doubly-linked-list-typed/dist/data-structures/binary-tree/bst.d.ts

Doubly Linked List

/**
 * data-structure-typed
 *
 * @author Pablo Zeng
 * @copyright Copyright (c) 2022 Pablo Zeng <zrwusa@gmail.com>
 * @license MIT License
 */
import type { BSTNOptKeyOrNode, BSTOptions, BTNRep, Comparable, Comparator, CP, DFSOrderPattern, EntryCallback, IterationType, NodeCallback, NodePredicate, OptNode } from '../../types';
import { BinaryTree, BinaryTreeNode } from './binary-tree';
import { IBinaryTree } from '../../interfaces';
import { Range } from '../../common';
export declare class BSTNode<K = any, V = any> extends BinaryTreeNode<K, V> {
    parent?: BSTNode<K, V>;
    /**
     * This TypeScript constructor function initializes an instance with a key and an optional value.
     * @param {K} key - The `key` parameter is typically used to uniquely identify an object or element
     * within a data structure. It serves as a reference or identifier for accessing or manipulating the
     * associated value.
     * @param {V} [value] - The `value` parameter in the constructor is optional, meaning it does not
     * have to be provided when creating an instance of the class. If a value is not provided, it will
     * default to `undefined`.
     */
    constructor(key: K, value?: V);
    _left?: BSTNode<K, V> | null | undefined;
    get left(): BSTNode<K, V> | null | undefined;
    set left(v: BSTNode<K, V> | null | undefined);
    _right?: BSTNode<K, V> | null | undefined;
    get right(): BSTNode<K, V> | null | undefined;
    set right(v: BSTNode<K, V> | null | undefined);
}
/**
 * 1. Node Order: Each node's left child has a lesser value, and the right child has a greater value.
 * 2. Unique Keys: No duplicate keys in a standard BST.
 * 3. Efficient Search: Enables quick search, minimum, and maximum operations.
 * 4. Inorder Traversal: Yields nodes in ascending order.
 * 5. Logarithmic Operations: Ideal operations like insertion, deletion, and searching are O(log n) time-efficient.
 * 6. Balance Variability: Can become unbalanced; special types maintain balance.
 * 7. No Auto-Balancing: Standard BSTs don't automatically balance themselves.
 * @example
 * // Merge 3 sorted datasets
 *     const dataset1 = new BST<number, string>([
 *       [1, 'A'],
 *       [7, 'G']
 *     ]);
 *     const dataset2 = [
 *       [2, 'B'],
 *       [6, 'F']
 *     ];
 *     const dataset3 = new BST<number, string>([
 *       [3, 'C'],
 *       [5, 'E'],
 *       [4, 'D']
 *     ]);
 *
 *     // Merge datasets into a single BinarySearchTree
 *     const merged = new BST<number, string>(dataset1);
 *     merged.addMany(dataset2);
 *     merged.merge(dataset3);
 *
 *     // Verify merged dataset is in sorted order
 *     console.log([...merged.values()]); // ['A', 'B', 'C', 'D', 'E', 'F', 'G']
 * @example
 * // Find elements in a range
 *     const bst = new BST<number>([10, 5, 15, 3, 7, 12, 18]);
 *     console.log(bst.search(new Range(5, 10))); // [5, 7, 10]
 *     console.log(bst.rangeSearch([4, 12], node => node.key.toString())); // ['5', '7', '10', '12']
 *     console.log(bst.search(new Range(4, 12, true, false))); // [5, 7, 10]
 *     console.log(bst.rangeSearch([15, 20])); // [15, 18]
 *     console.log(bst.search(new Range(15, 20, false))); // [18]
 * @example
 * // Find lowest common ancestor
 *     const bst = new BST<number>([20, 10, 30, 5, 15, 25, 35, 3, 7, 12, 18]);
 *
 *     // LCA helper function
 *     const findLCA = (num1: number, num2: number): number | undefined => {
 *       const path1 = bst.getPathToRoot(num1);
 *       const path2 = bst.getPathToRoot(num2);
 *       // Find the first common ancestor
 *       return findFirstCommon(path1, path2);
 *     };
 *
 *     function findFirstCommon(arr1: number[], arr2: number[]): number | undefined {
 *       for (const num of arr1) {
 *         if (arr2.indexOf(num) !== -1) {
 *           return num;
 *         }
 *       }
 *       return undefined;
 *     }
 *
 *     // Assertions
 *     console.log(findLCA(3, 10)); // 7
 *     console.log(findLCA(5, 35)); // 15
 *     console.log(findLCA(20, 30)); // 25
 */
export declare class BST<K = any, V = any, R = object, MK = any, MV = any, MR = object> extends BinaryTree<K, V, R, MK, MV, MR> implements IBinaryTree<K, V, R, MK, MV, MR> {
    /**
     * This TypeScript constructor initializes a binary search tree with optional options and adds
     * elements if provided.
