/**
 * data-structure-typed
 *
 * @author Pablo Zeng
 * @copyright Copyright (c) 2022 Pablo Zeng <zrwusa@gmail.com>
 * @license MIT License
 */

import type {
  BSTNOptKeyOrNode,
  BSTOptions,
  BTNRep,
  Comparator,
  CP,
  DFSOrderPattern,
  EntryCallback,
  FamilyPosition,
  IterationType,
  NodeCallback,
  NodePredicate,
  OptNode,
  RBTNColor
} from '../../types';
import { BinaryTree } from './binary-tree';
import { IBinaryTree } from '../../interfaces';
import { Queue } from '../queue';
import { isComparable } from '../../utils';
import { ERR, Range, raise } 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 class BSTNode<K = any, V = any> {
  key: K;
  value?: V;
  parent?: BSTNode<K, V> = undefined;

  /**
   * 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) {
    this.key = key;
    this.value = value;
  }

  _left?: BSTNode<K, V> | null | undefined = 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 {
    return this._left;
  }

  /**
   * 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) {
    if (v) v.parent = this;
    this._left = v;
  }

  _right?: BSTNode<K, V> | null | undefined = 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 {
    return this._right;
  }

  /**
   * 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) {
    if (v) v.parent = this;
    this._right = v;
  }

  _height: number = 0;

  /**
   * Gets the height of the node (used in self-balancing trees).
   * @remarks Time O(1), Space O(1)
   *
   * @returns The height.
   */
  /* istanbul ignore next -- covered by AVLTree/RedBlackTree tests (subclass uses height) */
  get height(): number {
    return this._height;
  }

  /**
   * Sets the height of the node.
   * @remarks Time O(1), Space O(1)
   *
   * @param value - The new height.
   */
  /* istanbul ignore next -- covered by AVLTree/RedBlackTree tests (subclass uses height) */
  set height(value: number) {
    this._height = value;
  }

  _color: RBTNColor = 'BLACK';

  /**
   * Gets the color of the node (used in Red-Black trees).
   * @remarks Time O(1), Space O(1)
   *
   * @returns The node's color.
   */
  /* istanbul ignore next -- covered by RedBlackTree tests (subclass uses color) */
  get color(): RBTNColor {
    return this._color;
  }

  /**
   * Sets the color of the node.
   * @remarks Time O(1), Space O(1)
   *
   * @param value - The new color.
   */
  /* istanbul ignore next -- covered by RedBlackTree tests (subclass uses color) */
  set color(value: RBTNColor) {
    this._color = value;
  }

  _count: number = 1;

  /**
   * 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.
   */
  /* istanbul ignore next -- internal field used by subclasses */
  get count(): number {
    return this._count;
  }

  /**
   * Sets the count of nodes in the subtree.
   * @remarks Time O(1), Space O(1)
   *
   * @param value - The new count.
   */
  /* istanbul ignore next -- internal field used by subclasses */
  set count(value: number) {
    this._count = value;
  }

  /**
   * 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 {
    if (!this.parent) {
      return this.left || this.right ? 'ROOT' : 'ISOLATED';
    }

    if (this.parent.left === this) {
      return this.left || this.right ? 'ROOT_LEFT' : 'LEFT';
    } else if (this.parent.right === this) {
      return this.left || this.right ? 'ROOT_RIGHT' : 'RIGHT';
    }

    return 'MAL_NODE';
  }
}

/**
 * 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
 * // 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 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>
  ) {
    super([], options);

    if (options) {
      // Use the 'in' operator to check if the field is present
      if ('comparator' in options && options.comparator !== undefined) {
        this._comparator = options.comparator;
      } else {
        this._comparator = this._createDefaultComparator();
      }
      if (options.enableOrderStatistic) {
        this._enableOrderStatistic = true;
      }
    } else {
      this._comparator = this._createDefaultComparator();
    }

    if (keysNodesEntriesOrRaws) this.setMany(keysNodesEntriesOrRaws);
  }

  protected override _root?: BSTNode<K, V> = undefined;

  protected _enableOrderStatistic: boolean = false;

  /**
   * Gets the root node of the tree.
   * @remarks Time O(1)
   *
   * @returns The root node.
   */
  override get root(): OptNode<BSTNode<K, V>> {
    return this._root;
  }

  /**
   * The comparator function used to determine the order of keys in the tree.

   * @remarks Time O(1) Space O(1)
   */
  protected readonly _comparator: Comparator<K>;

  /**
   * Gets the comparator function used by the tree.
   * @remarks Time O(1)
   *
   * @returns The comparator function.
   */
  get comparator(): Comparator<K> {
    return this._comparator;
  }

  /**
   * (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.
   */
  override createNode(key: K, value?: V): BSTNode<K, V> {
    return new BSTNode<K, V>(key, value);
  }

  /**
   * 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.
   */
  override ensureNode(
    keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined,
    iterationType: IterationType = this.iterationType
  ): OptNode<BSTNode<K, V>> {
    return super.ensureNode(keyNodeOrEntry, iterationType) ?? undefined;
  }

  /**
   * 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.
   */
  override isNode(
    keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined
  ): keyNodeOrEntry is BSTNode<K, V> {
    return keyNodeOrEntry instanceof BSTNode;
  }

  /**
   * 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.
   */
  override isValidKey(key: unknown): key is K {
    return isComparable(key);
  }

    /**
   * Depth-first search traversal
  
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Depth-first traversal
 *  const bst = new BST<number>([5, 3, 7, 1, 4]);
 *     const inOrder = bst.dfs(node => node.key, 'IN');
 *     console.log(inOrder); // [1, 3, 4, 5, 7];
   */
  override dfs(): (K | undefined)[];

  override 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>[];

  /**
   * Performs a Depth-First Search (DFS) traversal.
   * @remarks Time O(N), visits every node. Space O(log N) for the call/explicit stack. O(N) worst-case.
   *
   * @template C - The type of the callback function.
   * @param [callback=this._DEFAULT_NODE_CALLBACK] - Function to call on each node.
   * @param [pattern='IN'] - The traversal order ('IN', 'PRE', 'POST').
   * @param [onlyOne=false] - If true, stops after the first callback.
   * @param [startNode=this._root] - The node to start from.
   * @param [iterationType=this.iterationType] - The traversal method.
   * @returns An array of callback results.
   */
  override dfs<C extends NodeCallback<BSTNode<K, V>>>(
    callback: C = this._DEFAULT_NODE_CALLBACK as C,
    pattern: DFSOrderPattern = 'IN',
    onlyOne: boolean = false,
    startNode: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined = this._root,
    iterationType: IterationType = this.iterationType
  ): ReturnType<C>[] {
    return super.dfs(callback, pattern, onlyOne, startNode, iterationType);
  }

    /**
   * BinaryTree level-order traversal
  
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Breadth-first traversal
 *  const bst = new BST<number>([5, 3, 7]);
 *     const result = bst.bfs(node => node.key);
 *     console.log(result.length); // 3;
   */
  override bfs(): (K | undefined)[];
  override 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>[];

  /**
   * Performs a Breadth-First Search (BFS) or Level-Order traversal.
   * @remarks Time O(N), visits every node. Space O(N) in the worst case for the queue.
   *
   * @template C - The type of the callback function.
   * @param [callback=this._DEFAULT_NODE_CALLBACK] - Function to call on each node.
   * @param [startNode=this._root] - The node to start from.
   * @param [iterationType=this.iterationType] - The traversal method.
   * @returns An array of callback results.
   */
  override bfs<C extends NodeCallback<BSTNode<K, V>>>(
    callback: C = this._DEFAULT_NODE_CALLBACK as C,
    startNode: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined = this._root,
    iterationType: IterationType = this.iterationType
  ): ReturnType<C>[] {
    return super.bfs(callback, startNode, iterationType, false);
  }

