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I
|
// Copyright 2018-2025 the Deno authors. MIT license.
// This module is browser compatible.
import { ascend } from "./comparators.ts";
import { BinarySearchNode } from "./_binary_search_node.ts";
import { internals } from "./_binary_search_tree_internals.ts";
type Direction = "left" | "right";
/**
* An unbalanced binary search tree. The values are in ascending order by default,
* using JavaScript's built-in comparison operators to sort the values.
*
* For performance, it's recommended that you use a self-balancing binary search
* tree instead of this one unless you are extending this to create a
* self-balancing tree. See {@link RedBlackTree} for an example of how BinarySearchTree
* can be extended to create a self-balancing binary search tree.
*
* | Method | Average Case | Worst Case |
* | ------------- | ------------ | ---------- |
* | find(value) | O(log n) | O(n) |
* | insert(value) | O(log n) | O(n) |
* | remove(value) | O(log n) | O(n) |
* | min() | O(log n) | O(n) |
* | max() | O(log n) | O(n) |
*
* @example Usage
* ```ts
* import {
* BinarySearchTree,
* ascend,
* descend,
* } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const values = [3, 10, 13, 4, 6, 7, 1, 14];
* const tree = new BinarySearchTree<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 BinarySearchTree<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 BinarySearchTree<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",
* ]);
* ```
*
* @typeparam T The type of the values stored in the binary search tree.
*/
export class BinarySearchTree<T> implements Iterable<T> {
#root: BinarySearchNode<T> | null = null;
#size = 0;
#compare: (a: T, b: T) => number;
/**
* Construct an empty binary search tree.
*
* To create a binary search tree from an array like, an iterable object, or an
* existing binary search tree, use the {@link BinarySearchTree.from} method.
*
* @param compare A custom comparison function to sort the values in the tree.
* By default, the values are sorted in ascending order.
*/
constructor(compare: (a: T, b: T) => number = ascend) {
if (typeof compare !== "function") {
throw new TypeError(
"Cannot construct a BinarySearchTree: the 'compare' parameter is not a function, did you mean to call BinarySearchTree.from?",
);
}
this.#compare = compare;
}
static {
internals.getRoot = <T>(tree: BinarySearchTree<T>) => tree.#root;
internals.setRoot = <T>(
tree: BinarySearchTree<T>,
node: BinarySearchNode<T> | null,
) => {
tree.#root = node;
};
internals.getCompare = <T>(tree: BinarySearchTree<T>) => tree.#compare;
internals.findNode = <T>(
tree: BinarySearchTree<T>,
value: T,
): BinarySearchNode<T> | null => tree.#findNode(value);
internals.rotateNode = <T>(
tree: BinarySearchTree<T>,
node: BinarySearchNode<T>,
direction: Direction,
) => tree.#rotateNode(node, direction);
internals.insertNode = <T>(
tree: BinarySearchTree<T>,
Node: typeof BinarySearchNode,
value: T,
): BinarySearchNode<T> | null => tree.#insertNode(Node, value);
internals.removeNode = <T>(
tree: BinarySearchTree<T>,
node: BinarySearchNode<T>,
): BinarySearchNode<T> | null => tree.#removeNode(node);
internals.setSize = <T>(tree: BinarySearchTree<T>, size: number) =>
tree.#size = size;
}
/**
* Creates a new binary search tree from an array like, an iterable object,
* or an existing binary search tree.
*
* A custom comparison function can be provided to sort the values in a
* specific order. By default, the values are sorted in ascending order,
* unless a {@link BinarySearchTree} is passed, in which case the comparison
* function is copied from the input tree.
*
* @example Creating a binary search tree from an array like
* ```ts no-assert
* import { BinarySearchTree } from "@std/data-structures";
*
* const tree = BinarySearchTree.from<number>([42, 43, 41]);
* ```
*
* @example Creating a binary search tree from an iterable object
* ```ts no-assert
* import { BinarySearchTree } from "@std/data-structures";
*
* const tree = BinarySearchTree.from<number>((function*() {
* yield 42;
* yield 43;
* yield 41;
* })());
* ```
*
* @example Creating a binary search tree from an existing binary search tree
* ```ts no-assert
* import { BinarySearchTree } from "@std/data-structures";
*
* const tree = BinarySearchTree.from<number>([42, 43, 41]);
* const copy = BinarySearchTree.from(tree);
* ```
*
* @example Creating a binary search tree from an array like with a custom comparison function
* ```ts no-assert
* import { BinarySearchTree, descend } from "@std/data-structures";
*
* const tree = BinarySearchTree.from<number>(
* [42, 43, 41],
* { compare: descend }
* );
* ```
*
* @typeparam T The type of the values stored in the binary search tree.
* @param collection An array like, an iterable, or existing binary search tree.
* @param options An optional options object to customize the comparison function.