     * @param keysNodesEntriesOrRaws - The `keysNodesEntriesOrRaws` parameter in the constructor is an
     * iterable that can contain elements of type `K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  ` or `R`. It is used to
     * initialize the binary search tree with keys, nodes, entries, or raw data.
     * @param [options] - The `options` parameter is an optional object that can contain the following
     * properties:
     */
    constructor(keysNodesEntriesOrRaws?: Iterable<K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | R>, options?: BSTOptions<K, V, R>);
    protected _root?: BSTNode<K, V>;
    get root(): OptNode<BSTNode<K, V>>;
    protected _isReverse: boolean;
    get isReverse(): boolean;
    protected _comparator: Comparator<K>;
    get comparator(): Comparator<K>;
    protected _specifyComparable?: (key: K) => Comparable;
    get specifyComparable(): ((key: K) => Comparable) | undefined;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function creates a new BSTNode with the given key and value and returns it.
     * @param {K} key - The key parameter is of type K, which represents the type of the key for the node
     * being created.
     * @param {V} [value] - The "value" parameter is an optional parameter of type V. It represents the
     * value associated with the key in the node being created.
     * @returns The method is returning a new instance of the BSTNode class, casted as the BSTNode<K, V> type.
     */
    createNode(key: K, value?: V): BSTNode<K, V>;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function creates a new binary search tree with the specified options.
     * @param [options] - The `options` parameter is an optional object that allows you to customize the
     * behavior of the `createTree` method. It accepts a partial `BSTOptions` object, which has the
     * following properties:
     * @returns a new instance of the BST class with the provided options.
     */
    createTree(options?: BSTOptions<K, V, R>): BST<K, V, R, MK, MV, MR>;
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(log n)
     *
     * The function ensures the existence of a node in a data structure and returns it, or undefined if
     * it doesn't exist.
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  } keyNodeOrEntry - The parameter
     * `keyNodeOrEntry` can accept a value of type `R`, which represents the key, node,
     * entry, or raw element that needs to be ensured in the tree.
     * @param {IterationType} [iterationType=ITERATIVE] - The `iterationType` parameter is an optional
     * parameter that specifies the type of iteration to be used when ensuring a node. It has a default
     * value of `'ITERATIVE'`.
     * @returns The method is returning either the node that was ensured or `undefined` if the node could
     * not be ensured.
     */
    ensureNode(keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): OptNode<BSTNode<K, V>>;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function checks if the input is an instance of the BSTNode class.
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  } keyNodeOrEntry - The parameter
     * `keyNodeOrEntry` can be of type `R` or `K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  `.
     * @returns a boolean value indicating whether the input parameter `keyNodeOrEntry` is
     * an instance of the `BSTNode` class.
     */
    isNode(keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined): keyNodeOrEntry is BSTNode<K, V>;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function "override isValidKey" checks if a key is comparable based on a given comparator.
     * @param {any} key - The `key` parameter is a value that will be checked to determine if it is of
     * type `K`.