    /**
   * Level-order grouping
  
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Level-order grouping
 *  const bst = new BST<number>([5, 3, 7, 1, 4]);
 *     const levels = bst.listLevels(node => node.key);
 *     console.log(levels); // toBeInstanceOf;
 *     console.log(levels[0].length); // 1; // root level has 1 node
 *     const allKeys = levels.flat().sort((a, b) => a - b);
 *     console.log(allKeys); // [1, 3, 4, 5, 7];
   */
  override listLevels(): (K | undefined)[][];

  override 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>[][];

  /**
   * Returns a 2D array of nodes, grouped by level.
   * @remarks Time O(N), visits every node. Space O(N) for the result array and the queue/stack.
   *
   * @template C - The type of the callback function.
   * @param [callback=this._DEFAULT_NODE_CALLBACK] - Function to call on each node.
   * @param [startNode=this._root] - The node to start from.
   * @param [iterationType=this.iterationType] - The traversal method.
   * @returns A 2D array of callback results.
   */
  override listLevels<C extends NodeCallback<BSTNode<K, V>>>(
    callback: C = this._DEFAULT_NODE_CALLBACK as C,
    startNode: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined = this._root,
    iterationType: IterationType = this.iterationType
  ): ReturnType<C>[][] {
    return super.listLevels(callback, startNode, iterationType, false);
  }

  /**
   * 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Get node object by key
 *  const bst = new BST<number, string>([[5, 'root'], [3, 'left'], [7, 'right']]);
 *     const node = bst.getNode(3);
 *     console.log(node?.key); // 3;
 *     console.log(node?.value); // 'left';
   */
  override getNode(
    keyNodeEntryOrPredicate:
      | K
      | BSTNode<K, V>
      | [K | null | undefined, V | undefined]
      | null
      | undefined
      | NodePredicate<BSTNode<K, V>>,
    startNode: BSTNOptKeyOrNode<K, BSTNode<K, V>> = this._root,
    iterationType: IterationType = this.iterationType
  ): OptNode<BSTNode<K, V>> {
    // Fast-path: key lookup should not allocate arrays or build predicate closures.
    // (This is a hot path for get/has in Node Mode.)
    if (keyNodeEntryOrPredicate === null || keyNodeEntryOrPredicate === undefined) return undefined;

    // If a predicate is provided, defer to the full search logic.
    if (this._isPredicate(keyNodeEntryOrPredicate)) {
      return this.getNodes(keyNodeEntryOrPredicate, true, startNode, iterationType)[0] ?? undefined;
    }

    // NOTE: Range<K> is not part of this overload, but callers may still pass it at runtime.
    // Let search handle it.
    if (keyNodeEntryOrPredicate instanceof Range) {
      return (
        this.getNodes(
          keyNodeEntryOrPredicate,
          true,
          startNode as K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined,
          iterationType
        )[0] ?? undefined
      );
    }

    let targetKey: K | undefined;
    if (this.isNode(keyNodeEntryOrPredicate)) {
      targetKey = keyNodeEntryOrPredicate.key;
    } else if (this.isEntry(keyNodeEntryOrPredicate)) {
      const k = keyNodeEntryOrPredicate[0];
      if (k === null || k === undefined) return undefined;
      targetKey = k;
    } else {
      targetKey = keyNodeEntryOrPredicate;
    }

    const start = this.ensureNode(startNode);
    if (!start) return undefined;

    const NIL = this._NIL as unknown as BSTNode<K, V> | null | undefined;
    let cur: BSTNode<K, V> | null | undefined = start;
    const cmpFn = this._comparator;
    while (cur && cur !== NIL) {
      const c = cmpFn(targetKey, cur.key);
      if (c === 0) return cur;
      cur = c < 0 ? cur._left : cur._right;
    }

    return undefined;
  }


    /**
   * Search nodes by predicate
  
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Search nodes by predicate
 *  const bst = new BST<number, string>([[1, 'a'], [2, 'b'], [3, 'c'], [4, 'd']]);
 *     const found = bst.search(node => node.key > 2, true);
 *     console.log(found.length); // >= 1;
   */
  override search(
    keyNodeEntryOrPredicate:
      | K
      | BSTNode<K, V>
      | [K | null | undefined, V | undefined]
      | null
      | undefined
      | NodePredicate<BSTNode<K, V>>
      | Range<K>,
    onlyOne?: boolean
  ): (K | undefined)[];

  override 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>[];

  /**
   * Searches the tree for nodes matching a predicate, key, or range.
   * @remarks This is an optimized search for a BST. If searching by key or range, it prunes branches.
   * Time O(H + M) for key/range search (H=height, M=matches). O(N) for predicate search.
   * Space O(log N) for the stack.
   *
   * @template C - The type of the callback function.
   * @param keyNodeEntryOrPredicate - The key, node, entry, predicate, or range to search for.
   * @param [onlyOne=false] - If true, stops after finding the first match.
   * @param [callback=this._DEFAULT_NODE_CALLBACK] - A function to call on matching nodes.
   * @param [startNode=this._root] - The node to start the search from.
   * @param [iterationType=this.iterationType] - Whether to use 'RECURSIVE' or 'ITERATIVE' search.
   * @returns An array of results from the callback function for each matching node.
   */
  override 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 = false,
    callback: C = this._DEFAULT_NODE_CALLBACK as C,
    startNode: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined = this._root,
    iterationType: IterationType = this.iterationType
  ): ReturnType<C>[] {
    if (keyNodeEntryOrPredicate === undefined) return [];
    if (keyNodeEntryOrPredicate === null) return [];
    startNode = this.ensureNode(startNode);
    if (!startNode) return [];

    // Fast-path: key lookup (unique keys) using a tight BST walk (no allocations).
    // This is the hot path for get/has/search by key.
    const isRange = this.isRange(keyNodeEntryOrPredicate);
    const isPred = !isRange && this._isPredicate(keyNodeEntryOrPredicate);

    if (!isRange && !isPred) {
      let targetKey: K | undefined;
      if (this.isNode(keyNodeEntryOrPredicate)) {
        targetKey = keyNodeEntryOrPredicate.key;
      } else if (this.isEntry(keyNodeEntryOrPredicate)) {
        const k = keyNodeEntryOrPredicate[0];
        if (k !== null && k !== undefined) targetKey = k;
      } else {
        targetKey = keyNodeEntryOrPredicate;
      }
      if (targetKey === undefined) return [];

      const NIL = this._NIL as unknown as BSTNode<K, V> | null | undefined;
      const cmpFn = this._comparator;
      let cur: BSTNode<K, V> | null | undefined = startNode;

      // Loop intentionally avoids getters and extra type checks.
      while (cur && cur !== NIL) {
        const c = cmpFn(targetKey, cur.key);
        if (c === 0) return [callback(cur)];
        cur = c < 0 ? cur._left : cur._right;
      }
      return [];
    }

    let predicate: NodePredicate<BSTNode<K, V>>;
    if (isRange) {
      predicate = node => {
        /* istanbul ignore next -- node is always defined in iteration callbacks */
        if (!node) return false;
        return (keyNodeEntryOrPredicate).isInRange(node.key, this._comparator);
      };
    } else {
      predicate = this._ensurePredicate(keyNodeEntryOrPredicate);
    }

