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// Copyright 2018-2024 the Deno authors. All rights reserved. MIT license.// This module is browser compatible.
import { ascend } from "./comparators.ts";import { BinarySearchTree } from "./binary_search_tree.ts";import { Direction, RedBlackNode } from "./_red_black_node.ts";
/** * A red-black tree. This is a kind of self-balancing binary search tree. The * values are in ascending order by default, using JavaScript's built-in * comparison operators to sort the values. * * Red-Black Trees require fewer rotations than AVL Trees, so they can provide * faster insertions and removal operations. If you need faster lookups, you * should use an AVL Tree instead. AVL Trees are more strictly balanced than * Red-Black Trees, so they can provide faster lookups. * * | Method | Average Case | Worst Case | * | ------------- | ------------ | ---------- | * | find(value) | O(log n) | O(log n) | * | insert(value) | O(log n) | O(log n) | * | remove(value) | O(log n) | O(log n) | * | min() | O(log n) | O(log n) | * | max() | O(log n) | O(log n) | * * @example * ```ts * import { * ascend, * descend, * RedBlackTree, * } from "https://deno.land/std@$STD_VERSION/data_structures/mod.ts"; * import { assertEquals } from "https://deno.land/std@$STD_VERSION/assert/assert_equals.ts"; * * const values = [3, 10, 13, 4, 6, 7, 1, 14]; * const tree = new RedBlackTree<number>(); * values.forEach((value) => tree.insert(value)); * assertEquals([...tree], [1, 3, 4, 6, 7, 10, 13, 14]); * assertEquals(tree.min(), 1); * assertEquals(tree.max(), 14); * assertEquals(tree.find(42), null); * assertEquals(tree.find(7), 7); * assertEquals(tree.remove(42), false); * assertEquals(tree.remove(7), true); * assertEquals([...tree], [1, 3, 4, 6, 10, 13, 14]); * * const invertedTree = new RedBlackTree<number>(descend); * values.forEach((value) => invertedTree.insert(value)); * assertEquals([...invertedTree], [14, 13, 10, 7, 6, 4, 3, 1]); * assertEquals(invertedTree.min(), 14); * assertEquals(invertedTree.max(), 1); * assertEquals(invertedTree.find(42), null); * assertEquals(invertedTree.find(7), 7); * assertEquals(invertedTree.remove(42), false); * assertEquals(invertedTree.remove(7), true); * assertEquals([...invertedTree], [14, 13, 10, 6, 4, 3, 1]); * * const words = new RedBlackTree<string>((a, b) => * ascend(a.length, b.length) || ascend(a, b) * ); * ["truck", "car", "helicopter", "tank", "train", "suv", "semi", "van"] * .forEach((value) => words.insert(value)); * assertEquals([...words], [ * "car", * "suv", * "van", * "semi", * "tank", * "train", * "truck", * "helicopter", * ]); * assertEquals(words.min(), "car"); * assertEquals(words.max(), "helicopter"); * assertEquals(words.find("scooter"), null); * assertEquals(words.find("tank"), "tank"); * assertEquals(words.remove("scooter"), false); * assertEquals(words.remove("tank"), true); * assertEquals([...words], [ * "car", * "suv", * "van", * "semi", * "train", * "truck", * "helicopter", * ]); * ``` */export class RedBlackTree<T> extends BinarySearchTree<T> { declare protected root: RedBlackNode<T> | null;
constructor( compare: (a: T, b: T) => number = ascend, ) { super(compare); }
