deque-typed
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TypeScript
/**
* data-structure-typed
*
* @author Pablo Zeng
* @copyright Copyright (c) 2022 Pablo Zeng <zrwusa@gmail.com>
* @license MIT License
*/
import type { BinaryTreeDeleteResult, BSTNOptKeyOrNode, BSTOptions, BTNRep, Comparator, DFSOrderPattern, EntryCallback, FamilyPosition, IterationType, NodeCallback, NodePredicate, OptNode, RBTNColor } from '../../types';
import { BinaryTree } from './binary-tree';
import { IBinaryTree } from '../../interfaces';
import { Range } from '../../common';
/**
* Represents a Node in a Binary Search Tree.
*
* @template K - The type of the key.
* @template V - The type of the value.
*/
export declare class BSTNode<K = any, V = any> {
key: K;
value?: V;
parent?: BSTNode<K, V>;
/**
* Creates an instance of BSTNode.
* @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?: BSTNode<K, V> | null | undefined;
/**
* Gets the left child of the node.
* @remarks Time O(1), Space O(1)
*
* @returns The left child.
*/
get left(): BSTNode<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: BSTNode<K, V> | null | undefined);
_right?: BSTNode<K, V> | null | undefined;
/**
* Gets the right child of the node.
* @remarks Time O(1), Space O(1)
*
* @returns The right child.
*/
get right(): BSTNode<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: BSTNode<K, V> | null | undefined);
_height: number;
/**
* Gets the height of the node (used in self-balancing trees).
* @remarks Time O(1), Space O(1)
*
* @returns The height.
*/
get height(): number;
/**
* Sets the height of the node.
* @remarks Time O(1), Space O(1)
*
* @param value - The new height.
*/
set height(value: number);
_color: RBTNColor;
/**
* Gets the color of the node (used in Red-Black trees).
* @remarks Time O(1), Space O(1)
*
* @returns The node's color.
*/
get color(): RBTNColor;
/**
* Sets the color of the node.
* @remarks Time O(1), Space O(1)
*
* @param value - The new color.
*/
set color(value: RBTNColor);
_count: number;
/**
* Gets the count of nodes in the subtree rooted at this node (used in order-statistic trees).
* @remarks Time O(1), Space O(1)
*
* @returns The subtree node count.
*/
get count(): number;
/**
* Sets the count of nodes in the subtree.
* @remarks Time O(1), Space O(1)
*
* @param value - The new count.
*/
set count(value: number);
/**
* Gets the position of the node relative to its parent.
* @remarks Time O(1), Space O(1)
*
* @returns The family position (e.g., 'ROOT', 'LEFT', 'RIGHT').
*/
get familyPosition(): FamilyPosition;
}
/**
* Represents a Binary Search Tree (BST).
* Keys are ordered, allowing for faster search operations compared to a standard Binary Tree.
* @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. 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
* // basic BST creation and add operation
* // Create a simple BST with numeric keys
* const bst = new BST<number>([11, 3, 15, 1, 8, 13, 16, 2, 6, 9, 12, 14, 4, 7, 10, 5]);
*
* // Keep the example output in source comments but avoid noisy test logs.
* await withMutedConsole(() => bst.print());
* // _______8__________
* // / \
* // ___4___ ____12_____
* // / \ / \
* // _2_ _6_ _10__ _14__
* // / \ / \ / \ / \
* // 1 3 5 7 9 11 13 15__
* // \
* // 16
*
* // Verify size
* console.log(bst.size); // 16;
*
* // Add new elements
* bst.set(17);
* bst.set(0);
* console.log(bst.size); // 18;
*
* // Verify keys are searchable
* console.log(bst.has(11)); // true;
* console.log(bst.has(100)); // false;
* @example
* // BST delete and search after deletion
* const bst = new BST<number>([11, 3, 15, 1, 8, 13, 16, 2, 6, 9, 12, 14, 4, 7, 10, 5]);
*
* // Delete a leaf node
* bst.delete(1);
* console.log(bst.has(1)); // false;
*
* // Delete a node with one child
* bst.delete(2);
* console.log(bst.has(2)); // false;
*
* // Delete a node with two children
* bst.delete(3);
* console.log(bst.has(3)); // false;
*
* // Size decreases with each deletion
* console.log(bst.size); // 13;
*
* // Other nodes remain searchable
* console.log(bst.has(11)); // true;
* console.log(bst.has(15)); // true;
* @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.setMany(dataset2);
* merged.merge(dataset3);
*
* // Verify merged dataset is in sorted order
* console.log([...merged.values()]); // ['A', 'B', 'C', 'D', 'E', 'F', 'G'];
* @example
* // BST with custom objects for expression evaluation