    // Optimization: Pruning logic
    const shouldVisitLeft = (cur: BSTNode<K, V> | null | undefined) => {
      /* istanbul ignore next -- defensive: cur is always defined when called from iteration */ if (!cur) return false;
      if (!this.isRealNode(cur.left)) return false;
      if (isRange) {
        // Range search: Only go left if the current key is >= the lower bound
        const range = keyNodeEntryOrPredicate;
        const leftS = range.low;
        const leftI = range.includeLow;
        return (leftI && this._compare(cur.key, leftS) >= 0) || (!leftI && this._compare(cur.key, leftS) > 0);
      }
      if (!isRange && !this._isPredicate(keyNodeEntryOrPredicate)) {
        // Key search: Only go left if current key > target key
        const benchmarkKey = this._extractKey(keyNodeEntryOrPredicate);
        return benchmarkKey !== null && benchmarkKey !== undefined && this._compare(cur.key, benchmarkKey) > 0;
      }
      return true; // Predicate search: must visit all
    };

    const shouldVisitRight = (cur: BSTNode<K, V> | null | undefined) => {
      /* istanbul ignore next -- defensive */ if (!cur) return false;
      if (!this.isRealNode(cur.right)) return false;
      if (isRange) {
        // Range search: Only go right if current key <= upper bound
        const range = keyNodeEntryOrPredicate;
        const rightS = range.high;
        const rightI = range.includeHigh;
        return (rightI && this._compare(cur.key, rightS) <= 0) || (!rightI && this._compare(cur.key, rightS) < 0);
      }
      if (!isRange && !this._isPredicate(keyNodeEntryOrPredicate)) {
        // Key search: Only go right if current key < target key
        const benchmarkKey = this._extractKey(keyNodeEntryOrPredicate);
        return benchmarkKey !== null && benchmarkKey !== undefined && this._compare(cur.key, benchmarkKey) < 0;
      }
      return true; // Predicate search: must visit all
    };

    return super._dfs(
      callback,
      'IN', // In-order is efficient for range/key search
      onlyOne,
      startNode,
      iterationType,
      false,
      shouldVisitLeft,
      shouldVisitRight,
      () => true, // shouldVisitRoot (always visit)
      cur => !!cur && predicate(cur) // shouldProcessRoot (only process if predicate matches)
    );
  }

    /**
   * Find all keys in a range
  
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Find all keys in a range
 *  const bst = new BST<number>([10, 20, 30, 40, 50]);
 *     console.log(bst.rangeSearch([15, 35])); // [20, 30];
   */
  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>[];

  /**
   * Performs an optimized search for nodes within a given key range.
   * @remarks Time O(H + M), where H is tree height and M is the number of matches.
   *
   * @template C - The type of the callback function.
   * @param range - A `Range` object or a `[low, high]` tuple.
   * @param [callback=this._DEFAULT_NODE_CALLBACK] - A function to call on matching nodes.
   * @param [startNode=this._root] - The node to start the search from.
   * @param [iterationType=this.iterationType] - The traversal method.
   * @returns An array of callback results.
   */
  rangeSearch<C extends NodeCallback<BSTNode<K, V>>>(
    range: Range<K> | [K, K],
    callback: C = this._DEFAULT_NODE_CALLBACK as C,
    startNode: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined = this._root,
    iterationType: IterationType = this.iterationType
  ) {
    const searchRange: Range<K> = range instanceof Range ? range : new Range(range[0], range[1]);
    return this.search(searchRange, false, callback, startNode, iterationType);
  }

  // ─── Order-Statistic Methods ───────────────────────────

  /**
   * Returns the element at the k-th position in tree order (0-indexed).
   * @remarks Time O(log n), Space O(1) iterative / O(log n) recursive. Requires `enableOrderStatistic: true`.
   * Tree order is defined by the comparator — ascending by default, but respects custom comparators (e.g. descending).
   *
   * @param k - The 0-based position in tree order (0 = first element).
   * @returns The key at position k, or `undefined` if out of bounds.
    * @example
 * // Order-statistic on BST
 *  const tree = new BST<number>([30, 10, 50, 20, 40], { enableOrderStatistic: true });
 *       console.log(tree.getByRank(0)); // 10;
 *       console.log(tree.getByRank(4)); // 50;
 *       console.log(tree.getRank(30)); // 2;
   */
  getByRank(k: number): K | undefined;

  /**
   * Returns the element at the k-th position in tree order and applies a callback.
   * @remarks Time O(log n), Space O(1) iterative / O(log n) recursive. Requires `enableOrderStatistic: true`.
   *
   * @param k - The 0-based position in tree order (0 = first element).
   * @param callback - Callback to apply to the found node.
   * @param iterationType - Iteration strategy ('ITERATIVE' or 'RECURSIVE').
   * @returns The callback result, or `undefined` if out of bounds.
   */
  getByRank<C extends NodeCallback<BSTNode<K, V>>>(
    k: number,
    callback: C,
    iterationType?: IterationType
  ): ReturnType<C> | undefined;

  getByRank<C extends NodeCallback<BSTNode<K, V>>>(
    k: number,
    callback: C = this._DEFAULT_NODE_CALLBACK as C,
    iterationType: IterationType = this.iterationType
  ): K | undefined | ReturnType<C> | undefined {
    if (!this._enableOrderStatistic) {
      raise(Error, ERR.orderStatisticNotEnabled('getByRank'));
    }
    if (k < 0 || k >= this._size) return undefined;

    let actualCallback: C | undefined = undefined;
    let actualIterationType: IterationType = this.iterationType;

    if (typeof callback === 'string') {
      actualIterationType = callback;
    } else if (callback) {
      actualCallback = callback;
      if (iterationType) {
        actualIterationType = iterationType;
      }
    }

    const node = actualIterationType === 'RECURSIVE'
      ? this._getByRankRecursive(this._root, k)
      : this._getByRankIterative(this._root, k);

    if (!node) return undefined;
    return actualCallback ? actualCallback(node) : node.key;
  }

  /**
   * Returns the 0-based rank of a key (number of elements that precede it in tree order).
   * @remarks Time O(log n), Space O(1) iterative / O(log n) recursive. Requires `enableOrderStatistic: true`.
   * Tree order is defined by the comparator. When the key is not found, returns the insertion position.
   *
   * @param keyNodeEntryOrPredicate - The key, node, entry `[K, V]`, or predicate to find.
   * @returns The rank (0-indexed), or -1 if the tree is empty or input is invalid.
   */
  getRank(
    keyNodeEntryOrPredicate:
      | K
      | BSTNode<K, V>
      | [K | null | undefined, V | undefined]
      | null
      | undefined
      | NodePredicate<BSTNode<K, V>>
  ): number;

  /**
   * Returns the 0-based rank (number of preceding elements in tree order) with explicit iteration type.
   * @remarks Time O(log n), Space O(1) iterative / O(log n) recursive. Requires `enableOrderStatistic: true`.
   *
   * @param keyNodeEntryOrPredicate - The key, node, entry, or predicate to find.
   * @param iterationType - Iteration strategy ('ITERATIVE' or 'RECURSIVE').
   * @returns The rank (0-indexed), or -1 if the tree is empty or input is invalid.
   */
  getRank(
    keyNodeEntryOrPredicate:
      | K
      | BSTNode<K, V>
      | [K | null | undefined, V | undefined]
      | null
      | undefined
      | NodePredicate<BSTNode<K, V>>,
    iterationType: IterationType
  ): number;

  getRank(
    keyNodeEntryOrPredicate:
      | K
      | BSTNode<K, V>
      | [K | null | undefined, V | undefined]
      | null
      | undefined
      | NodePredicate<BSTNode<K, V>>,
    iterationType: IterationType = this.iterationType
  ): number {
    if (!this._enableOrderStatistic) {
      raise(Error, ERR.orderStatisticNotEnabled('getRank'));
    }
    if (!this._root || this._size === 0) return -1;

    let actualIterationType: IterationType = this.iterationType;
    if (iterationType) actualIterationType = iterationType;

    // Resolve key from input
    let key: K | undefined;
    if (typeof keyNodeEntryOrPredicate === 'function') {
      // Predicate: find first matching node
      const results = this.search(keyNodeEntryOrPredicate as NodePredicate<BSTNode<K, V>>, true);
      if (results.length === 0 || results[0] === undefined) return -1;
      key = results[0];
    } else if (keyNodeEntryOrPredicate === null || keyNodeEntryOrPredicate === undefined) {
      return -1;
    } else if (this.isNode(keyNodeEntryOrPredicate)) {
      key = keyNodeEntryOrPredicate.key;
    } else if (Array.isArray(keyNodeEntryOrPredicate)) {
      key = keyNodeEntryOrPredicate[0] ?? undefined;
      if (key === undefined || key === null) return -1;
    } else {
      key = keyNodeEntryOrPredicate as K;
    }

    if (key === undefined) return -1;

    return actualIterationType === 'RECURSIVE'
      ? this._getRankRecursive(this._root, key)
      : this._getRankIterative(this._root, key);
  }

