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A self-balancing AVL tree maintains near-perfect binary search tree height after each insertion or deletion by ensuring that for any given node, the height difference between its left and right subtrees is at most one. This property prevents the performance degradation associated with skewed binary search trees. The core implementation revolves ...

Valid Binary Search Tree (BST) properties: A node's left subtree contains only nodes with values less than the node's value. A node's right subtreee contains only nodes with values greater than the node's value. Both left and right subtrees must also be valid BSTs. Example 1: Input: root = [2,1,3] Output: true Example 2: Input: root = [5,1,4 ...

Self-Balancing Tree Structures Self-balancing binary search trees maintain logaritmhic height during insertions and deletions. This ensures efficietn search, insertion, and deletion operations. Below are implementations for three common variants: SBT, Treap, and Splay trees. Size Balanced Tree (SBT) #include <iostream> #include <cstdli ...

Splay trees are self-adjusting binary search trees where each accessed node is rotated to the root through a sequence of tree rotations. Although the initial structure satisfies BST ordering, intermediate states may not, yet the in-order traversal remains consistent. Rotation Mechanics Rotations follow the same scheme as Treaps: zig (single rot ...

Constructing Binary Trees from Inorder and Preorder TraversalsGiven the preorder and inorder traversal sequences of a binary tree, the tree structure can be uniquely reconstructed. The first element in the preorder sequence always represents the root of the current subtree. By locating this root value within the inorder sequence, one can partit ...

Recovering a Swapped Binary Search Tree A binary search tree (BST) has two of its nodes swapped by mistake. The task is to restore the tree to its correct BST form without altering its structure. The challenge is to achieve this with constant space complexity (O(1) space), avoiding the use of a full in-order traversal list. Approach The key obs ...

A Binary Search Tree (BST) is defined as either an empty tree or a tree satisfying these conditions: for any node, all values in its left subtree are less than its own value, and all values in its right subtree are greater. Both subtrees must also be BSTs. Given a sequence of unique integers, insert them sequentially into an initial empty BST. ...

Building a Maximum Binary Tree The algorithm constructs a binary tree from an integer array with distinct elemnets by recursively selecting the maximum value as the root. The process involves finding the largest element within the current array segment to create a node, then recursively applying the same logic to the left and right subarrays. I ...

Recall the properties of a BST: The left subtree of a node contains only nodes with keys less than the node's key. The right subtree of a node contains only nodes with keys greater than the node's key. Both the left and right subtrees must also be binary search trees. Example Scenarios Input: [4,1,6,0,2,5,7,null,null,null,3,null,null,null,8] ...

Minimal Absolute Difference in BST Since an in-order traversal of a binary search tree produces a sorted sequence, the smallest absolute difference between any two nodes corresponds to the minimal gap between adjacent elements in this sequence. The strategy involves tracking the previously visited node and comparing its value with the current n ...