* interface Expression {
* id: number;
* operator: string;
* precedence: number;
* }
*
* // BST efficiently stores and retrieves operators by precedence
* const operatorTree = new BST<number, Expression>(
* [
* [1, { id: 1, operator: '+', precedence: 1 }],
* [2, { id: 2, operator: '*', precedence: 2 }],
* [3, { id: 3, operator: '/', precedence: 2 }],
* [4, { id: 4, operator: '-', precedence: 1 }],
* [5, { id: 5, operator: '^', precedence: 3 }]
* ],
* { isMapMode: false }
* );
*
* console.log(operatorTree.size); // 5;
*
* // Quick lookup of operators
* const mult = operatorTree.get(2);
* console.log(mult?.operator); // '*';
* console.log(mult?.precedence); // 2;
*
* // Check if operator exists
* console.log(operatorTree.has(5)); // true;
* console.log(operatorTree.has(99)); // false;
*
* // Retrieve operator by precedence level
* const expNode = operatorTree.getNode(3);
* console.log(expNode?.key); // 3;
* console.log(expNode?.value?.precedence); // 2;
*
* // Delete operator and verify
* operatorTree.delete(1);
* console.log(operatorTree.has(1)); // false;
* console.log(operatorTree.size); // 4;
*
* // Get tree height for optimization analysis
* const treeHeight = operatorTree.getHeight();
* console.log(treeHeight); // > 0;
*
* // Remaining operators are still accessible
* const remaining = operatorTree.get(2);
* console.log(remaining); // defined;
* @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 | undefined)[], arr2: (number | undefined)[]): 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 = any> extends BinaryTree<K, V, R> implements IBinaryTree<K, V, R> {
/**
* Creates an instance of BST.
* @remarks Time O(N log N) or O(N^2) depending on `isBalanceAdd` in `addMany` and input order. Space O(N).
*
* @param [keysNodesEntriesOrRaws=[]] - An iterable of items to set.
* @param [options] - Configuration options for the BST, including comparator.
*/
constructor(keysNodesEntriesOrRaws?: Iterable<K | BSTNode | [K | null | undefined, V | undefined] | null | undefined | R>, options?: BSTOptions<K, V, R>);
protected _root?: BSTNode<K, V>;
/**
* Gets the root node of the tree.
* @remarks Time O(1)
*
* @returns The root node.
*/
get root(): OptNode<BSTNode<K, V>>;
/**
* The comparator function used to determine the order of keys in the tree.
* @remarks Time O(1) Space O(1)
*/
protected _comparator: Comparator<K>;
/**
* Gets the comparator function used by the tree.
* @remarks Time O(1)
*
* @returns The comparator function.
*/
get comparator(): Comparator<K>;
/**
* (Protected) Creates a new BST node.
* @remarks Time O(1), Space O(1)
*
* @param key - The key for the new node.
* @param [value] - The value for the new node (used if not in Map mode).
* @returns The newly created BSTNode.
*/
createNode(key: K, value?: V): BSTNode<K, V>;
/**
* Ensures the input is a node. If it's a key or entry, it searches for the node.
* @remarks Time O(log N) (height of the tree), O(N) worst-case.
*
* @param keyNodeOrEntry - The item to resolve to a node.
* @param [iterationType=this.iterationType] - The traversal method to use if searching.
* @returns The resolved node, or undefined if not found.
*/
ensureNode(keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): OptNode<BSTNode<K, V>>;
/**
* Checks if the given item is a `BSTNode` instance.
* @remarks Time O(1), Space O(1)
*
* @param keyNodeOrEntry - The item to check.
* @returns True if it's a BSTNode, false otherwise.
*/
isNode(keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined): keyNodeOrEntry is BSTNode<K, V>;
/**
* Checks if the given key is valid (comparable).
* @remarks Time O(1)
*
* @param key - The key to validate.
* @returns True if the key is valid, false otherwise.
*/
isValidKey(key: any): key is K;
dfs(): (K | undefined)[];
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>[];
bfs(): (K | undefined)[];
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>[];
listLevels(): (K | undefined)[][];
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>[][];
/**
* Gets the first node matching a predicate.
* @remarks Time O(log N) if searching by key, O(N) if searching by predicate. Space O(log N) or O(N).
*
* @param keyNodeEntryOrPredicate - The key, node, entry, or predicate function to search for.
* @param [startNode=this._root] - The node to start the search from.
* @param [iterationType=this.iterationType] - The traversal method.