  /**
   * Returns elements by position range in tree order (0-indexed, inclusive on both ends).
   * @remarks Time O(log n + k), Space O(k), where k = end - start + 1. Requires `enableOrderStatistic: true`.
   *
   * @param start - Start position (inclusive, 0-indexed). Clamped to 0 if negative.
   * @param end - End position (inclusive, 0-indexed). Clamped to size-1 if too large.
   * @returns Array of keys in tree order within the specified range.
   */
  rangeByRank(start: number, end: number): (K | undefined)[];

  /**
   * Returns elements by position range in tree order with callback and optional iteration type.
   * @remarks Time O(log n + k), Space O(k), where k = end - start + 1. Requires `enableOrderStatistic: true`.
   *
   * @param start - Start rank (inclusive, 0-indexed).
   * @param end - End rank (inclusive, 0-indexed).
   * @param callback - Callback to apply to each node in the range.
   * @param iterationType - Iteration strategy ('ITERATIVE' or 'RECURSIVE').
   * @returns Array of callback results for nodes in the rank range.
   */
  rangeByRank<C extends NodeCallback<BSTNode<K, V>>>(
    start: number,
    end: number,
    callback: C,
    iterationType?: IterationType
  ): ReturnType<C>[];

  rangeByRank<C extends NodeCallback<BSTNode<K, V>>>(
    start: number,
    end: number,
    callback: C = this._DEFAULT_NODE_CALLBACK as C,
    iterationType: IterationType = this.iterationType
  ): (K | undefined)[] | ReturnType<C>[] {
    if (!this._enableOrderStatistic) {
      raise(Error, ERR.orderStatisticNotEnabled('rangeByRank'));
    }
    if (this._size === 0) return [];

    // Clamp
    const lo = Math.max(0, start);
    const hi = Math.min(this._size - 1, end);
    if (lo > hi) return [];

    let actualCallback: C | undefined = undefined;
    let actualIterationType: IterationType = this.iterationType;

    if (typeof callback === 'string') {
      actualIterationType = callback;
    } else if (callback) {
      actualCallback = callback;
      if (iterationType) {
        actualIterationType = iterationType;
      }
    }

    const results: (K | undefined | ReturnType<C>)[] = [];
    const count = hi - lo + 1;

    // Find the lo-th node, then in-order traverse count nodes
    const startNode = actualIterationType === 'RECURSIVE'
      ? this._getByRankRecursive(this._root, lo)
      : this._getByRankIterative(this._root, lo);

    if (!startNode) return [];

    // In-order traversal from startNode collecting count elements
    let collected = 0;
    const cb = actualCallback ?? this._DEFAULT_NODE_CALLBACK as C;

    // Use higher() to iterate — it's already O(log n) amortized per step
    let current: BSTNode<K, V> | undefined = startNode;
    while (current && collected < count) {
      results.push(cb(current));
      collected++;
      if (collected < count) {
        // Find next in-order node
        current = this._next(current);
      }
    }

    return results as (K | undefined)[] | 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Set a key-value pair
 *  const bst = new BST<number, string>();
 *     bst.set(1, 'one');
 *     bst.set(2, 'two');
 *     console.log(bst.get(1)); // 'one';
   */
  override set(
    keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined,
    value?: V
  ): boolean {
    const [newNode] = this._keyValueNodeOrEntryToNodeAndValue(keyNodeOrEntry, value);
    if (newNode === undefined) return false;

    if (this._root === undefined) {
      this._setRoot(newNode);
      if (this._isMapMode && this.isRealNode(newNode)) this._store.set(newNode.key, newNode);
      this._size++;
      this._updateCount(newNode);
      return true;
    }

    let current = this._root;
    while (current !== undefined) {
      if (this._compare(current.key, newNode.key) === 0) {
        // Key exists, replace node
        this._replaceNode(current, newNode);
        if (this._isMapMode && this.isRealNode(newNode)) this._store.set(current.key, newNode);
        return true;
      } else if (this._compare(current.key, newNode.key) > 0) {
        // Go left
        if (current.left === undefined) {
          current.left = newNode;
          if (this._isMapMode && this.isRealNode(newNode)) this._store.set(newNode.key, newNode);
          this._size++;
          this._updateCountAlongPath(newNode);
          return true;
        }
        if (current.left !== null) current = current.left;
      } else {
        // Go right
        if (current.right === undefined) {
          current.right = newNode;
          if (this._isMapMode && this.isRealNode(newNode)) this._store.set(newNode.key, newNode);
          this._size++;
          this._updateCountAlongPath(newNode);
          return true;
        }
        if (current.right !== null) current = current.right;
      }
    }
    /* istanbul ignore next -- defensive: traversal always finds undefined slot before exhausting tree */
    return false;
  }

  /**
   * 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Set multiple key-value pairs
 *  const bst = new BST<number, string>();
 *     bst.setMany([[1, 'a'], [2, 'b'], [3, 'c']]);
 *     console.log(bst.size); // 3;
 *     console.log(bst.get(2)); // 'b';
   */
  override setMany(
    keysNodesEntriesOrRaws: Iterable<R | BTNRep<K, V, BSTNode<K, V>>>,
    values?: Iterable<V | undefined>,
    isBalanceAdd = true,
    iterationType: IterationType = this.iterationType
  ): boolean[] {
    const inserted: boolean[] = [];
    const valuesIterator: Iterator<V | undefined> | undefined = values?.[Symbol.iterator]();

    if (!isBalanceAdd) {
      // Standard O(N*H) insertion
      for (let kve of keysNodesEntriesOrRaws) {
        const val = valuesIterator?.next().value;
        if (this.isRaw(kve)) kve = this._toEntryFn!(kve);
        inserted.push(this.set(kve, val));
      }
      return inserted;
    }

    // Balanced O(N log N) insertion
    const realBTNExemplars: {
      key: R | K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined;
      value: V | undefined;
      orgIndex: number;
    }[] = [];

    let i = 0;
    for (const kve of keysNodesEntriesOrRaws) {
      realBTNExemplars.push({ key: kve, value: valuesIterator?.next().value, orgIndex: i++ });
    }

    // Sort items by key
    const sorted = realBTNExemplars.sort(({ key: a }, { key: b }) => {
      let keyA: K | undefined | null, keyB: K | undefined | null;
      if (this.isRaw(a)) keyA = this._toEntryFn!(a)[0];
      else if (this.isEntry(a)) keyA = a[0];
      else if (this.isRealNode(a)) keyA = a.key;
      else keyA = a as K;

      if (this.isRaw(b)) keyB = this._toEntryFn!(b)[0];
      else if (this.isEntry(b)) keyB = b[0];
      else if (this.isRealNode(b)) keyB = b.key;
      else keyB = b as K;

      if (keyA != null && keyB != null) return this._compare(keyA, keyB);
      return 0;
    });

    // Recursive balanced build
    const _dfs = (arr: typeof realBTNExemplars) => {
      if (arr.length === 0) return;
      const mid = Math.floor((arr.length - 1) / 2);
      const { key, value, orgIndex } = arr[mid];
      if (this.isRaw(key)) {
        const entry = this._toEntryFn!(key);
        inserted[orgIndex] = this.set(entry);
      } else {
        inserted[orgIndex] = this.set(key, value);
      }
      _dfs(arr.slice(0, mid));
      _dfs(arr.slice(mid + 1));
    };

