undirected-graph-typed
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text/typescript
/**
* TreeMultiSet (ordered multiset) — a restricted, native-like API backed by RedBlackTree.
*
* Design goals:
* - No node exposure
* - Strict default comparator (number/string/Date), otherwise require comparator
* - Default iteration is expanded (each element yielded `count(x)` times)
* - `delete(x)` removes one occurrence by default
*/
import type { Comparator, TreeMultiSetOptions } from '../../types';
import { ERR, raise } from '../../common';
import { RedBlackTree } from './red-black-tree';
import { TreeSet } from './tree-set';
export class TreeMultiSet<K = any, R = K> implements Iterable<K> {
readonly #core: RedBlackTree<K, number>;
readonly #isDefaultComparator: boolean;
private _size = 0; // total occurrences (sumCounts)
/**
* Creates a new TreeMultiSet.
* @param elements - Initial elements to add, or raw elements if `toElementFn` is provided.
* @param options - Configuration options including optional `toElementFn` to transform raw elements.
* @remarks Time O(m log m), Space O(m) where m is the number of initial elements
* @example
* // Standard usage with elements
* const mset = new TreeMultiSet([1, 2, 2, 3]);
*
* // Using toElementFn to transform raw objects
* const items = [{ score: 100 }, { score: 200 }, { score: 100 }];
* const mset = new TreeMultiSet<number, Item>(items, { toElementFn: item => item.score });
*/
constructor(elements: Iterable<R> | Iterable<K> = [], options: TreeMultiSetOptions<K, R> = {}) {
const toElementFn = options.toElementFn;
const comparator = options.comparator ?? TreeSet.createDefaultComparator<K>();
this.#isDefaultComparator = options.comparator === undefined;
this.#core = new RedBlackTree<K, number>([], { comparator, isMapMode: options.isMapMode, enableOrderStatistic: options.enableOrderStatistic });
for (const item of elements) {
const k = toElementFn ? toElementFn(item as R) : (item as K);
this.add(k);
}
}
/**
* Validates the key against the default comparator rules.
* @remarks Time O(1), Space O(1)
*/
private _validateKey(key: K): void {
if (!this.#isDefaultComparator) return;
if (typeof key === 'number') {
if (Number.isNaN(key)) raise(TypeError, ERR.invalidNaN('TreeMultiSet'));
return;
}
if (typeof key === 'string') return;
if (key instanceof Date) {
if (Number.isNaN(key.getTime())) raise(TypeError, ERR.invalidDate('TreeMultiSet'));
return;
}
raise(TypeError, ERR.comparatorRequired('TreeMultiSet'));
}
/**
* Validates that count is a non-negative safe integer.
* @remarks Time O(1), Space O(1)
*/
private _validateCount(n: number): void {
if (!Number.isSafeInteger(n) || n < 0) raise(RangeError, ERR.invalidArgument('count must be a safe integer >= 0.', 'TreeMultiSet'));
}
/**
* Total occurrences (sumCounts).
* @remarks Time O(1), Space O(1)
*/
get size(): number {
return this._size;
}
/**
* Number of distinct keys.
* @remarks Time O(1), Space O(1)
* @example
* // Unique key count
* const ms = new TreeMultiSet<number>();
* ms.add(1, 3);
* ms.add(2, 2);
* console.log(ms.distinctSize); // 2;
*/
get distinctSize(): number {
return this.#core.size;
}
/**
* Whether the multiset is empty.
* @remarks Time O(1), Space O(1)
* @example
* // Check empty
* console.log(new TreeMultiSet().isEmpty()); // true;
*/
isEmpty(): boolean {
return this.size === 0;
}
/**
* Whether the multiset contains the given key.
* @remarks Time O(log n), Space O(1)
* @example
* // Check existence
* const ms = new TreeMultiSet<number>();
* ms.add(1);
* console.log(ms.has(1)); // true;
* console.log(ms.has(2)); // false;
*/
has(key: K): boolean {
this._validateKey(key);
return this.count(key) > 0;
}
/**
* Returns the count of occurrences for the given key.
