search Tree (BST) and a positive integer k, find the k’th largest element in the Binary Search Tree.&nbsp; For example, in the following BST, if k = 3, then output should be 14, and if k = 5, then output should be 10.K’th Largest Element in BST when modification to BST is not allowed &nbsp;: <a href="https://www.geeksforgeeks.org/kth-largest-element-in-bst-when-modification-to-bst-is-not-allowed/">https://www.geeksforgeeks.org/kth-largest-element-in-bst-when-modification-to-bst-is-not-allowed/</a>

K’th Largest Element in BST when modification to BST is not allowed

The idea is to traverse BST in inorder traversal. Note that Inorder traversal of BST accesses elements in sorted (or increasing) order. While traversing, we keep track of count of visited Nodes and keep adding Nodes until the count becomes k.&nbsp; Input : &nbsp;K = 3 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;8 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;/ &nbsp; \ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 7 &nbsp; &nbsp; 10 &nbsp; &nbsp; &nbsp; &nbsp; / &nbsp; &nbsp; &nbsp;/ &nbsp; \ &nbsp; &nbsp; &nbsp; &nbsp;2 &nbsp; &nbsp; &nbsp;9 &nbsp; &nbsp; 13 Output : 17 Explanation : Kth smallest element is 8 so sum of all &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;element smaller than or equal to 8 are &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2 + 7 + 8Sum of k smallest elements in BST : <a href="https://www.geeksforgeeks.org/sum-k-smallest-elements-bst/">https://www.geeksforgeeks.org/sum-k-smallest-elements-bst/</a>

Sum of k smallest elements in BST

Welcome to the daily solving of our PROBLEM OF THE DAY with Shivam Sinha We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Binary Search Tree but also build up problem-solving skills.Given two BSTs, return elements of merged BSTs in sorted form.Examples :Input:
BST1:
 &nbsp; &nbsp; &nbsp; 5
&nbsp; &nbsp; &nbsp;/ &nbsp; \
&nbsp; &nbsp; 3 &nbsp; &nbsp; 6
&nbsp; &nbsp;/ \
&nbsp; 2 &nbsp; 4 &nbsp;
BST2:
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;2
&nbsp; &nbsp; &nbsp; / &nbsp; \
&nbsp; &nbsp; &nbsp;1 &nbsp; &nbsp; 3
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;7
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; /
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6
Output: 1 2 2 3 3 4 5 6 6 7
Explanation: After merging and sorting the two BST we get 1 2 2 3 3 4 5 6 6 7.Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/merge-two-bst-s/1">https://practice.geeksforgeeks.org/problems/merge-two-bst-s/1</a>

PROBLEM OF THE DAY : 30/09/2024 | Merge two BST 's

This video is part of the Binary Search Tree section under GFG SDE Sheet. Given two BSTs, return elements of merged BSTs in sorted form.Examples :Input:
BST1:
 &nbsp; &nbsp; &nbsp; 5
&nbsp; &nbsp; &nbsp;/ &nbsp; \
&nbsp; &nbsp; 3 &nbsp; &nbsp; 6
&nbsp; &nbsp;/ \
&nbsp; 2 &nbsp; 4 &nbsp;
BST2:
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;2
&nbsp; &nbsp; &nbsp; / &nbsp; \
&nbsp; &nbsp; &nbsp;1 &nbsp; &nbsp; 3
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;7
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; /
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6
Output: 1 2 2 3 3 4 5 6 6 7
Explanation: After merging and sorting the two BST we get 1 2 2 3 3 4 5 6 6 7.Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/merge-two-bst-s/1">https://www.geeksforgeeks.org/problems/merge-two-bst-s/1</a> SDE Sheet Link: <a href="https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/">https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/</a> Article Link: <a href="https://www.geeksforgeeks.org/merge-two-balanced-binary-search-trees/">https://www.geeksforgeeks.org/merge-two-balanced-binary-search-trees/</a>

SDE Sheet - Merge Two Balanced Binary Search Trees

This video is part of the Binary Search Tree section under GFG SDE Sheet. Given a binary tree. Find the size of its largest subtree which is a Binary Search Tree. Note: Here Size equals the number of nodes in the subtree.Examples :Input: &nbsp; &nbsp;1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; / &nbsp;\ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 4&nbsp; &nbsp; &nbsp;4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;/ \&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6 &nbsp;&nbsp; 8 Output: 1&nbsp; Explanation: There's no sub-tree with size greater than 1 which forms a BST. All the leaf Nodes are the BSTs with size equal to 1.Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/largest-bst/1">https://www.geeksforgeeks.org/problems/largest-bst/1</a> SDE Sheet Link: <a href="https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/">https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/</a> Article Link: <a href="https://www.geeksforgeeks.org/largest-bst-binary-tree-set-2/">https://www.geeksforgeeks.org/largest-bst-binary-tree-set-2/</a>

SDE Sheet - Largest BST in Binary Tree

This video is part of the Binary Search Tree section under GFG SDE Sheet. Given a sorted array. Convert it into a Height Balanced Binary Search Tree (BST). Return the root of the BST.Height-balanced BST means a binary tree in which the depth of the left subtree and the right subtree of every node never differ by more than 1.Note: The driver code will check the BST, if it is a Height-balanced BST, the output will be true otherwise the output will be false.Examples :Input: nums = [1, 2, 3, 4]
Output: true
Explanation: The preorder traversal of the following BST formed is [2, 1, 3, 4]:
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;/ &nbsp; \
 &nbsp; &nbsp; &nbsp; &nbsp;1 &nbsp; &nbsp; 3
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;\
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 4Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/array-to-bst4443/1">https://www.geeksforgeeks.org/problems/array-to-bst4443/1</a> SDE Sheet Link: <a href="https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/">https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/</a> Article Link: <a href="https://www.geeksforgeeks.org/sorted-array-to-balanced-bst/">https://www.geeksforgeeks.org/sorted-array-to-balanced-bst/</a>

SDE Sheet - Sorted Array to Balanced BST