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trie-typed

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/** * data-structure-typed * * @author Pablo Zeng * @copyright Copyright (c) 2022 Pablo Zeng <zrwusa@gmail.com> * @license MIT License */ import { BST, BSTNode } from './bst'; import type { AVLTreeOptions, BinaryTreeDeleteResult, BinaryTreeOptions, BSTNOptKeyOrNode, EntryCallback, IterationType } from '../../types'; import { BSTOptions } from '../../types'; import { IBinaryTree } from '../../interfaces'; /** * Represents a Node in an AVL (Adelson-Velsky and Landis) Tree. * It extends a BSTNode and ensures the 'height' property is maintained. * * @template K - The type of the key. * @template V - The type of the value. */ export declare class AVLTreeNode<K = any, V = any> extends BSTNode<K, V> { parent?: AVLTreeNode<K, V>; /** * Creates an instance of AVLTreeNode. * @remarks Time O(1), Space O(1) * * @param key - The key of the node. * @param [value] - The value associated with the key. */ constructor(key: K, value?: V); _left?: AVLTreeNode<K, V> | null | undefined; /** * Gets the left child of the node. * @remarks Time O(1), Space O(1) * * @returns The left child. */ get left(): AVLTreeNode<K, V> | null | undefined; /** * Sets the left child of the node and updates its parent reference. * @remarks Time O(1), Space O(1) * * @param v - The node to set as the left child. */ set left(v: AVLTreeNode<K, V> | null | undefined); _right?: AVLTreeNode<K, V> | null | undefined; /** * Gets the right child of the node. * @remarks Time O(1), Space O(1) * * @returns The right child. */ get right(): AVLTreeNode<K, V> | null | undefined; /** * Sets the right child of the node and updates its parent reference. * @remarks Time O(1), Space O(1) * * @param v - The node to set as the right child. */ set right(v: AVLTreeNode<K, V> | null | undefined); } /** * Represents a self-balancing AVL (Adelson-Velsky and Landis) Tree. * This tree extends BST and performs rotations on add/delete to maintain balance. * * @template K - The type of the key. * @template V - The type of the value. * @template R - The type of the raw data object (if using `toEntryFn`). * * 1. Height-Balanced: Each node's left and right subtrees differ in height by no more than one. * 2. Automatic Rebalancing: AVL trees rebalance themselves automatically during insertions and deletions. * 3. Rotations for Balancing: Utilizes rotations (single or double) to maintain balance after updates. * 4. Order Preservation: Maintains the binary search tree property where left child values are less than the parent, and right child values are greater. * 5. Efficient Lookups: Offers O(log n) search time, where 'n' is the number of nodes, due to its balanced nature. * 6. Complex Insertions and Deletions: Due to rebalancing, these operations are more complex than in a regular BST. * 7. Path Length: The path length from the root to any leaf is longer compared to an unbalanced BST, but shorter than a linear chain of nodes.@example * // Find elements in a range * // In interval queries, AVL trees, with their strictly balanced structure and lower height, offer better query efficiency, making them ideal for frequent and high-performance interval queries. In contrast, Red-Black trees, with lower update costs, are more suitable for scenarios involving frequent insertions and deletions where the requirements for interval queries are less demanding. * type Datum = { timestamp: Date; temperature: number }; * // Fixed dataset of CPU temperature readings * const cpuData: Datum[] = [ * { timestamp: new Date('2024-12-02T00:00:00'), temperature: 55.1 }, * { timestamp: new Date('2024-12-02T00:01:00'), temperature: 56.3 }, * { timestamp: new Date('2024-12-02T00:02:00'), temperature: 54.8 }, * { timestamp: new Date('2024-12-02T00:03:00'), temperature: 57.2 }, * { timestamp: new Date('2024-12-02T00:04:00'), temperature: 58.0 }, * { timestamp: new Date('2024-12-02T00:05:00'), temperature: 59.4 }, * { timestamp: new Date('2024-12-02T00:06:00'), temperature: 60.1 }, * { timestamp: new Date('2024-12-02T00:07:00'), temperature: 61.3 }, * { timestamp: new Date('2024-12-02T00:08:00'), temperature: 62.0 }, * { timestamp: new Date('2024-12-02T00:09:00'), temperature: 63.5 }, * { timestamp: new Date('2024-12-02T00:10:00'), temperature: 64.0 }, * { timestamp: new Date('2024-12-02T00:11:00'), temperature: 62.8 }, * { timestamp: new Date('2024-12-02T00:12:00'), temperature: 61.5 }, * { timestamp: new Date('2024-12-02T00:13:00'), temperature: 