/** Creates a new red-black tree from an array like or iterable object. */ static override from<T>( collection: ArrayLike<T> | Iterable<T> | RedBlackTree<T>, ): RedBlackTree<T>; static override from<T>( collection: ArrayLike<T> | Iterable<T> | RedBlackTree<T>, options: { Node?: typeof RedBlackNode; compare?: (a: T, b: T) => number; }, ): RedBlackTree<T>; static override from<T, U, V>( collection: ArrayLike<T> | Iterable<T> | RedBlackTree<T>, options: { compare?: (a: U, b: U) => number; map: (value: T, index: number) => U; thisArg?: V; }, ): RedBlackTree<U>; static override from<T, U, V>( collection: ArrayLike<T> | Iterable<T> | RedBlackTree<T>, options?: { compare?: (a: U, b: U) => number; map?: (value: T, index: number) => U; thisArg?: V; }, ): RedBlackTree<U> { let result: RedBlackTree<U>; let unmappedValues: ArrayLike<T> | Iterable<T> = []; if (collection instanceof RedBlackTree) { result = new RedBlackTree( options?.compare ?? (collection as unknown as RedBlackTree<U>).compare, ); if (options?.compare || options?.map) { unmappedValues = collection; } else { const nodes: RedBlackNode<U>[] = []; if (collection.root) { result.root = RedBlackNode.from( collection.root as unknown as RedBlackNode<U>, ); nodes.push(result.root); } while (nodes.length) { const node: RedBlackNode<U> = nodes.pop()!; const left: RedBlackNode<U> | null = node.left ? RedBlackNode.from(node.left) : null; const right: RedBlackNode<U> | null = node.right ? RedBlackNode.from(node.right) : null;
if (left) { left.parent = node; nodes.push(left); } if (right) { right.parent = node; nodes.push(right); } } } } else { result = (options?.compare ? new RedBlackTree(options.compare) : new RedBlackTree()) as RedBlackTree<U>; unmappedValues = collection; } const values: Iterable<U> = options?.map ? Array.from(unmappedValues, options.map, options.thisArg) : unmappedValues as U[]; for (const value of values) result.insert(value); return result; }
protected removeFixup( parent: RedBlackNode<T> | null, current: RedBlackNode<T> | null, ) { while (parent && !current?.red) { const direction: Direction = parent.left === current ? "left" : "right"; const siblingDirection: Direction = direction === "right" ? "left" : "right"; let sibling: RedBlackNode<T> | null = parent[siblingDirection];
if (sibling?.red) { sibling.red = false; parent.red = true; this.rotateNode(parent, direction); sibling = parent[siblingDirection]; } if (sibling) { if (!sibling.left?.red && !sibling.right?.red) { sibling!.red = true; current = parent; parent = current.parent; } else { if (!sibling[siblingDirection]?.red) { sibling[direction]!.red = false; sibling.red = true; this.rotateNode(sibling, siblingDirection); sibling = parent[siblingDirection!]; } sibling!.red = parent.red; parent.red = false; sibling![siblingDirection]!.red = false; this.rotateNode(parent, direction); current = this.root; parent = null; } } } if (current) current.red = false; }
/** * Adds the value to the binary search tree if it does not already exist in it. * Returns true if successful. */ override insert(value: T): boolean { let node = this.insertNode(RedBlackNode, value) as (RedBlackNode<T> | null); if (node) { while (node.parent?.red) { let parent: RedBlackNode<T> = node.parent!; const parentDirection: Direction = parent.directionFromParent()!; const uncleDirection: Direction = parentDirection === "right" ? "left" : "right"; const uncle: RedBlackNode<T> | null = parent.parent![uncleDirection] ?? null;
if (uncle?.red) { parent.red = false; uncle.red = false; parent.parent!.red = true; node = parent.parent!; } else { if (node === parent[uncleDirection]) { node = parent; this.rotateNode(node, parentDirection); parent = node.parent!; } parent.red = false; parent.parent!.red = true; this.rotateNode(parent.parent!, uncleDirection); } } this.root!.red = false; } return !!node; }
/** * Removes node value from the binary search tree if found. * Returns true if found and removed. */ override remove(value: T): boolean { const node = this.findNode(value) as (RedBlackNode<T> | null);
if (!node) { return false; }
const removedNode = this.removeNode(node) as ( | RedBlackNode<T> | null );
if (removedNode && !removedNode.red) { this.removeFixup( removedNode.parent, removedNode.left ?? removedNode.right, ); }
return true; }}