    // Iterative balanced build
    const _iterate = () => {
      const n = sorted.length;
      const stack: Array<[number, number]> = [[0, n - 1]];
      while (stack.length > 0) {
        const popped = stack.pop();
        /* istanbul ignore next -- stack.pop() on non-empty stack always returns a value */
        if (!popped) continue;
        const [l, r] = popped;
        if (l > r) continue;
        const m = l + Math.floor((r - l) / 2);
        const { key, value, orgIndex } = sorted[m];
        if (this.isRaw(key)) {
          const entry = this._toEntryFn!(key);
          inserted[orgIndex] = this.set(entry);
        } else {
          inserted[orgIndex] = this.set(key, value);
        }
        stack.push([m + 1, r]);
        stack.push([l, m - 1]);
      }
    };

    if (iterationType === 'RECURSIVE') _dfs(sorted);
    else _iterate();

    return inserted;
  }

  /**
   * 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Find the least key ≥ target
 *  const bst = new BST<number>([10, 20, 30, 40, 50]);
 *     console.log(bst.ceiling(25)); // 30;
 *     console.log(bst.ceiling(30)); // 30;
 *     console.log(bst.ceiling(55)); // undefined;
   */
  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>;

  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 = this._DEFAULT_NODE_CALLBACK as C,
    iterationType?: IterationType
  ): K | undefined | ReturnType<C> {
    let actualCallback: C | undefined = undefined;
    let actualIterationType: IterationType = this.iterationType;

    if (typeof callback === 'string') {
      actualIterationType = callback;
    } else if (callback) {
      actualCallback = callback;
      if (iterationType) {
        actualIterationType = iterationType;
      }
    }

    const node = this._bound(keyNodeEntryOrPredicate, true, actualIterationType);

    if (!actualCallback) {
      return node?.key;
    }

    return node ? actualCallback(node) : undefined;
  }

  /**
   * 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Find the least key strictly > target
 *  const bst = new BST<number>([10, 20, 30, 40]);
 *     console.log(bst.higher(20)); // 30;
 *     console.log(bst.higher(40)); // undefined;
   */
  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>;

  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 = this._DEFAULT_NODE_CALLBACK as C,
    iterationType?: IterationType
  ): K | undefined | ReturnType<C> {
    let actualCallback: C | undefined = undefined;
    let actualIterationType: IterationType = this.iterationType;

    if (typeof callback === 'string') {
      actualIterationType = callback;
    } else if (callback) {
      actualCallback = callback;
      if (iterationType) {
        actualIterationType = iterationType;
      }
    }

    const node = this._bound(keyNodeEntryOrPredicate, false, actualIterationType);

    if (!actualCallback) {
      return node?.key;
    }

    return node ? actualCallback(node) : undefined;
  }

  /**
   * 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Find the greatest key ≤ target
 *  const bst = new BST<number>([10, 20, 30, 40, 50]);
 *     console.log(bst.floor(25)); // 20;
 *     console.log(bst.floor(10)); // 10;
 *     console.log(bst.floor(5)); // undefined;
   */
  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>;

  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 = this._DEFAULT_NODE_CALLBACK as C,
    iterationType?: IterationType
  ): K | undefined | ReturnType<C> {
    if (keyNodeEntryOrPredicate === null || keyNodeEntryOrPredicate === undefined) {
      /* istanbul ignore next */ if (typeof callback === 'string' || !callback) {
        return undefined;
      }
      return undefined;
    }

    let actualCallback: C | undefined = undefined;
    let actualIterationType: IterationType = this.iterationType;

    if (typeof callback === 'string') {
      actualIterationType = callback;
    } else if (callback) {
      actualCallback = callback;
      if (iterationType) {
        actualIterationType = iterationType;
      }
    }

    if (this._isPredicate(keyNodeEntryOrPredicate)) {
      const node = this._floorByPredicate(keyNodeEntryOrPredicate, actualIterationType);

      if (!actualCallback) {
        return node?.key;
      }

      return node ? actualCallback(node) : undefined;
    }

    let targetKey: K | undefined;
    if (this.isNode(keyNodeEntryOrPredicate)) {
      targetKey = keyNodeEntryOrPredicate.key;
    } else if (this.isEntry(keyNodeEntryOrPredicate)) {
      const key = keyNodeEntryOrPredicate[0];
      if (key === null || key === undefined) {
        /* istanbul ignore next */ if (typeof callback === 'string' || !callback) {
          return undefined;
        }
        return undefined;
      }
      targetKey = key;
    } else {
      targetKey = keyNodeEntryOrPredicate;
    }

    if (targetKey !== undefined) {
      const node = this._floorByKey(targetKey, actualIterationType);

      /* istanbul ignore next */
      if (!actualCallback) {
        return node?.key;
      }

      return node ? actualCallback(node) : undefined;
    }

    /* istanbul ignore next -- targetKey is always defined if we reach here (null/undefined caught above) */
    if (typeof callback === 'string' || !callback) {
      return undefined;
    }
    /* istanbul ignore next */
    return undefined;
  }

  /**
   * 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Find the greatest key strictly < target
 *  const bst = new BST<number>([10, 20, 30, 40]);
 *     console.log(bst.lower(30)); // 20;
 *     console.log(bst.lower(10)); // undefined;
   */
  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>;

  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?: IterationType
  ): K | undefined | ReturnType<C> {
    if (keyNodeEntryOrPredicate === null || keyNodeEntryOrPredicate === undefined) {
      /* istanbul ignore next */ if (typeof callback === 'string' || !callback) {
        return undefined;
      }
      /* istanbul ignore next */
      return undefined;
    }

    let actualCallback: C | undefined = undefined;
    let actualIterationType: IterationType = this.iterationType;

    if (typeof callback === 'string') {
      actualIterationType = callback;
    } else if (callback) {
      actualCallback = callback;
      if (iterationType) {
        actualIterationType = iterationType;
      }
    }

    if (this._isPredicate(keyNodeEntryOrPredicate)) {
      const node = this._lowerByPredicate(keyNodeEntryOrPredicate, actualIterationType);

      if (!actualCallback) {
        return node?.key;
      }

      return node ? actualCallback(node) : undefined;
    }

    let targetKey: K | undefined;
    if (this.isNode(keyNodeEntryOrPredicate)) {
      targetKey = keyNodeEntryOrPredicate.key;
    } else if (this.isEntry(keyNodeEntryOrPredicate)) {
      const key = keyNodeEntryOrPredicate[0];
      if (key === null || key === undefined) {
        /* istanbul ignore next */ if (typeof callback === 'string' || !callback) {
          return undefined;
        }
      /* istanbul ignore next */
        return undefined;
      }
      targetKey = key;
    } else {
      targetKey = keyNodeEntryOrPredicate;
    }

    if (targetKey !== undefined) {
      const node = this._lowerByKey(targetKey, actualIterationType);

      if (!actualCallback) {
        return node?.key;
      }

      return node ? actualCallback(node) : undefined;
    }

    /* istanbul ignore next -- targetKey is always defined if we reach here (null/undefined caught above) */
    if (typeof callback === 'string' || !callback) {
      return undefined;
    }
    /* istanbul ignore next */
    return undefined;
  }

  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>[];