* @returns The first matching node, or undefined if not 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>>;
search(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>> | Range<K>, onlyOne?: boolean): (K | undefined)[];
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>[];
rangeSearch(range: Range<K> | [K, K]): (K | undefined)[];
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>[];
/**
* Adds a new node to the BST based on key comparison.
* @remarks Time O(log N), where H is tree height. O(N) worst-case (unbalanced tree), O(log N) average. Space O(1).
*
* @param keyNodeOrEntry - The key, node, or entry to set.
* @param [value] - The value, if providing just a key.
* @returns True if the addition was successful, false otherwise.
*/
set(keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, value?: V): boolean;
/**
* Adds multiple items to the tree.
* @remarks If `isBalanceAdd` is true, sorts the input and builds a balanced tree. Time O(N log N) (due to sort and balanced set).
* If false, adds items one by one. Time O(N * H), which is O(N^2) worst-case.
* Space O(N) for sorting and recursion/iteration stack.
*
* @param keysNodesEntriesOrRaws - An iterable of items to set.
* @param [values] - An optional parallel iterable of values.
* @param [isBalanceAdd=true] - If true, builds a balanced tree from the items.
* @param [iterationType=this.iterationType] - The traversal method for balanced set (recursive or iterative).
* @returns An array of booleans indicating the success of each individual `set` operation.
*/
setMany(keysNodesEntriesOrRaws: Iterable<R | BTNRep<K, V, BSTNode<K, V>>>, values?: Iterable<V | undefined>, isBalanceAdd?: boolean, iterationType?: IterationType): boolean[];
/**
* Returns the first key with a value >= target.
* Equivalent to Java TreeMap.ceiling.
* Time Complexity: O(log n) average, O(h) worst case.
* Space Complexity: O(h) for recursion, O(1) for iteration.
*/
ceiling(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>): K | undefined;
/**
* Returns the first node with a key >= target and applies callback.
* Time Complexity: O(log n) average, O(h) worst case.
* Space Complexity: O(h) for recursion, O(1) for iteration.
*/
ceiling<C extends NodeCallback<BSTNode<K, V>>>(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>, callback: C, iterationType?: IterationType): ReturnType<C>;
/**
* Returns the first key with a value > target.
* Equivalent to Java TreeMap.higher.
* Time Complexity: O(log n) average, O(h) worst case.
* Space Complexity: O(h) for recursion, O(1) for iteration.
*/
higher(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>): K | undefined;
/**
* Returns the first node with a key > target and applies callback.
* Time Complexity: O(log n) average, O(h) worst case.
* Space Complexity: O(h) for recursion, O(1) for iteration.
*/
higher<C extends NodeCallback<BSTNode<K, V>>>(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>, callback: C, iterationType?: IterationType): ReturnType<C>;
/**
* Returns the first key with a value <= target.
* Equivalent to Java TreeMap.floor.
* Time Complexity: O(log n) average, O(h) worst case.
* Space Complexity: O(h) for recursion, O(1) for iteration.
*/
floor(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>): K | undefined;
/**
* Returns the first node with a key <= target and applies callback.
* Time Complexity: O(log n) average, O(h) worst case.
* Space Complexity: O(h) for recursion, O(1) for iteration.
*/
floor<C extends NodeCallback<BSTNode<K, V>>>(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>, callback: C, iterationType?: IterationType): ReturnType<C>;
/**
* Returns the first key with a value < target.
* Equivalent to Java TreeMap.lower.
* Time Complexity: O(log n) average, O(h) worst case.
* Space Complexity: O(h) for recursion, O(1) for iteration.
*/
lower(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>): K | undefined;
/**
* Returns the first node with a key < target and applies callback.
* Time Complexity: O(log n) average, O(h) worst case.
* Space Complexity: O(h) for recursion, O(1) for iteration.
*/
lower<C extends NodeCallback<BSTNode<K, V>>>(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>, callback: C, iterationType?: IterationType): ReturnType<C>;
lesserOrGreaterTraverse(): (K | undefined)[];
lesserOrGreaterTraverse<C extends NodeCallback<BSTNode<K, V>>>(callback: C, lesserOrGreater?: number, targetNode?: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): ReturnType<C>[];
/**
* Rebuilds the tree to be perfectly balanced.
* @remarks 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;
/**
* Checks if the tree meets the AVL balance condition (height difference <= 1).
* @remarks Time O(N), as it must visit every node to compute height. Space O(log N) for recursion or O(N) for iterative map.
*
* @param [iterationType=this.iterationType] - The traversal method.
* @returns True if the tree is AVL balanced, false otherwise.
*/
isAVLBalanced(iterationType?: IterationType): boolean;
/**
* Creates a new BST by mapping each [key, value] pair to a new entry.