* @returns A new binary search tree created from the passed collection.
*/
static from<T>(
collection: ArrayLike<T> | Iterable<T> | BinarySearchTree<T>,
options?: {
compare?: (a: T, b: T) => number;
},
): BinarySearchTree<T>;
/**
* Create a new binary search tree from an array like, an iterable object, or
* an existing binary search tree.
*
* A custom mapping function can be provided to transform the values before
* inserting them into the tree.
*
* A custom comparison function can be provided to sort the values in a
* specific order. A custom mapping function can be provided to transform the
* values before inserting them into the tree. By default, the values are
* sorted in ascending order, unless a {@link BinarySearchTree} is passed, in
* which case the comparison function is copied from the input tree. The
* comparison operator is used to sort the values in the tree after mapping
* the values.
*
* @example Creating a binary search tree from an array like with a custom mapping function
* ```ts no-assert
* import { BinarySearchTree } from "@std/data-structures";
*
* const tree = BinarySearchTree.from<number, string>(
* [42, 43, 41],
* { map: (value) => value.toString() }
* );
* ```
*
* @typeparam T The type of the values in the passed collection.
* @typeparam U The type of the values stored in the binary search tree.
* @typeparam V The type of the `this` value when calling the mapping function. Defaults to `undefined`.
* @param collection An array like, an iterable, or existing binary search tree.
* @param options The options object to customize the mapping and comparison functions. The `thisArg` property can be used to set the `this` value when calling the mapping function.
* @returns A new binary search tree containing the mapped values from the passed collection.
*/
static from<T, U, V = undefined>(
collection: ArrayLike<T> | Iterable<T> | BinarySearchTree<T>,
options: {
compare?: (a: U, b: U) => number;
map: (value: T, index: number) => U;
thisArg?: V;
},
): BinarySearchTree<U>;
static from<T, U, V>(
collection: ArrayLike<T> | Iterable<T> | BinarySearchTree<T>,
options?: {
compare?: (a: U, b: U) => number;
map?: (value: T, index: number) => U;
thisArg?: V;
},
): BinarySearchTree<U> {
let result: BinarySearchTree<U>;
let unmappedValues: ArrayLike<T> | Iterable<T> = [];
if (collection instanceof BinarySearchTree) {
result = new BinarySearchTree(
options?.compare ??
(collection as unknown as BinarySearchTree<U>).#compare,
);
if (options?.compare || options?.map) {
unmappedValues = collection;
} else {
const nodes: BinarySearchNode<U>[] = [];
if (collection.#root) {
result.#root = BinarySearchNode.from(
collection.#root as unknown as BinarySearchNode<U>,
);
nodes.push(result.#root);
}
while (nodes.length) {
const node: BinarySearchNode<U> = nodes.pop()!;
const left: BinarySearchNode<U> | null = node.left
? BinarySearchNode.from(node.left)
: null;
const right: BinarySearchNode<U> | null = node.right
? BinarySearchNode.from(node.right)
: null;
if (left) {
left.parent = node;
nodes.push(left);
}
if (right) {
right.parent = node;
nodes.push(right);
}
}
result.#size = collection.#size;
}
} else {
result = (options?.compare
? new BinarySearchTree(options.compare)
: new BinarySearchTree()) as BinarySearchTree<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;
}
/**
* The count of values stored in the binary search tree.
*
* The complexity of this operation is O(1).
*
* @example Getting the size of the tree
* ```ts no-assert
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from<number>([42, 43, 41]);
*
* assertEquals(tree.size, 3);
* ```
*
* @returns The count of values stored in the binary search tree.
*/
get size(): number {
return this.#size;
}
#findNode(value: T): BinarySearchNode<T> | null {
let node: BinarySearchNode<T> | null = this.#root;
while (node) {
const order: number = this.#compare(value as T, node.value);
if (order === 0) break;
const direction: "left" | "right" = order < 0 ? "left" : "right";
node = node[direction];
}
return node;
}
#rotateNode(node: BinarySearchNode<T>, direction: Direction) {
const replacementDirection: Direction = direction === "left"
? "right"
: "left";
if (!node[replacementDirection]) {
throw new TypeError(
`Cannot rotate ${direction} without ${replacementDirection} child`,
);
}
const replacement: BinarySearchNode<T> = node[replacementDirection]!;
node[replacementDirection] = replacement[direction] ?? null;
if (replacement[direction]) replacement[direction]!.parent = node;
replacement.parent = node.parent;
if (node.parent) {
const parentDirection: Direction = node === node.parent[direction]
? direction
: replacementDirection;
node.parent[parentDirection] = replacement;
} else {
this.#root = replacement;
}
replacement[direction] = node;
node.parent = replacement;
}
#insertNode(
Node: typeof BinarySearchNode,
value: T,
): BinarySearchNode<T> | null {
if (!this.#root) {
this.#root = new Node(null, value);
this.#size++;
return this.#root;
} else {
let node: BinarySearchNode<T> = this.#root;
while (true) {
const order: number = this.#compare(value, node.value);
if (order === 0) break;
const direction: Direction = order < 0 ? "left" : "right";
if (node[direction]) {
node = node[direction]!;
} else {
node[direction] = new Node(node, value);
this.#size++;
return node[direction];
}
}
}
return null;
}
/** Removes the given node, and returns the node that was physically removed from the tree. */
#removeNode(
node: BinarySearchNode<T>,
): BinarySearchNode<T> | null {
/**
* The node to physically remove from the tree.