  /**
   * Traverses the tree and returns nodes that are lesser or greater than a target node.
   * @remarks Time O(N), as it performs a full traversal. Space O(log N) or O(N).
   *
   * @template C - The type of the callback function.
   * @param [callback=this._DEFAULT_NODE_CALLBACK] - Function to call on matching nodes.
   * @param [lesserOrGreater=-1] - -1 for lesser, 1 for greater, 0 for equal.
   * @param [targetNode=this._root] - The node to compare against.
   * @param [iterationType=this.iterationType] - The traversal method.
   * @returns An array of callback results.
   */
  lesserOrGreaterTraverse<C extends NodeCallback<BSTNode<K, V>>>(
    callback: C = this._DEFAULT_NODE_CALLBACK as C,
    lesserOrGreater: CP = -1,
    targetNode: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined = this._root,
    iterationType: IterationType = this.iterationType
  ): ReturnType<C>[] {
    const targetNodeEnsured = this.ensureNode(targetNode);
    const ans: ReturnType<NodeCallback<BSTNode<K, V>>>[] = [];
    if (!this._root || !targetNodeEnsured) return ans;

    const targetKey = targetNodeEnsured.key;

    if (iterationType === 'RECURSIVE') {
      const dfs = (cur: BSTNode<K, V>) => {
        const compared = this._compare(cur.key, targetKey);
        if (Math.sign(compared) == lesserOrGreater) ans.push(callback(cur));

        if (this.isRealNode(cur.left)) dfs(cur.left);
        if (this.isRealNode(cur.right)) dfs(cur.right);
      };
      dfs(this._root);
      return ans;
    } else {
      const queue = new Queue<BSTNode<K, V>>([this._root]);
      while (queue.length > 0) {
        const cur = queue.shift();
        if (this.isRealNode(cur)) {
          const compared = this._compare(cur.key, targetKey);
          if (Math.sign(compared) == lesserOrGreater) ans.push(callback(cur));
          if (this.isRealNode(cur.left)) queue.push(cur.left);
          if (this.isRealNode(cur.right)) queue.push(cur.right);
        }
      }
      return ans;
    }
  }

  /**
   * 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Rebalance the tree
 *  const bst = new BST<number>();
 *     // Insert in sorted order (worst case for BST)
 *     for (let i = 1; i <= 7; i++) bst.add(i);
 *     console.log(bst.isAVLBalanced()); // false;
 *     bst.perfectlyBalance();
 *     console.log(bst.isAVLBalanced()); // true;
   */
  perfectlyBalance(iterationType: IterationType = this.iterationType): boolean {
    const nodes = this.dfs(node => node, 'IN', false, this._root, iterationType);
    const n = nodes.length;
    this._clearNodes();
    if (n === 0) return false;

    // Build balanced tree from sorted array
    const build = (l: number, r: number, parent?: BSTNode<K, V>): BSTNode<K, V> | undefined => {
      if (l > r) return undefined;
      const m = l + ((r - l) >> 1);
      const root = nodes[m]! as BSTNode<K, V>;
      const leftChild = build(l, m - 1, root);
      const rightChild = build(m + 1, r, root);
      root.left = leftChild;
      root.right = rightChild;
      root.parent = parent;
      return root;
    };

    const newRoot = build(0, n - 1, undefined);
    this._setRoot(newRoot);
    this._size = n;
    return true;
  }

  /**
   * 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Check if tree is height-balanced
 *  const bst = new BST<number>([3, 1, 5, 2, 4]);
 *     console.log(bst.isAVLBalanced()); // true;
   */
  isAVLBalanced(iterationType: IterationType = this.iterationType): boolean {
    if (!this._root) return true;
    let balanced = true;

    if (iterationType === 'RECURSIVE') {
      // Recursive height check
      const _height = (cur: BSTNode<K, V> | null | undefined): number => {
        if (!cur) return 0;
        const leftHeight = _height(cur.left);
        const rightHeight = _height(cur.right);
        if (Math.abs(leftHeight - rightHeight) > 1) balanced = false;
        return Math.max(leftHeight, rightHeight) + 1;
      };
      _height(this._root);
    } else {
      // Iterative post-order height check
      const stack: BSTNode<K, V>[] = [];
      let node: OptNode<BSTNode<K, V>> = this._root,
        last: OptNode<BSTNode<K, V>> = undefined;
      const depths: Map<BSTNode<K, V>, number> = new Map();

      while (stack.length > 0 || node) {
        if (node) {
          stack.push(node);
          if (node.left !== null) node = node.left;
        } else {
          node = stack[stack.length - 1];
          if (!node.right || last === node.right) {
            node = stack.pop();
            if (node) {
              const left = node.left ? depths.get(node.left)! : -1;
              const right = node.right ? depths.get(node.right)! : -1;
              if (Math.abs(left - right) > 1) return false;
              depths.set(node, 1 + Math.max(left, right));
              last = node;
              node = undefined;
            }
          } else node = node.right;
        }
      }
    }
    return balanced;
  }

  /**
   * 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.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
    * @example
 * // Transform to new tree
 *  const bst = new BST<number, number>([[1, 10], [2, 20], [3, 30]]);
 *     const doubled = bst.map((value, key) => [key, (value ?? 0) * 2] as [number, number]);
 *     console.log([...doubled.values()]); // [20, 40, 60];
   */
  override 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> {
    const out = this._createLike<MK, MV, MR>([], options);
    let index = 0;
    // Iterates in-order
    for (const [key, value] of this) {
      out.set(callback.call(thisArg, value, key, index++, this));
    }
    return out;
  }

  /**
   * 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 = false,
    startNode: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined = this._root,
    iterationType: IterationType = this.iterationType
  ): boolean {
    const toDelete = this.search(keyNodeEntryOrPredicate, onlyOne, node => node, startNode, iterationType);

    let deleted = false;
    for (const node of toDelete) {
      if (this.delete(node)) deleted = true;
    }

    return deleted;
  }

  /**
   * (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> {
    return (a: K, b: K): number => {
      // If both keys are comparable (primitive types), use direct comparison
      if (isComparable(a) && isComparable(b)) {
        if (a > b) return 1;
        if (a < b) return -1;
        return 0;
      }

      /* istanbul ignore next -- Date objects satisfy isComparable(), so this branch is unreachable via default comparator */
      // Date keys: compare by getTime()
      if (a instanceof Date && b instanceof Date) {
        const ta = a.getTime();
        const tb = b.getTime();
        if (Number.isNaN(ta) || Number.isNaN(tb)) raise(TypeError, ERR.invalidDate('BST'));
        return ta > tb ? 1 : ta < tb ? -1 : 0;
      }

      // If keys are objects and no comparator is provided, throw an error
      if (typeof a === 'object' || typeof b === 'object') {
        raise(TypeError, ERR.comparatorRequired('BST'));
      }

      // Default: keys are equal (fallback case)
      return 0;
    };
  }

  /**
   * (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 {
    if (iterationType === 'RECURSIVE') {
      // Recursive binary search implementation
      const dfs = (cur: BSTNode<K, V> | null | undefined): BSTNode<K, V> | undefined => {
        if (!this.isRealNode(cur)) return undefined;

        const cmp = this.comparator(cur.key!, key);

        if (cmp <= 0) {
          // Current node satisfies the floor condition (cur.key <= target).
          // Try to find a larger candidate in the right subtree.
          const rightResult = dfs(cur.right);
          return rightResult ?? cur;
        } else {
          // Current node is too large, move left to find smaller keys.
          return dfs(cur.left);
        }
      };

      return dfs(this.root);
    } else {
      // Iterative binary search implementation
      let current: BSTNode<K, V> | undefined = this.root;
      let result: BSTNode<K, V> | undefined = undefined;

      while (this.isRealNode(current)) {
        const cmp = this.comparator(current.key!, key);

        if (cmp <= 0) {
          // Current node is a candidate. Save it and try right subtree for a larger key.
          result = current;
          current = current.right ?? undefined;
        } else {
          // Current node is too large, move left.
          current = current.left ?? undefined;
        }
      }

      return result;
    }
  }

  /**
   * (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 {
    if (iterationType === 'RECURSIVE') {
      // Recursive in-order traversal
      let result: BSTNode<K, V> | undefined = undefined;

      const dfs = (cur: BSTNode<K, V> | null | undefined): void => {
        if (!this.isRealNode(cur)) return;

        // In-order: process left subtree first
        if (this.isRealNode(cur.left)) dfs(cur.left);

        // Check current node
        if (predicate(cur)) {
          result = cur;
        }

        // Process right subtree
        if (this.isRealNode(cur.right)) dfs(cur.right);
      };

      dfs(this.root);
      return result;
    } else {
      // Iterative in-order traversal using explicit stack
      const stack: (BSTNode<K, V> | null | undefined)[] = [];
      let current: BSTNode<K, V> | null | undefined = this.root;
      let result: BSTNode<K, V> | undefined = undefined;

      while (stack.length > 0 || this.isRealNode(current)) {
        if (this.isRealNode(current)) {
          // Go to the leftmost node
          stack.push(current);
          current = current.left;
        } else {
          // Pop from stack and process
          const node = stack.pop();
          if (!this.isRealNode(node)) break;