* @remarks Time O(log n), Space O(1)
* @example
* // Get occurrence count
* const ms = new TreeMultiSet<number>();
* ms.add(1, 5);
* console.log(ms.count(1)); // 5;
*/
count(key: K): number {
this._validateKey(key);
return this.#core.get(key) ?? 0;
}
/**
* Add `n` occurrences of `key`.
* @returns True if the multiset changed.
* @remarks Time O(log n), Space O(1)
* @example
* // Add elements
* const ms = new TreeMultiSet<number>();
* ms.add(1);
* ms.add(1);
* ms.add(2);
* console.log(ms.count(1)); // 2;
* console.log(ms.size); // 3;
*/
add(key: K, n = 1): boolean {
this._validateKey(key);
this._validateCount(n);
if (n === 0) return false;
const old = this.#core.get(key) ?? 0;
const next = old + n;
this.#core.set(key, next);
this._size += n;
return true;
}
/**
* Set count for `key` to exactly `n`.
* @returns True if changed.
* @remarks Time O(log n), Space O(1)
* @example
* // Set occurrence count
* const ms = new TreeMultiSet<number>();
* ms.setCount(1, 3);
* console.log(ms.count(1)); // 3;
*/
setCount(key: K, n: number): boolean {
this._validateKey(key);
this._validateCount(n);
const old = this.#core.get(key) ?? 0;
if (old === n) return false;
if (n === 0) {
if (old !== 0) this.#core.delete(key);
} else {
this.#core.set(key, n);
}
this._size += n - old;
return true;
}
/**
* Delete `n` occurrences of `key` (default 1).
* @returns True if any occurrence was removed.
* @remarks Time O(log n), Space O(1)
* @example
* // Remove one occurrence
* const ms = new TreeMultiSet<number>();
* ms.add(1, 3);
* ms.delete(1);
* console.log(ms.count(1)); // 2;
*/
delete(key: K, n = 1): boolean {
this._validateKey(key);
this._validateCount(n);
if (n === 0) return false;
const old = this.#core.get(key) ?? 0;
if (old === 0) return false;
const removed = Math.min(old, n);
const next = old - removed;
if (next === 0) this.#core.delete(key);
else this.#core.set(key, next);
this._size -= removed;
return true;
}
/**
* Delete all occurrences of the given key.
* @returns True if any occurrence was removed.
* @remarks Time O(log n), Space O(1)
* @example
* // Remove all occurrences
* const ms = new TreeMultiSet<number>();
* ms.add(1, 3);
* ms.deleteAll(1);
* console.log(ms.has(1)); // false;
*/
deleteAll(key: K): boolean {
this._validateKey(key);
const old = this.#core.get(key) ?? 0;
if (old === 0) return false;
this.#core.delete(key);
this._size -= old;
return true;
}
/**
* Iterates over distinct keys (each key yielded once).
* @remarks Time O(n), Space O(1)
* @example
* // Iterate unique keys
* const ms = new TreeMultiSet<number>();
* ms.add(1, 2);
* ms.add(2);
* console.log([...ms.keysDistinct()]); // [1, 2];
*/
*keysDistinct(): IterableIterator<K> {
yield* this.#core.keys();
}
/**
* Iterates over entries as [key, count] pairs.
* @remarks Time O(n), Space O(1)
* @example
* // Iterate entries
* const ms = new TreeMultiSet<number>();
* ms.add(1, 2);
* console.log([...ms.entries()].length); // > 0;
*/
*entries(): IterableIterator<[K, number]> {
for (const [k, v] of this.#core) {
yield [k, v ?? 0];
}
}
/**
* Expanded iteration (default). Each key is yielded `count(key)` times.
* @remarks Time O(size), Space O(1) where size is total occurrences
*/
*[Symbol.iterator](): Iterator<K> {
for (const [k, c] of this.entries()) {
for (let i = 0; i < c; i++) yield k;
}
}
/**
* Iterate over all elements with multiplicity (Set-compatible, alias for `[Symbol.iterator]`).