* @remarks Time O(N * H), where N is nodes in this tree, and H is height of the new tree during insertion.
* 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 BST.
* @param [thisArg] - `this` context for the callback.
* @returns A new, mapped BST.
*/
map<MK = K, MV = V, MR = any>(callback: EntryCallback<K, V | undefined, [MK, MV]>, options?: Partial<BSTOptions<MK, MV, MR>>, thisArg?: unknown): BST<MK, MV, MR>;
/**
* Deletes nodes that match a key, node, entry, predicate, or range.
*
* @remarks
* Time Complexity: O(N) for search + O(M log N) for M deletions, where N is tree size.
* Space Complexity: O(M) for storing matched nodes and result map.
*
* @template K - The key type.
* @template V - The value type.
*
* @param keyNodeEntryOrPredicate - The search criteria. Can be one of:
* - A key (type K): searches for exact key match using the comparator.
* - A BSTNode: searches for the matching node in the tree.
* - An entry tuple: searches for the key-value pair.
* - A NodePredicate function: tests each node and returns true for matches.
* - A Range object: searches for nodes whose keys fall within the specified range (inclusive/exclusive based on range settings).
* - null or undefined: treated as no match, returns empty results.
*
* @param onlyOne - If true, stops the search after finding the first match and only deletes that one node.
* If false (default), searches for and deletes all matching nodes.
*
* @param startNode - The node to start the search from. Can be:
* - A key, node, or entry: the method resolves it to a node and searches from that subtree.
* - null or undefined: defaults to the root, searching the entire tree.
* - Default value: this._root (the tree's root).
*
* @param iterationType - Controls the internal traversal implementation:
* - 'RECURSIVE': uses recursive function calls for traversal.
* - 'ITERATIVE': uses explicit stack-based iteration.
* - Default: this.iterationType (the tree's default iteration mode).
*
* @returns A Map<K, boolean> containing the deletion results:
* - Key: the matched node's key.
* - Value: true if the deletion succeeded, false if it failed (e.g., key not found during deletion phase).
* - If no nodes match the search criteria, the returned map is empty.
*/
deleteWhere(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>> | Range<K>, onlyOne?: boolean, startNode?: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, iterationType?: IterationType): BinaryTreeDeleteResult<BSTNode<K, V>>[];
/**
* (Protected) Creates the default comparator function for keys that don't have a custom comparator.
* @remarks Time O(1) Space O(1)
* @returns The default comparator function.
*/
protected _createDefaultComparator(): Comparator<K>;
/**
* (Protected) Binary search for floor by key with pruning optimization.
* Performs standard BST binary search, choosing left or right subtree based on comparator result.
* Finds first node where key <= target.
* @remarks Time O(h) where h is tree height.
*
* @param key - The target key to search for.
* @param iterationType - The iteration type (RECURSIVE or ITERATIVE).
* @returns The first node with key <= target, or undefined if none exists.
*/
protected _floorByKey(key: K, iterationType: IterationType): BSTNode<K, V> | undefined;
/**
* (Protected) In-order traversal search for floor by predicate.
* Falls back to linear in-order traversal when predicate-based search is required.
* Returns the last node that satisfies the predicate function.
* @remarks Time Complexity: O(n) since it may visit every node.
* Space Complexity: O(h) for recursion, O(h) for iterative stack.
*
* @param predicate - The predicate function to test nodes.
* @param iterationType - The iteration type (RECURSIVE or ITERATIVE).
* @returns The last node satisfying predicate (highest key), or undefined if none found.
*/
protected _floorByPredicate(predicate: NodePredicate<BSTNode<K, V>>, iterationType: IterationType): BSTNode<K, V> | undefined;
/**
* (Protected) Binary search for lower by key with pruning optimization.
* Performs standard BST binary search, choosing left or right subtree based on comparator result.
* Finds first node where key < target.
* @remarks Time O(h) where h is tree height.
*
* @param key - The target key to search for.
* @param iterationType - The iteration type (RECURSIVE or ITERATIVE).
* @returns The first node with key < target, or undefined if none exists.
*/
protected _lowerByKey(key: K, iterationType: IterationType): BSTNode<K, V> | undefined;
/**
* (Protected) In-order traversal search for lower by predicate.
* Falls back to linear in-order traversal when predicate-based search is required.
* Returns the node that satisfies the predicate and appears last in in-order traversal.
* @remarks Time Complexity: O(n) since it may visit every node.
* Space Complexity: O(h) for recursion, O(h) for iterative stack.
*
* @param predicate - The predicate function to test nodes.
* @param iterationType - The iteration type (RECURSIVE or ITERATIVE).