          // Check if current node satisfies predicate
          if (predicate(node)) {
            result = node;
          }

          // Visit right subtree
          current = node.right;
        }
      }

      return result;
    }
  }

  /**
   * (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 {
    if (iterationType === 'RECURSIVE') {
      // Recursive binary search implementation
      const dfs = (cur: BSTNode<K, V> | null | undefined): BSTNode<K, V> | undefined => {
        if (!this.isRealNode(cur)) return undefined;

        const cmp = this.comparator(cur.key!, key);

        if (cmp < 0) {
          // Current node satisfies the lower condition (cur.key < target).
          // Try to find a larger candidate in the right subtree.
          const rightResult = dfs(cur.right);
          return rightResult ?? cur;
        } else {
          // Current node is too large or equal, move left to find smaller keys.
          return dfs(cur.left);
        }
      };

      return dfs(this.root);
    } else {
      // Iterative binary search implementation
      let current: BSTNode<K, V> | undefined = this.root;
      let result: BSTNode<K, V> | undefined = undefined;

      while (this.isRealNode(current)) {
        const cmp = this.comparator(current.key!, key);

        if (cmp < 0) {
          // Current node is a candidate. Save it and try right subtree for a larger key.
          result = current;
          current = current.right ?? undefined;
        } else {
          // Current node is too large or equal, move left.
          current = current.left ?? undefined;
        }
      }

      return result;
    }
  }

  /**
   * (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 {
    if (iterationType === 'RECURSIVE') {
      // Recursive in-order traversal
      let result: BSTNode<K, V> | undefined = undefined;

      const dfs = (cur: BSTNode<K, V> | null | undefined): void => {
        if (!this.isRealNode(cur)) return;

        // In-order: process left subtree first
        if (this.isRealNode(cur.left)) dfs(cur.left);

        // Check current node
        if (predicate(cur)) {
          result = cur;
        }

        // Process right subtree
        if (this.isRealNode(cur.right)) dfs(cur.right);
      };

      dfs(this.root);
      return result;
    } else {
      // Iterative in-order traversal using explicit stack
      const stack: (BSTNode<K, V> | null | undefined)[] = [];
      let current: BSTNode<K, V> | null | undefined = this.root;
      let result: BSTNode<K, V> | undefined = undefined;

      while (stack.length > 0 || this.isRealNode(current)) {
        if (this.isRealNode(current)) {
          // Go to the leftmost node
          stack.push(current);
          current = current.left;
        } else {
          // Pop from stack and process
          const node = stack.pop();
          if (!this.isRealNode(node)) break;

          // Check if current node satisfies predicate
          if (predicate(node)) {
            result = node;
          }

          // Visit right subtree
          current = node.right;
        }
      }

      return result;
    }
  }

  /**
   * (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 {
    if (keyNodeEntryOrPredicate === null || keyNodeEntryOrPredicate === undefined) {
      return undefined;
    }

    // Check if input is a predicate function first
    if (this._isPredicate(keyNodeEntryOrPredicate)) {
      return this._boundByPredicate(keyNodeEntryOrPredicate, iterationType);
    }

    // Resolve input to a comparable key
    let targetKey: K | undefined;

    if (this.isNode(keyNodeEntryOrPredicate)) {
      // Input is a BSTNode - extract its key
      targetKey = keyNodeEntryOrPredicate.key;
    } else if (this.isEntry(keyNodeEntryOrPredicate)) {
      // Input is a [key, value] entry - extract the key
      const key = keyNodeEntryOrPredicate[0];
      if (key === null || key === undefined) {
        return undefined;
      }
      targetKey = key;
    } else {
      // Input is a raw key
      targetKey = keyNodeEntryOrPredicate;
    }

    // Execute key-based search with binary search optimization
    if (targetKey !== undefined) {
      return this._boundByKey(targetKey, isLower, iterationType);
    }

    /* istanbul ignore next -- defensive: targetKey is always defined if predicate path was skipped */
    return 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 {
    if (iterationType === 'RECURSIVE') {
      // Recursive binary search implementation
      const dfs = (cur: BSTNode<K, V> | null | undefined): BSTNode<K, V> | undefined => {
        if (!this.isRealNode(cur)) return undefined;

        const cmp = this.comparator(cur.key!, key);
        const condition = isLower ? cmp >= 0 : cmp > 0;

        if (condition) {
          // Current node satisfies the bound condition.
          // Try to find a closer (smaller key) candidate in the left subtree.
          const leftResult = dfs(cur.left);
          return leftResult ?? cur;
        } else {
          // Current node does not satisfy the condition.
          // Move right to find larger keys.
          return dfs(cur.right);
        }
      };

      return dfs(this.root);
    } else {
      // Iterative binary search implementation
      let current: BSTNode<K, V> | undefined = this.root;
      let result: BSTNode<K, V> | undefined = undefined;

      while (this.isRealNode(current)) {
        const cmp = this.comparator(current.key!, key);
        const condition = isLower ? cmp >= 0 : cmp > 0;

        if (condition) {
          // Current node is a candidate. Save it and try left subtree for a closer match.
          result = current;
          current = current.left ?? undefined;
        } else {
          // Move right to find larger keys.
          current = current.right ?? undefined;
        }
      }

      return result;
    }
  }

  /**
   * (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 {
    if (iterationType === 'RECURSIVE') {
      // Recursive in-order traversal
      let result: BSTNode<K, V> | undefined = undefined;

      const dfs = (cur: BSTNode<K, V> | null | undefined): void => {
        if (result || !this.isRealNode(cur)) return;

        // In-order: process left subtree first
        if (this.isRealNode(cur.left)) dfs(cur.left);

        // Check current node
        if (!result && predicate(cur)) {
          result = cur;
        }

        // Process right subtree
        if (!result && this.isRealNode(cur.right)) dfs(cur.right);
      };

      dfs(this.root);
      return result;
    } else {
      // Iterative in-order traversal using explicit stack
      const stack: (BSTNode<K, V> | null | undefined)[] = [];
      let current: BSTNode<K, V> | null | undefined = this.root;

      while (stack.length > 0 || this.isRealNode(current)) {
        if (this.isRealNode(current)) {
          // Go to the leftmost node
          stack.push(current);
          current = current.left;
        } else {
          // Pop from stack and process
          const node = stack.pop();
          if (!this.isRealNode(node)) break;

          // Check if current node satisfies predicate
          if (predicate(node)) {
            return node;
          }

          // Visit right subtree
          current = node.right;
        }
      }

      return 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 override _createInstance<TK = K, TV = V, TR = R>(options?: Partial<BSTOptions<TK, TV, TR>>): this {
    const Ctor = this.constructor as unknown as new (
      iter?: Iterable<TK | BSTNode<TK, TV> | [TK | null | undefined, TV | undefined] | null | undefined | TR>,
      opts?: BSTOptions<TK, TV, TR>
    ) => BST<TK, TV, TR>;
    return new Ctor([], { ...this._snapshotOptions<TK, TV, TR>(), ...(options ?? {}) }) as unknown as 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 override _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> {
    const Ctor = this.constructor as unknown as new (
      iter?: Iterable<TK | BSTNode<TK, TV> | [TK | null | undefined, TV | undefined] | null | undefined | TR>,
      opts?: BSTOptions<TK, TV, TR>
    ) => BST<TK, TV, TR>;
    return new Ctor(iter, { ...this._snapshotOptions<TK, TV, TR>(), ...(options ?? {}) });
  }