     * @returns The `override isValidKey(key: any): key is K` function is returning a boolean value based on
     * the result of the `isComparable` function with the condition `this._compare !==
     * this._DEFAULT_COMPARATOR`.
     */
    isValidKey(key: any): key is K;
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(log n)
     *
     * The `add` function in TypeScript adds a new node to a binary search tree based on the key value.
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  } keyNodeOrEntry - The parameter
     * `keyNodeOrEntry` can accept a value of type `R` or `K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  `.
     * @param {V} [value] - The `value` parameter is an optional value that can be associated with the
     * key in the binary search tree. If provided, it will be stored in the node along with the key.
     * @returns a boolean value.
     */
    add(keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, value?: V): boolean;
    /**
     * Time Complexity: O(k log n)
     * Space Complexity: O(k + log n)
     *
     * The `addMany` function in TypeScript adds multiple keys or nodes to a data structure and returns
     * an array indicating whether each key or node was successfully inserted.
     * @param keysNodesEntriesOrRaws - An iterable containing keys, nodes, entries, or raw
     * elements to be added to the data structure.
     * @param [values] - An optional iterable of values to be associated with the keys or nodes being
     * added. If provided, the values will be assigned to the corresponding keys or nodes in the same
     * order. If not provided, undefined will be assigned as the value for each key or node.
     * @param [isBalanceAdd=true] - A boolean flag indicating whether the tree should be balanced after
     * adding the elements. If set to true, the tree will be balanced using a binary search tree
     * algorithm. If set to false, the elements will be added without balancing the tree. The default
     * value is true.
     * @param {IterationType} iterationType - The `iterationType` parameter is an optional parameter that
     * specifies the type of iteration to use when adding multiple keys or nodes to the binary search
     * tree. It can have two possible values:
     * @returns The function `addMany` returns an array of booleans indicating whether each element was
     * successfully inserted into the data structure.
     */
    addMany(keysNodesEntriesOrRaws: Iterable<R | BTNRep<K, V, BSTNode<K, V>>>, values?: Iterable<V | undefined>, isBalanceAdd?: boolean, iterationType?: IterationType): boolean[];
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(k + log n)
     *
     * The function `search` in TypeScript overrides the search behavior in a binary tree structure based
     * on specified criteria.
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined   | NodePredicate<BSTNode<K, V>>} keyNodeEntryOrPredicate - The
     * `keyNodeEntryOrPredicate` parameter in the `override search` method can accept one of the
     * following types:
     * @param [onlyOne=false] - The `onlyOne` parameter is a boolean flag that determines whether the
     * search should stop after finding the first matching node. If `onlyOne` is set to `true`, the
     * search will return as soon as a matching node is found. If `onlyOne` is set to `false`, the
     * @param {C} callback - The `callback` parameter in the `override search` function is a function
     * that will be called on each node that matches the search criteria. It is of type `C`, which
     * extends `NodeCallback<BSTNode<K, V> | null>`. The callback function should accept a node of type `BSTNode<K, V>` as its
     * argument and
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  } startNode - The `startNode` parameter in the `override search`
     * method represents the node from which the search operation will begin. It is the starting point
     * for searching within the tree data structure. The method ensures that the `startNode` is a valid
     * node before proceeding with the search operation. If the `
     * @param {IterationType} iterationType - The `iterationType` parameter in the `override search`
     * function determines the type of iteration to be used during the search operation. It can have two
     * possible values:
     * @returns The `override search` method returns an array of values that match the search criteria
     * specified by the input parameters. The method performs a search operation on a binary tree
     * structure based on the provided key, predicate, and other options. The search results are
     * collected in an array and returned as the output of the method.
     */
    search<C extends NodeCallback<BSTNode<K, V>>>(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>> | Range<K>, onlyOne?: boolean, callback?: C, startNode?: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): ReturnType<C>[];
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(k + log n)
     *
     * The `rangeSearch` function searches for nodes within a specified range in a binary search tree.
     * @param {Range<K> | [K, K]} range - The `range` parameter in the `rangeSearch` function can be
     * either a `Range` object or an array of two elements representing the range boundaries.
