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Splay tree is a self-adjusting binary search tree introduced by Daniel Sleator and Robert Tarjan. Unlike Treap which assigns random priorities to nodes, Splay tree performs rotations to move accessed nodes to the root, thereby maintaining balance during operations. Core Operations Node Clearing Reset all fields of a node to zero: void clear(int ...

A binary search tree (BST) organizes data such that each node's left subtree contains only keys less than the node, and the right subtree contains only keys greater. This ordering allows efficient search, insertion, and deletion. Node Structure and Tree Definition Basic node template storing a key and pointers to children: template <class K& ...

Counting Unique Binary Search Trees A binary search tree requires that all keys in the left subtree are smaller than the root, and all keys in the right subtree are larger. The number of structurally unique BSTs that store n distinct values depends only on n. Let ways[i] be the number of unique BSTs with i nodes. For the root, if the left subtr ...

Trimming a Binary Search Tree The task involves removing nodes from a binary search tree (BST) such that every remaining node's value falls within a specified range [low, high]. If the root node falls outside this range, the structure of the tree must be adjusted, potentially returning a new root. struct TreeNode* prune_bst(struct TreeNode* nod ...

Serializing Binary Search Trees To serialize a binary search tree (BST), we can utilize the properties of pre-order traversal. By recording node values as they are visited, we capture the structure necessary to reconstruct the tree. During deserialization, the bounds constraint imposed by the BST property (left subtree values must be smaller th ...

Tree Definiiton and Characteristics A tree is a data structure with n (n ≥ 0) finite nodes in a hierarchical relationship. Called a "tree" as it resembles an upside - down tree (root up, leaves down). Key traits: A node may have 0+ child nodes. The root node has no parent. Every non - root node has exactly one parent. Except the root ...

Trimming a Binary Search TreeGiven a Binary Search Tree (BST) and a valid range [low, high], the task is to trim the tree so that all node values fall within this inclusive range. The structure of the resulting tree should maintain BST properties.A common mistake is to simply return null when encountering a node outside the range:class Solution ...

Recursive Strategies: Traversal vs. Divide and ConquerRecursive solutions for binary trees typically fall into two categories:Traversal (Top-Down): The result is passed as a parameter during the recursive calls. The logic processes the node and propagates data downwards.Divide and Conquer (Bottom-Up): The result is returned by the function. The ...

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 ...