60.2 }, * { timestamp: new Date('2024-12-02T00:14:00'), temperature: 59.8 }, * { timestamp: new Date('2024-12-02T00:15:00'), temperature: 58.6 }, * { timestamp: new Date('2024-12-02T00:16:00'), temperature: 57.4 }, * { timestamp: new Date('2024-12-02T00:17:00'), temperature: 56.2 }, * { timestamp: new Date('2024-12-02T00:18:00'), temperature: 55.7 }, * { timestamp: new Date('2024-12-02T00:19:00'), temperature: 54.5 }, * { timestamp: new Date('2024-12-02T00:20:00'), temperature: 53.2 }, * { timestamp: new Date('2024-12-02T00:21:00'), temperature: 52.8 }, * { timestamp: new Date('2024-12-02T00:22:00'), temperature: 51.9 }, * { timestamp: new Date('2024-12-02T00:23:00'), temperature: 50.5 }, * { timestamp: new Date('2024-12-02T00:24:00'), temperature: 49.8 }, * { timestamp: new Date('2024-12-02T00:25:00'), temperature: 48.7 }, * { timestamp: new Date('2024-12-02T00:26:00'), temperature: 47.5 }, * { timestamp: new Date('2024-12-02T00:27:00'), temperature: 46.3 }, * { timestamp: new Date('2024-12-02T00:28:00'), temperature: 45.9 }, * { timestamp: new Date('2024-12-02T00:29:00'), temperature: 45.0 } * ]; * * // Create an AVL tree to store CPU temperature data * const cpuTemperatureTree = new AVLTree<Date, number, Datum>(cpuData, { * toEntryFn: ({ timestamp, temperature }) => [timestamp, temperature] * }); * * // Query a specific time range (e.g., from 00:05 to 00:15) * const rangeStart = new Date('2024-12-02T00:05:00'); * const rangeEnd = new Date('2024-12-02T00:15:00'); * const rangeResults = cpuTemperatureTree.rangeSearch([rangeStart, rangeEnd], node => ({ * minute: node ? node.key.getMinutes() : 0, * temperature: cpuTemperatureTree.get(node ? node.key : undefined) * })); * * console.log(rangeResults); // [ * // { minute: 5, temperature: 59.4 }, * // { minute: 6, temperature: 60.1 }, * // { minute: 7, temperature: 61.3 }, * // { minute: 8, temperature: 62 }, * // { minute: 9, temperature: 63.5 }, * // { minute: 10, temperature: 64 }, * // { minute: 11, temperature: 62.8 }, * // { minute: 12, temperature: 61.5 }, * // { minute: 13, temperature: 60.2 }, * // { minute: 14, temperature: 59.8 }, * // { minute: 15, temperature: 58.6 } * // ] */ export declare class AVLTree<K = any, V = any, R extends object = object> extends BST<K, V, R> implements IBinaryTree<K, V, R> { /** * Creates an instance of AVLTree. * @remarks Time O(N log N) (from `addMany` with balanced add). Space O(N). * * @param [keysNodesEntriesOrRaws=[]] - An iterable of items to add. * @param [options] - Configuration options for the AVL tree. */ constructor(keysNodesEntriesOrRaws?: Iterable<K | AVLTreeNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | R>, options?: AVLTreeOptions<K, V, R>); /** * (Protected) Creates a new AVL tree node. * @remarks Time O(1), Space O(1) * * @param key - The key for the new node. * @param [value] - The value for the new node. * @returns The newly created AVLTreeNode. */ _createNode(key: K, value?: V): AVLTreeNode<K, V>; /** * Checks if the given item is an `AVLTreeNode` instance. * @remarks Time O(1), Space O(1) * * @param keyNodeOrEntry - The item to check. * @returns True if it's an AVLTreeNode, false otherwise. */ isNode(keyNodeOrEntry: K | AVLTreeNode<K, V> | [K | null | undefined, V | undefined] | null | undefined): keyNodeOrEntry is AVLTreeNode<K, V>; /** * Adds a new node to the AVL tree and balances the tree path. * @remarks Time O(log N) (O(H) for BST add + O(H) for `_balancePath`). Space O(H) for path/recursion. * * @param keyNodeOrEntry - The key, node, or entry to add. * @param [value] - The value, if providing just a key. * @returns True if the addition was successful, false otherwise. */ add(keyNodeOrEntry: K | AVLTreeNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, value?: V): boolean; /** * Deletes a node from the AVL tree and re-balances the tree. * @remarks Time O(log N) (O(H) for BST delete + O(H) for `_balancePath`). Space O(H) for path/recursion. * * @param keyNodeOrEntry - The node to delete. * @returns An array containing deletion results. */ delete(keyNodeOrEntry: K | AVLTreeNode<K, V> | [K | null | undefined, V | undefined] | null | undefined): BinaryTreeDeleteResult<AVLTreeNode<K, V>>[]; /** * Rebuilds the tree to be perfectly balanced. * @remarks AVL trees are already height-balanced, but this makes them *perfectly* balanced (minimal height and all leaves at N or N-1). * Time O(N) (O(N) for DFS, O(N) for sorted build). Space O(N) for node array and recursion stack. * * @param [iterationType=this.iterationType] - The