     * @param {C} callback - The `callback` parameter in the `rangeSearch` function is a callback
     * function that is used to process each node that is found within the specified range during the
     * search operation. It is of type `NodeCallback<BSTNode<K, V> | null>`, where `BSTNode<K, V>` is the type of nodes in the
     * data structure.
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  } startNode - The `startNode` parameter in the `rangeSearch`
     * function represents the node from which the search for nodes within the specified range will
     * begin. It is the starting point for the range search operation.
     * @param {IterationType} iterationType - The `iterationType` parameter in the `rangeSearch` function
     * is used to specify the type of iteration to be performed during the search operation. It has a
     * default value of `this.iterationType`, which suggests that it is likely a property of the class or
     * object that the `rangeSearch`
     * @returns The `rangeSearch` function is returning the result of calling the `search` method with
     * the specified parameters.
     */
    rangeSearch<C extends NodeCallback<BSTNode<K, V>>>(range: Range<K> | [K, K], callback?: C, startNode?: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): ReturnType<C>[];
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(log n)
     *
     * This function retrieves a node based on a given keyNodeEntryOrPredicate within a binary search tree structure.
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined   | NodePredicate<BSTNode<K, V>>} keyNodeEntryOrPredicate - The `keyNodeEntryOrPredicate`
     * parameter can be of type `K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  `, `R`, or `NodePredicate<BSTNode<K, V>>`.
     * @param {BSTNOptKeyOrNode<K, BSTNode<K, V>>} startNode - The `startNode` parameter in the `getNode` method
     * is used to specify the starting point for searching nodes in the binary search tree. If no
     * specific starting point is provided, the default value is set to `this._root`, which is the root
     * node of the binary search tree.
     * @param {IterationType} iterationType - The `iterationType` parameter in the `getNode` method is a
     * parameter that specifies the type of iteration to be used. It has a default value of
     * `this.iterationType`, which means it will use the iteration type defined in the class instance if
     * no value is provided when calling the method.
     * @returns The `getNode` method is returning an optional binary search tree node (`OptNode<BSTNode<K, V>>`).
     * It is using the `getNodes` method to find the node based on the provided keyNodeEntryOrPredicate, beginning at
     * the specified root node (`startNode`) and using the specified iteration type. The method then
     * returns the first node found or `undefined` if no node is found.
     */
    getNode(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>, startNode?: BSTNOptKeyOrNode<K, BSTNode<K, V>>, iterationType?: IterationType): OptNode<BSTNode<K, V>>;
    /**
     * Time complexity: O(n)
     * Space complexity: O(n)
     *
     * The function `dfs` in TypeScript overrides the base class method with default parameters and
     * returns the result of the super class `dfs` method.
     * @param {C} callback - The `callback` parameter is a function that will be called for each node
     * visited during the Depth-First Search traversal. It is a generic type `C` that extends the
     * `NodeCallback` interface for `BSTNode<K, V>`. The default value for `callback` is `this._
     * @param {DFSOrderPattern} [pattern=IN] - The `pattern` parameter in the `override dfs` method
     * specifies the order in which the Depth-First Search (DFS) traversal should be performed on the
     * Binary Search Tree (BST). The possible values for the `pattern` parameter are:
     * @param {boolean} [onlyOne=false] - The `onlyOne` parameter in the `override dfs` method is a
     * boolean flag that indicates whether you want to stop the depth-first search traversal after
     * finding the first matching node or continue searching for all matching nodes. If `onlyOne` is set
     * to `true`, the traversal will stop after finding
     * @param {K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined} startNode -
     * The `startNode` parameter in the `override dfs` method can be one of the following types:
     * @param {IterationType} iterationType - The `iterationType` parameter in the `override dfs` method
     * specifies the type of iteration to be performed during the Depth-First Search (DFS) traversal of a
     * Binary Search Tree (BST). It is used to determine the order in which nodes are visited during the
     * traversal. The possible values for `
     * @returns The `override` function is returning the result of calling the `dfs` method from the
     * superclass, with the provided arguments `callback`, `pattern`, `onlyOne`, `startNode`, and
     * `iterationType`. The return type is an array of the return type of the callback function `C`.