* @remarks Each key is yielded `count(key)` times. Time O(size), Space O(1) per step.
* @example
* // Iterate with multiplicity
* const ms = new TreeMultiSet<number>();
* ms.add(1); ms.add(1); ms.add(2); ms.add(3); ms.add(3); ms.add(3);
* console.log([...ms.keys()]); // [1, 1, 2, 3, 3, 3];
*/
*keys(): IterableIterator<K> {
yield* this;
}
/**
* Iterate over all elements with multiplicity (Set-compatible, alias for `[Symbol.iterator]`).
* @remarks Each key is yielded `count(key)` times. Time O(size), Space O(1) per step.
* @example
* // Iterate with multiplicity
* const ms = new TreeMultiSet<number>();
* ms.add(5); ms.add(5); ms.add(10);
* console.log([...ms.values()]); // [5, 5, 10];
*/
*values(): IterableIterator<K> {
yield* this;
}
/**
* Returns an array with all elements (expanded).
* @remarks Time O(size), Space O(size)
* @example
* // All elements (with duplicates)
* const ms = new TreeMultiSet<number>();
* ms.add(1, 2);
* ms.add(2);
* console.log(ms.toArray()); // [1, 1, 2];
*/
toArray(): K[] {
return [...this];
}
/**
* Returns an array with distinct keys only.
* @remarks Time O(n), Space O(n)
* @example
* // Unique keys only
* const ms = new TreeMultiSet<number>();
* ms.add(1, 3);
* ms.add(2);
* console.log(ms.toDistinctArray()); // [1, 2];
*/
toDistinctArray(): K[] {
return [...this.keysDistinct()];
}
/**
* Returns an array of [key, count] entries.
* @remarks Time O(n), Space O(n)
* @example
* // Key-count pairs
* const ms = new TreeMultiSet<number>();
* ms.add(1, 2);
* ms.add(3);
* console.log(ms.toEntries()); // [[1, 2], [3, 1]];
*/
toEntries(): Array<[K, number]> {
return [...this.entries()];
}
/**
* Expose comparator for advanced usage/testing (read-only).
* @remarks Time O(1), Space O(1)
*/
get comparator(): Comparator<K> {
return this.#core.comparator;
}
// ━━━ clear ━━━
/**
* Remove all elements from the multiset.
* @remarks Time O(1), Space O(1)
* @example
* // Remove all
* const ms = new TreeMultiSet<number>();
* ms.add(1);
* ms.clear();
* console.log(ms.isEmpty()); // true;
*/
clear(): void {
this.#core.clear();
this._size = 0;
}
// ━━━ Navigable methods ━━━
/**
* Returns the smallest key, or undefined if empty.
* @remarks Time O(log n), Space O(1)
* @example
* // Smallest element
* const ms = new TreeMultiSet<number>();
* ms.add(3);
* ms.add(1);
* console.log(ms.first()); // 1;
*/
first(): K | undefined {
return this.#core.getLeftMost();
}
/**
* Returns the largest key, or undefined if empty.
* @remarks Time O(log n), Space O(1)
* @example
* // Largest element
* const ms = new TreeMultiSet<number>();
* ms.add(1);
* ms.add(3);
* console.log(ms.last()); // 3;
*/
last(): K | undefined {
return this.#core.getRightMost();
}
/**
* Removes all occurrences of the smallest key and returns it.
* @remarks Time O(log n), Space O(1)
* @example
* // Remove and return smallest
* const ms = new TreeMultiSet<number>();
* ms.add(2);
* ms.add(1);
* console.log(ms.pollFirst()); // 1;
* console.log(ms.has(1)); // false;
*/
pollFirst(): K | undefined {
const key = this.first();
if (key === undefined) return undefined;
this.deleteAll(key);
return key;
}
/**
* Removes all occurrences of the largest key and returns it.