traversal method for the initial node export. * @returns True if successful, false if the tree was empty. */ perfectlyBalance(iterationType?: IterationType): boolean; /** * Creates a new AVLTree by mapping each [key, value] pair. * @remarks Time O(N log N) (O(N) iteration + O(log M) `add` for each item into the new tree). Space O(N) for the new tree. * * @template MK - New key type. * @template MV - New value type. * @template MR - New raw type. * @param callback - A function to map each [key, value] pair. * @param [options] - Options for the new AVLTree. * @param [thisArg] - `this` context for the callback. * @returns A new, mapped AVLTree. */ map<MK = K, MV = V, MR extends object = object>(callback: EntryCallback<K, V | undefined, [MK, MV]>, options?: Partial<BinaryTreeOptions<MK, MV, MR>>, thisArg?: unknown): AVLTree<MK, MV, MR>; /** * (Protected) Creates a new, empty instance of the same AVLTree constructor. * @remarks Time O(1) * * @template TK, TV, TR - Generic types for the new instance. * @param [options] - Options for the new tree. * @returns A new, empty tree. */ protected _createInstance<TK = K, TV = V, TR extends object = R>(options?: Partial<BSTOptions<TK, TV, TR>>): this; /** * (Protected) Creates a new instance of the same AVLTree constructor, potentially with different generic types. * @remarks Time O(N log N) (from constructor) due to processing the iterable. * * @template TK, TV, TR - Generic types for the new instance. * @param [iter=[]] - An iterable to populate the new tree. * @param [options] - Options for the new tree. * @returns A new AVLTree. */ protected _createLike<TK = K, TV = V, TR extends object = R>(iter?: Iterable<TK | BSTNode<TK, TV> | [TK | null | undefined, TV | undefined] | null | undefined | TR>, options?: Partial<BSTOptions<TK, TV, TR>>): AVLTree<TK, TV, TR>; /** * (Protected) Swaps properties of two nodes, including height. * @remarks Time O(H) (due to `ensureNode`), but O(1) if nodes are passed directly. * * @param srcNode - The source node. * @param destNode - The destination node. * @returns The `destNode` (now holding `srcNode`'s properties). */ protected _swapProperties(srcNode: BSTNOptKeyOrNode<K, AVLTreeNode<K, V>>, destNode: BSTNOptKeyOrNode<K, AVLTreeNode<K, V>>): AVLTreeNode<K, V> | undefined; /** * (Protected) Calculates the balance factor (height(right) - height(left)). * @remarks Time O(1) (assumes heights are stored). * * @param node - The node to check. * @returns The balance factor (positive if right-heavy, negative if left-heavy). */ protected _balanceFactor(node: AVLTreeNode<K, V>): number; /** * (Protected) Recalculates and updates the height of a node based on its children's heights. * @remarks Time O(1) (assumes children's heights are correct). * * @param node - The node to update. */ protected _updateHeight(node: AVLTreeNode<K, V>): void; /** * (Protected) Performs a Left-Left (LL) rotation (a single right rotation). * @remarks Time O(1), Space O(1) * * @param A - The unbalanced node (root of the unbalanced subtree). */ protected _balanceLL(A: AVLTreeNode<K, V>): void; /** * (Protected) Performs a Left-Right (LR) double rotation. * @remarks Time O(1), Space O(1) * * @param A - The unbalanced node (root of the unbalanced subtree). */ protected _balanceLR(A: AVLTreeNode<K, V>): void; /** * (Protected) Performs a Right-Right (RR) rotation (a single left rotation). * @remarks Time O(1), Space O(1) * * @param A - The unbalanced node (root of the unbalanced subtree). */ protected _balanceRR(A: AVLTreeNode<K, V>): void; /** * (Protected) Performs a Right-Left (RL) double rotation. * @remarks Time O(1), Space O(1) * * @param A - The unbalanced node (root of the unbalanced subtree). */ protected _balanceRL(A: AVLTreeNode<K, V>): void; /** * (Protected) Traverses up the tree from the specified node, updating heights and performing rotations as needed. * @remarks Time O(log N) (O(H)), as it traverses the path to root. Space O(H) for the path array. * * @param node - The node to start balancing from (e.g., the newly inserted node or parent of the deleted node). */ protected _balancePath(node: K | AVLTreeNode<K, V> | [K | null | undefined, V | undefined] | null | undefined): void; /** * (Protected) Replaces a node, ensuring height is copied. * @remarks Time O(1) * * @param oldNode - The node to be replaced. * @param newNode - The node to insert. * @returns The `newNode`. */ protected _replaceNode(oldNode: AVLTreeNode<K, V>, newNode: AVLTreeNode<K, V>): AVLTreeNode<K, V>; }