     */
    dfs<C extends NodeCallback<BSTNode<K, V>>>(callback?: C, pattern?: DFSOrderPattern, onlyOne?: boolean, startNode?: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): ReturnType<C>[];
    /**
     * Time complexity: O(n)
     * Space complexity: O(n)
     *
     * The function overrides the breadth-first search method and returns an array of the return types of
     * the callback function.
     * @param {C} callback - The `callback` parameter is a function that will be called for each node
     * visited during the breadth-first search. It should take a single argument, which is the current
     * node being visited, and it can return a value of any type.
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  } startNode - The `startNode` parameter is the starting
     * point for the breadth-first search. It can be either a root node, a key-value pair, or an entry
     * object. If no value is provided, the default value is the root of the tree.
     * @param {IterationType} iterationType - The `iterationType` parameter is used to specify the type
     * of iteration to be performed during the breadth-first search (BFS) traversal. It can have one of
     * the following values:
     * @returns an array of the return type of the callback function.
     */
    bfs<C extends NodeCallback<BSTNode<K, V>>>(callback?: C, startNode?: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): ReturnType<C>[];
    /**
     * Time complexity: O(n)
     * Space complexity: O(n)
     *
     * The function overrides the listLevels method from the superclass and returns an array of arrays
     * containing the results of the callback function applied to each level of the tree.
     * @param {C} callback - The `callback` parameter is a generic type `C` that extends
     * `NodeCallback<BSTNode<K, V> | null>`. It represents a callback function that will be called for each node in the
     * tree during the iteration process.
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  } startNode - The `startNode` parameter is the starting
     * point for listing the levels of the binary tree. It can be either a root node of the tree, a
     * key-value pair representing a node in the tree, or a key representing a node in the tree. If no
     * value is provided, the root of
     * @param {IterationType} iterationType - The `iterationType` parameter is used to specify the type
     * of iteration to be performed on the tree. It can have one of the following values:
     * @returns The method is returning a two-dimensional array of the return type of the callback
     * function.
     */
    listLevels<C extends NodeCallback<BSTNode<K, V>>>(callback?: C, startNode?: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): ReturnType<C>[][];
    /**
     * Time complexity: O(n)
     * Space complexity: O(n)
     *
     * The `lesserOrGreaterTraverse` function traverses a binary tree and applies a callback function to
     * each node that meets a certain condition based on a target node and a comparison value.
     * @param {C} callback - The `callback` parameter is a function that will be called for each node
     * that meets the condition specified by the `lesserOrGreater` parameter. It takes a single argument,
     * which is the current node being traversed, and returns a value of any type.
     * @param {CP} lesserOrGreater - The `lesserOrGreater` parameter is used to determine whether to
     * traverse nodes that are lesser, greater, or both than the `targetNode`. It accepts the values -1,
     * 0, or 1, where:
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  } targetNode - The `targetNode` parameter is the node in
     * the binary tree that you want to start traversing from. It can be specified either by providing
     * the key of the node, the node itself, or an entry containing the key and value of the node. If no
     * `targetNode` is provided,
     * @param {IterationType} iterationType - The `iterationType` parameter determines the type of
     * traversal to be performed on the binary tree. It can have two possible values:
     * @returns The function `lesserOrGreaterTraverse` returns an array of values of type
     * `ReturnType<C>`, which is the return type of the callback function passed as an argument.
     */
    lesserOrGreaterTraverse<C extends NodeCallback<BSTNode<K, V>>>(callback?: C, lesserOrGreater?: CP, targetNode?: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): ReturnType<C>[];
    /**
     * Time complexity: O(n)
     * Space complexity: O(n)
     *
     * The `perfectlyBalance` function takes an optional `iterationType` parameter and returns `true` if
     * the binary search tree is perfectly balanced, otherwise it returns `false`.