* @remarks Time O(log n), Space O(1)
* @example
* // Remove and return largest
* const ms = new TreeMultiSet<number>();
* ms.add(1);
* ms.add(3);
* console.log(ms.pollLast()); // 3;
*/
pollLast(): K | undefined {
const key = this.last();
if (key === undefined) return undefined;
this.deleteAll(key);
return key;
}
/**
* Returns the smallest key >= given key, or undefined.
* @remarks Time O(log n), Space O(1)
* @example
* // Least key ≥ target
* const ms = new TreeMultiSet<number>();
* ms.add(10);
* ms.add(20);
* ms.add(30);
* console.log(ms.ceiling(15)); // 20;
*/
ceiling(key: K): K | undefined {
this._validateKey(key);
return this.#core.ceiling(key);
}
/**
* Returns the largest key <= given key, or undefined.
* @remarks Time O(log n), Space O(1)
* @example
* // Greatest key ≤ target
* const ms = new TreeMultiSet<number>();
* ms.add(10);
* ms.add(20);
* ms.add(30);
* console.log(ms.floor(25)); // 20;
*/
floor(key: K): K | undefined {
this._validateKey(key);
return this.#core.floor(key);
}
/**
* Returns the smallest key > given key, or undefined.
* @remarks Time O(log n), Space O(1)
* @example
* // Least key > target
* const ms = new TreeMultiSet<number>();
* ms.add(10);
* ms.add(20);
* console.log(ms.higher(10)); // 20;
*/
higher(key: K): K | undefined {
this._validateKey(key);
return this.#core.higher(key);
}
/**
* Returns the largest key < given key, or undefined.
* @remarks Time O(log n), Space O(1)
* @example
* // Greatest key < target
* const ms = new TreeMultiSet<number>();
* ms.add(10);
* ms.add(20);
* console.log(ms.lower(20)); // 10;
*/
lower(key: K): K | undefined {
this._validateKey(key);
return this.#core.lower(key);
}
// ━━━ Functional methods ━━━
/**
* Iterates over distinct keys with their counts.
* @remarks Time O(n), Space O(1)
* @example
* // Iterate
* const ms = new TreeMultiSet<number>();
* ms.add(1, 2);
* ms.add(2);
* const pairs: [number, number][] = [];
* ms.forEach((k, c) => pairs.push([k, c]));
* console.log(pairs); // [[1, 2], [2, 1]];
*/
forEach(callback: (key: K, count: number) => void): void {
for (const [k, c] of this.entries()) {
callback(k, c);
}
}
/**
* Creates a new TreeMultiSet with entries that match the predicate.
* @remarks Time O(n log n), Space O(n)
* @example
* // Filter
* const ms = new TreeMultiSet<number>();
* ms.add(1, 3);
* ms.add(2, 1);
* ms.add(3, 2);
* const filtered = ms.filter((k, c) => c > 1);
* console.log([...filtered.keysDistinct()]); // [1, 3];
*/
filter(predicate: (key: K, count: number) => boolean): TreeMultiSet<K> {
const result = new TreeMultiSet<K>([], {
comparator: this.#isDefaultComparator ? undefined : this.comparator,
isMapMode: this.#core.isMapMode
});
for (const [k, c] of this.entries()) {
if (predicate(k, c)) {
result.add(k, c);
}
}
return result;
}
/**
* Reduces the multiset to a single value.
* @remarks Time O(n), Space O(1)
* @example
* // Aggregate
* const ms = new TreeMultiSet<number>();
* ms.add(1, 2);
* ms.add(2, 3);
* const sum = ms.reduce((acc, k, c) => acc + k * c, 0);
* console.log(sum); // 8;
*/
reduce<U>(callback: (accumulator: U, key: K, count: number) => U, initialValue: U): U {
let acc = initialValue;
for (const [k, c] of this.entries()) {
acc = callback(acc, k, c);
}
return acc;
}
/**
* Maps keys and counts to a new TreeMultiSet.
* When multiple keys map to the same new key, counts are merged (added).