* Guaranteed to have at most one child.
*/
const flaggedNode: BinarySearchNode<T> | null = !node.left || !node.right
? node
: node.findSuccessorNode()!;
/** Replaces the flagged node. */
const replacementNode: BinarySearchNode<T> | null = flaggedNode.left ??
flaggedNode.right;
if (replacementNode) replacementNode.parent = flaggedNode.parent;
if (!flaggedNode.parent) {
this.#root = replacementNode;
} else {
flaggedNode.parent[flaggedNode.directionFromParent()!] = replacementNode;
}
if (flaggedNode !== node) {
/** Swaps values, in case value of the removed node is still needed by consumer. */
const swapValue = node.value;
node.value = flaggedNode.value;
flaggedNode.value = swapValue;
}
this.#size--;
return flaggedNode;
}
/**
* Add a value to the binary search tree if it does not already exist in the
* tree.
*
* The complexity of this operation is on average O(log n), where n is the
* number of values in the tree. In the worst case, the complexity is O(n).
*
* @example Inserting values into the tree
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = new BinarySearchTree<number>();
*
* assertEquals(tree.insert(42), true);
* assertEquals(tree.insert(42), false);
* ```
*
* @param value The value to insert into the binary search tree.
* @returns `true` if the value was inserted, `false` if the value already exists in the tree.
*/
insert(value: T): boolean {
return !!this.#insertNode(BinarySearchNode, value);
}
/**
* Remove a value from the binary search tree if it exists in the tree.
*
* The complexity of this operation is on average O(log n), where n is the
* number of values in the tree. In the worst case, the complexity is O(n).
*
* @example Removing values from the tree
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from<number>([42]);
*
* assertEquals(tree.remove(42), true);
* assertEquals(tree.remove(42), false);
* ```
*
* @param value The value to remove from the binary search tree.
* @returns `true` if the value was found and removed, `false` if the value was not found in the tree.
*/
remove(value: T): boolean {
const node: BinarySearchNode<T> | null = this.#findNode(value);
if (node) this.#removeNode(node);
return node !== null;
}
/**
* Check if a value exists in the binary search tree.
*
* The complexity of this operation depends on the underlying structure of the
* tree. Refer to the documentation of the structure itself for more details.
*
* @example Finding values in the tree
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from<number>([42]);
*
* assertEquals(tree.find(42), 42);
* assertEquals(tree.find(43), null);
* ```
*
* @param value The value to search for in the binary search tree.
* @returns The value if it was found, or null if not found.
*/
find(value: T): T | null {
return this.#findNode(value)?.value ?? null;
}
/**
* Retrieve the lowest (left most) value in the binary search tree, or null if
* the tree is empty.
*
* The complexity of this operation depends on the underlying structure of the
* tree. Refer to the documentation of the structure itself for more details.
*
* @example Finding the minimum value in the tree
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from<number>([42, 43, 41]);
*
* assertEquals(tree.min(), 41);
* ```
*
* @returns The minimum value in the binary search tree, or null if the tree is empty.
*/
min(): T | null {
return this.#root ? this.#root.findMinNode().value : null;
}
/**
* Retrieve the highest (right most) value in the binary search tree, or null
* if the tree is empty.
*
* The complexity of this operation depends on the underlying structure of the
* tree. Refer to the documentation of the structure itself for more details.
*
* @example Finding the maximum value in the tree
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from<number>([42, 43, 41]);
*
* assertEquals(tree.max(), 43);
* ```
*
* @returns The maximum value in the binary search tree, or null if the tree is empty.
*/
max(): T | null {
return this.#root ? this.#root.findMaxNode().value : null;
}
/**
* Remove all values from the binary search tree.
*
* The complexity of this operation is O(1).
*
* @example Clearing the tree
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from<number>([42, 43, 41]);
* tree.clear();
*
* assertEquals(tree.size, 0);
* assertEquals(tree.find(42), null);
* ```
*/
clear() {
this.#root = null;
this.#size = 0;
}
/**
* Check if the binary search tree is empty.
*
* The complexity of this operation is O(1).