     * @param {IterationType} iterationType - The `iterationType` parameter is an optional parameter that
     * specifies the type of iteration to use when building a balanced binary search tree. It has a
     * default value of `this.iterationType`, which means it will use the iteration type specified in the
     * current instance of the class.
     * @returns The function `perfectlyBalance` returns a boolean value.
     */
    perfectlyBalance(iterationType?: IterationType): boolean;
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(log n)
     *
     * The function `isAVLBalanced` checks if a binary tree is AVL balanced using either a recursive or
     * iterative approach.
     * @param {IterationType} iterationType - The `iterationType` parameter is an optional parameter that
     * specifies the type of iteration to use when checking if the AVL tree is balanced. It has a default
     * value of `this.iterationType`, which means it will use the iteration type specified in the current
     * instance of the AVL tree.
     * @returns a boolean value.
     */
    isAVLBalanced(iterationType?: IterationType): boolean;
    /**
     * Time complexity: O(n)
     * Space complexity: O(n)
     *
     * The `map` function in TypeScript overrides the default map behavior for a binary search tree by
     * applying a callback function to each entry and creating a new tree with the results.
     * @param callback - A function that will be called for each entry in the BST. It takes four
     * arguments: the key, the value (which can be undefined), the index of the entry, and a reference to
     * the BST itself.
     * @param [options] - The `options` parameter in the `override map` method is of type `BSTOptions<MK,
     * MV, MR>`. It is an optional parameter that allows you to specify additional options for the Binary
     * Search Tree (BST) being created in the `map` method. These options could include configuration
     * @param {any} [thisArg] - The `thisArg` parameter in the `override map` method is used to specify
     * the value of `this` that should be used when executing the `callback` function. It allows you to
     * set the context or scope in which the callback function will be called. This can be useful when
     * you want
     * @returns The `map` method is returning a new Binary Search Tree (`BST`) instance with the entries
     * transformed by the provided callback function.
     */
    map(callback: EntryCallback<K, V | undefined, [MK, MV]>, options?: BSTOptions<MK, MV, MR>, thisArg?: any): BST<MK, MV, MR>;
    /**
     * Time complexity: O(n)
     * Space complexity: O(n)
     *
     * The function `clone` overrides the default cloning behavior to create a deep copy of a tree
     * structure.
     * @returns The `cloned` object is being returned.
     */
    clone(): BST<K, V, R, MK, MV, MR>;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function overrides a method and converts a key, value pair or entry or raw element to a node.
     * @param {K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  } keyNodeOrEntry - A variable that can be of
     * type R or K |  BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined  . It represents either a key, a node, an entry, or a raw
     * element.
     * @param {V} [value] - The `value` parameter is an optional value of type `V`. It represents the
     * value associated with a key in a key-value pair.
     * @returns either a BSTNode<K, V> object or undefined.
     */
    protected _keyValueNodeOrEntryToNodeAndValue(keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, value?: V): [OptNode<BSTNode<K, V>>, V | undefined];
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function sets the root of a tree-like structure and updates the parent property of the new
     * root.
     * @param {OptNode<BSTNode<K, V>>} v - v is a parameter of type BSTNode<K, V> or undefined.
     */
    protected _setRoot(v: OptNode<BSTNode<K, V>>): void;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The _compare function compares two values using a specified comparator function and optionally
     * reverses the result.
     * @param {K} a - The parameter `a` is of type `K`, which is used as an input for comparison in the
     * `_compare` method.
     * @param {K} b - The parameter `b` in the `_compare` function is of type `K`.
     * @returns The `_compare` method is returning the result of the ternary expression. If `_isReverse`
     * is true, it returns the negation of the result of calling the `_comparator` function with
     * arguments `a` and `b`. If `_isReverse` is false, it returns the result of calling the
     * `_comparator` function with arguments `a` and `b`.
     */
    protected _compare(a: K, b: K): number;
}