* @remarks Time O(n log n), Space O(n)
* @example
* // Transform
* const ms = new TreeMultiSet<number>();
* ms.add(1, 2);
* ms.add(2, 3);
* const doubled = ms.map((k, c) => [k * 10, c] as [number, number]);
* console.log([...doubled.keysDistinct()]); // [10, 20];
*/
map<K2>(
mapper: (key: K, count: number) => [K2, number],
options?: { comparator?: Comparator<K2> }
): TreeMultiSet<K2> {
const result = new TreeMultiSet<K2>([], {
comparator: options?.comparator,
isMapMode: this.#core.isMapMode
});
for (const [k, c] of this.entries()) {
const [newKey, newCount] = mapper(k, c);
result.add(newKey, newCount);
}
return result;
}
/**
* Creates an independent copy of this multiset.
* @remarks Time O(n log n), Space O(n)
* @example
* // Order-statistic on BST
* const tree = new TreeMultiSet<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;
*/
// ─── Order-Statistic Methods ───────────────────────────
getByRank(k: number): K | undefined {
return this.#core.getByRank(k);
}
/**
* Get the rank of a key in sorted order
* @example
* // Get the rank of a key in sorted order
* const tree = new TreeMultiSet<number>(
* [10, 20, 30, 40, 50],
* { enableOrderStatistic: true }
* );
* console.log(tree.getRank(10)); // 0; // smallest → rank 0
* console.log(tree.getRank(30)); // 2; // 2 elements before 30 in tree order
* console.log(tree.getRank(50)); // 4; // largest → rank 4
* console.log(tree.getRank(25)); // 2;
*/
getRank(key: K): number {
return this.#core.getRank(key);
}
/**
* Get elements by rank range
* @example
* // Pagination by position in tree order
* const tree = new TreeMultiSet<number>(
* [10, 20, 30, 40, 50, 60, 70, 80, 90],
* { enableOrderStatistic: true }
* );
* const pageSize = 3;
*
* // Page 1
* console.log(tree.rangeByRank(0, pageSize - 1)); // [10, 20, 30];
* // Page 2
* console.log(tree.rangeByRank(pageSize, 2 * pageSize - 1)); // [40, 50, 60];
* // Page 3
* console.log(tree.rangeByRank(2 * pageSize, 3 * pageSize - 1)); // [70, 80, 90];
*/
rangeByRank(start: number, end: number): K[] {
return this.#core.rangeByRank(start, end).filter((k): k is K => k !== undefined);
}
/**
* Deep copy
* @example
* // Deep clone
* const ms = new TreeMultiSet<number>();
* ms.add(1, 3);
* const copy = ms.clone();
* copy.deleteAll(1);
* console.log(ms.has(1)); // true;
*/
clone(): TreeMultiSet<K> {
const result = new TreeMultiSet<K>([], {
comparator: this.#isDefaultComparator ? undefined : this.comparator,
isMapMode: this.#core.isMapMode
});
for (const [k, c] of this.entries()) {
result.add(k, c);
}
return result;
}
// ━━━ Tree utilities ━━━
/**
* Returns keys within the given range.
* @remarks Time O(log n + k), Space O(k) where k is result size
* @example
* // Find in range
* const ms = new TreeMultiSet<number>();
* ms.add(10);
* ms.add(20);
* ms.add(30);
* const result = ms.rangeSearch([15, 25]);
* console.log(result.length); // 1;
*/
rangeSearch<C extends (key: K) => any>(
range: [K, K],
callback?: C
): (C extends undefined ? K : ReturnType<C>)[] {
const cb = callback ?? ((k: K) => k);
return this.#core.rangeSearch(range, node => cb(node.key));
}
/**
* Prints the internal tree structure (for debugging).
* @remarks Time O(n), Space O(n)
* @example
* // Display
* const ms = new TreeMultiSet<number>();
* ms.add(1);
* expect(() => ms.print()).not.toThrow();
*/
print(): void {
this.#core.print();
}
}