*
* @example Checking if the tree is empty
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = new BinarySearchTree<number>();
*
* assertEquals(tree.isEmpty(), true);
*
* tree.insert(42);
*
* assertEquals(tree.isEmpty(), false);
* ```
*
* @returns `true` if the binary search tree is empty, `false` otherwise.
*/
isEmpty(): boolean {
return this.size === 0;
}
/**
* Create an iterator over this tree that traverses the tree in-order (LNR,
* Left-Node-Right).
*
* @example Using the in-order LNR iterator
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from([4, 1, 2, 5, 3]);
*
* assertEquals([...tree.lnrValues()], [1, 2, 3, 4, 5]);
* ```
*
* @returns An iterator that traverses the tree in-order (LNR).
*/
*lnrValues(): IterableIterator<T> {
const nodes: BinarySearchNode<T>[] = [];
let node: BinarySearchNode<T> | null = this.#root;
while (nodes.length || node) {
if (node) {
nodes.push(node);
node = node.left;
} else {
node = nodes.pop()!;
yield node.value;
node = node.right;
}
}
}
/**
* Create an iterator over this tree that traverses the tree in reverse
* in-order (RNL, Right-Node-Left).
*
* @example Using the reverse in-order RNL iterator
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from([4, 1, 2, 5, 3]);
* [...tree.rnlValues()] // 5, 4, 3, 2, 1
* ```
*
* @returns An iterator that traverses the tree in reverse in-order (RNL).
*/
*rnlValues(): IterableIterator<T> {
const nodes: BinarySearchNode<T>[] = [];
let node: BinarySearchNode<T> | null = this.#root;
while (nodes.length || node) {
if (node) {
nodes.push(node);
node = node.right;
} else {
node = nodes.pop()!;
yield node.value;
node = node.left;
}
}
}
/**
* Create an iterator over this tree that traverses the tree in pre-order (NLR,
* Node-Left-Right).
*
* @example Using the pre-order NLR iterator
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from([4, 1, 2, 5, 3]);
*
* assertEquals([...tree.nlrValues()], [4, 1, 2, 3, 5]);
* ```
*
* @returns An iterator that traverses the tree in pre-order (NLR).
*/
*nlrValues(): IterableIterator<T> {
const nodes: BinarySearchNode<T>[] = [];
if (this.#root) nodes.push(this.#root);
while (nodes.length) {
const node: BinarySearchNode<T> = nodes.pop()!;
yield node.value;
if (node.right) nodes.push(node.right);
if (node.left) nodes.push(node.left);
}
}
/**
* Create an iterator over this tree that traverses the tree in post-order (LRN,
* Left-Right-Node).
*
* @example Using the post-order LRN iterator
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from([4, 1, 2, 5, 3]);
*
* assertEquals([...tree.lrnValues()], [3, 2, 1, 5, 4]);
* ```
*
* @returns An iterator that traverses the tree in post-order (LRN).
*/
*lrnValues(): IterableIterator<T> {
const nodes: BinarySearchNode<T>[] = [];
let node: BinarySearchNode<T> | null = this.#root;
let lastNodeVisited: BinarySearchNode<T> | null = null;
while (nodes.length || node) {
if (node) {
nodes.push(node);
node = node.left;
} else {
const lastNode: BinarySearchNode<T> = nodes.at(-1)!;
if (lastNode.right && lastNode.right !== lastNodeVisited) {
node = lastNode.right;
} else {
yield lastNode.value;
lastNodeVisited = nodes.pop()!;
}
}
}
}
/**
* Create an iterator over this tree that traverses the tree in level-order (BFS,
* Breadth-First Search).
*
* @example Using the level-order BFS iterator
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from([4, 1, 2, 5, 3]);
*
* assertEquals([...tree.lvlValues()], [4, 1, 5, 2, 3]);
* ```
*
* @returns An iterator that traverses the tree in level-order (BFS).
*/
*lvlValues(): IterableIterator<T> {
const children: BinarySearchNode<T>[] = [];
let cursor: BinarySearchNode<T> | null = this.#root;
while (cursor) {
yield cursor.value;
if (cursor.left) children.push(cursor.left);
if (cursor.right) children.push(cursor.right);
cursor = children.shift() ?? null;
}
}
/**
* Create an iterator over this tree that traverses the tree in-order (LNR,
* Left-Node-Right).
*
* @example Using the in-order iterator
* ```ts
* import { BinarySearchTree } from "@std/data-structures";
* import { assertEquals } from "@std/assert";
*
* const tree = BinarySearchTree.from([4, 1, 2, 5, 3]);
*
* assertEquals([...tree], [1, 2, 3, 4, 5]);
* ```
*
* See {@link BinarySearchTree.prototype.lnrValues}.
*
* @returns An iterator that traverses the tree in-order (LNR).
*/
*[Symbol.iterator](): IterableIterator<T> {
yield* this.lnrValues();
}
}
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