* @returns The last node satisfying predicate (highest key < target), or undefined if none found.
*/
protected _lowerByPredicate(predicate: NodePredicate<BSTNode<K, V>>, iterationType: IterationType): BSTNode<K, V> | undefined;
/**
* (Protected) Core bound search implementation supporting all parameter types.
* Unified logic for both lowerBound and upperBound.
* Resolves various input types (Key, Node, Entry, Predicate) using parent class utilities.
* @param keyNodeEntryOrPredicate - The key, node, entry, or predicate function to search for.
* @param isLower - True for lowerBound (>=), false for upperBound (>).
* @param iterationType - The iteration type (RECURSIVE or ITERATIVE).
* @returns The first matching node, or undefined if no such node exists.
*/
protected _bound(keyNodeEntryOrPredicate: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined | NodePredicate<BSTNode<K, V>>, isLower: boolean, iterationType: IterationType): BSTNode<K, V> | undefined;
/**
* (Protected) Binary search for bound by key with pruning optimization.
* Performs standard BST binary search, choosing left or right subtree based on comparator result.
* For lowerBound: finds first node where key >= target.
* For upperBound: finds first node where key > target.
* @param key - The target key to search for.
* @param isLower - True for lowerBound (>=), false for upperBound (>).
* @param iterationType - The iteration type (RECURSIVE or ITERATIVE).
* @returns The first node matching the bound condition, or undefined if none exists.
*/
protected _boundByKey(key: K, isLower: boolean, iterationType: IterationType): BSTNode<K, V> | undefined;
/**
* (Protected) In-order traversal search by predicate.
* Falls back to linear in-order traversal when predicate-based search is required.
* Returns the first node that satisfies the predicate function.
* Note: Predicate-based search cannot leverage BST's binary search optimization.
* Time Complexity: O(n) since it may visit every node.
* @param predicate - The predicate function to test nodes.
* @param iterationType - The iteration type (RECURSIVE or ITERATIVE).
* @returns The first node satisfying predicate, or undefined if none found.
*/
protected _boundByPredicate(predicate: NodePredicate<BSTNode<K, V>>, iterationType: IterationType): BSTNode<K, V> | undefined;
/**
* (Protected) Creates a new, empty instance of the same BST constructor.
* @remarks Time O(1)
*
* @template TK, TV, TR - Generic types for the new instance.
* @param [options] - Options for the new BST.
* @returns A new, empty BST.
*/
protected _createInstance<TK = K, TV = V, TR = R>(options?: Partial<BSTOptions<TK, TV, TR>>): this;
/**
* (Protected) Creates a new instance of the same BST constructor, potentially with different generic types.
* @remarks Time O(N log N) or O(N^2) (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 BST.
* @param [options] - Options for the new BST.
* @returns A new BST.
*/
protected _createLike<TK = K, TV = V, TR = R>(iter?: Iterable<TK | BSTNode<TK, TV> | [TK | null | undefined, TV | undefined] | null | undefined | TR>, options?: Partial<BSTOptions<TK, TV, TR>>): BST<TK, TV, TR>;
/**
* (Protected) Snapshots the current BST's configuration options.
* @remarks Time O(1)
*
* @template TK, TV, TR - Generic types for the options.
* @returns The options object.
*/
protected _snapshotOptions<TK = K, TV = V, TR = R>(): BSTOptions<TK, TV, TR>;
/**
* (Protected) Converts a key, node, or entry into a standardized [node, value] tuple.
* @remarks Time O(1)
*
* @param keyNodeOrEntry - The input item.
* @param [value] - An optional value (used if input is just a key).
* @returns A tuple of [node, value].
*/
protected _keyValueNodeOrEntryToNodeAndValue(keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined, value?: V): [OptNode<BSTNode<K, V>>, V | undefined];
/**
* (Protected) Sets the root node and clears its parent reference.
* @remarks Time O(1)
*
* @param v - The node to set as root.
*/
protected _setRoot(v: OptNode<BSTNode<K, V>>): void;
/**
* (Protected) Compares two keys using the tree's comparator and reverse setting.
* @remarks Time O(1) Space O(1)
*
* @param a - The first key.
* @param b - The second key.
* @returns A number (1, -1, or 0) representing the comparison.
*/
protected _compare(a: K, b: K): number;
/**
* (Private) Deletes a node by its key.
* @remarks Standard BST deletion algorithm. Time O(log N), O(N) worst-case. Space O(1).
*
* @param key - The key of the node to delete.
* @returns True if the node was found and deleted, false otherwise.
*/
protected _deleteByKey(key: K): boolean;
}