  /**
   * (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 override _snapshotOptions<TK = K, TV = V, TR = R>(): BSTOptions<TK, TV, TR> {
    return {
      ...super._snapshotOptions<TK, TV, TR>(),
      comparator: this._comparator as unknown as BSTOptions<TK, TV, TR>['comparator'],
      enableOrderStatistic: this._enableOrderStatistic
    };
  }

  /**
   * (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 override _keyValueNodeOrEntryToNodeAndValue(
    keyNodeOrEntry: K | BSTNode<K, V> | [K | null | undefined, V | undefined] | null | undefined,
    value?: V
  ): [OptNode<BSTNode<K, V>>, V | undefined] {
    const [node, entryValue] = super._keyValueNodeOrEntryToNodeAndValue(keyNodeOrEntry, value);
    if (node === null) return [undefined, undefined]; // BST handles null differently (as undefined)
    return [node, value ?? entryValue];
  }

  /**
   * (Protected) Sets the root node and clears its parent reference.
   * @remarks Time O(1)
   *
   * @param v - The node to set as root.
   */
  /**
   * (Protected) Recalculates the subtree count for a single node.
   * @remarks Time O(1). Only active when enableOrderStatistic is true.
   */
  protected _updateCount(node: BSTNode<K, V>): void {
    if (!this._enableOrderStatistic) return;
    node._count = 1
      + (this.isRealNode(node.left) ? node.left._count : 0)
      + (this.isRealNode(node.right) ? node.right._count : 0);
  }

  /**
   * (Protected) Updates subtree counts from a node up to the root.
   * @remarks Time O(log n). Only active when enableOrderStatistic is true.
   */
  protected _updateCountAlongPath(node: OptNode<BSTNode<K, V>>): void {
    if (!this._enableOrderStatistic) return;
    let current = node;
    while (current) {
      this._updateCount(current);
      current = current.parent as BSTNode<K, V> | undefined;
    }
  }

  /**
   * (Protected) Finds the node at position k in tree order (iterative).
   * @remarks Time O(log n), Space O(1)
   */
  protected _getByRankIterative(node: OptNode<BSTNode<K, V>>, k: number): BSTNode<K, V> | undefined {
    let current = node;
    let remaining = k;
    while (current) {
      const leftCount = this.isRealNode(current.left) ? current.left._count : 0;
      if (remaining < leftCount) {
        current = current.left as BSTNode<K, V> | undefined;
      } else if (remaining === leftCount) {
        return current;
      } else {
        remaining = remaining - leftCount - 1;
        current = current.right as BSTNode<K, V> | undefined;
      }
    }
    return undefined;
  }

  /**
   * (Protected) Finds the node at position k in tree order (recursive).
   * @remarks Time O(log n), Space O(log n) call stack
   */
  protected _getByRankRecursive(node: OptNode<BSTNode<K, V>>, k: number): BSTNode<K, V> | undefined {
    if (!node) return undefined;
    const leftCount = this.isRealNode(node.left) ? node.left._count : 0;
    if (k < leftCount) return this._getByRankRecursive(node.left as BSTNode<K, V> | undefined, k);
    if (k === leftCount) return node;
    return this._getByRankRecursive(node.right as BSTNode<K, V> | undefined, k - leftCount - 1);
  }

  /**
   * (Protected) Computes the rank of a key iteratively.
   * @remarks Time O(log n), Space O(1)
   */
  protected _getRankIterative(node: OptNode<BSTNode<K, V>>, key: K): number {
    let rank = 0;
    let current = node;
    while (this.isRealNode(current)) {
      const cmp = this._compare(current.key, key);
      if (cmp > 0) {
        // key < current.key, go left
        current = current.left as BSTNode<K, V> | undefined;
      } else if (cmp < 0) {
        // key > current.key
        rank += (this.isRealNode(current.left) ? current.left._count : 0) + 1;
        current = current.right as BSTNode<K, V> | undefined;
      } else {
        // Found
        rank += this.isRealNode(current.left) ? current.left._count : 0;
        return rank;
      }
    }
    // Key not found, rank = insertion position
    return rank;
  }

  /**
   * (Protected) Computes the rank of a key recursively.
   * @remarks Time O(log n), Space O(log n) call stack
   */
  protected _getRankRecursive(node: OptNode<BSTNode<K, V>>, key: K): number {
    if (!node) return 0;
    const cmp = this._compare(node.key, key);
    if (cmp > 0) {
      return this._getRankRecursive(node.left as BSTNode<K, V> | undefined, key);
    } else if (cmp < 0) {
      return (this.isRealNode(node.left) ? node.left._count : 0) + 1
        + this._getRankRecursive(node.right as BSTNode<K, V> | undefined, key);
    } else {
      return this.isRealNode(node.left) ? node.left._count : 0;
    }
  }

  /**
   * (Protected) Finds the in-order successor of a node.
   * @remarks Time O(log n), Space O(1)
   */
  protected _next(node: BSTNode<K, V>): BSTNode<K, V> | undefined {
    if (this.isRealNode(node.right)) {
      // Leftmost in right subtree
      let current = node.right as BSTNode<K, V>;
      while (this.isRealNode(current.left)) {
        current = current.left as BSTNode<K, V>;
      }
      return current;
    }
    // Go up until we come from a left child
    let current: BSTNode<K, V> | undefined = node;
    let parent = current.parent as BSTNode<K, V> | undefined;
    while (parent && current === parent.right) {
      current = parent;
      parent = parent.parent as BSTNode<K, V> | undefined;
    }
    return parent;
  }

  protected override _setRoot(v: OptNode<BSTNode<K, V>>) {
    if (v) v.parent = undefined;
    this._root = v;
  }

  /**
   * (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) {
    return this._comparator(a, b);
  }

  /**
   * (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 {
    let node = this._root as BSTNode<K, V> | undefined;

    // 1. Find the node
    while (node) {
      const cmp = this._compare(node.key, key);
      if (cmp === 0) break;
      node = cmp > 0 ? (node.left as BSTNode<K, V> | undefined) : (node.right as BSTNode<K, V> | undefined);
    }
    if (!node) return false; // Not found

    // Helper to replace node `u` with node `v`
    const transplant = (u: BSTNode<K, V> | undefined, v: BSTNode<K, V> | undefined) => {
      const p = u?.parent as BSTNode<K, V> | undefined;
      if (!p) {
        this._setRoot(v);
      } else if (p.left === u) {
        p.left = v;
      } else {
        p.right = v;
      }
      if (v) v.parent = p;
    };

    // Helper to find the minimum node in a subtree
    const minNode = (x: BSTNode<K, V> | undefined): BSTNode<K, V> | undefined => {
      if (!x) return undefined;
      while (x.left !== undefined && x.left !== null) x = x.left as BSTNode<K, V>;
      return x;
    };

    // 2. Perform deletion
    let countUpdateStart: BSTNode<K, V> | undefined;
    if (node.left === undefined) {
      // Case 1: No left child
      countUpdateStart = node.parent as BSTNode<K, V> | undefined;
      transplant(node, node.right as BSTNode<K, V> | undefined);
    } else if (node.right === undefined) {
      // Case 2: No right child
      countUpdateStart = node.parent as BSTNode<K, V> | undefined;
      transplant(node, node.left as BSTNode<K, V> | undefined);
    } else {
      // Case 3: Two children
      const succ = minNode(node.right as BSTNode<K, V> | undefined)!; // Find successor
      if (succ.parent !== node) {
        countUpdateStart = succ.parent as BSTNode<K, V> | undefined;
        transplant(succ, succ.right as BSTNode<K, V> | undefined);
        succ.right = node.right as BSTNode<K, V> | undefined;
        if (succ.right) (succ.right as BSTNode<K, V>).parent = succ;
      } else {
        countUpdateStart = succ;
      }
      transplant(node, succ);
      succ.left = node.left as BSTNode<K, V> | undefined;
      if (succ.left) (succ.left as BSTNode<K, V>).parent = succ;
    }

    this._updateCountAlongPath(countUpdateStart);
    this._size = Math.max(0, this._size - 1);
    return true;
  }
}