|
|
@@ -0,0 +1,407 @@
|
|
|
+/**
|
|
|
+ * Copyright (c) 2022 mol* contributors, licensed under MIT, See LICENSE file for more info.
|
|
|
+ *
|
|
|
+ * @author Gianluca Tomasello <giagitom@gmail.com>
|
|
|
+ *
|
|
|
+ * Adapted from https://github.com/gwtw/ts-fibonacci-heap, Copyright (c) 2014 Daniel Imms, MIT
|
|
|
+ */
|
|
|
+
|
|
|
+interface INode<K, V> {
|
|
|
+ key: K;
|
|
|
+ value?: V;
|
|
|
+}
|
|
|
+
|
|
|
+type CompareFunction<K, V> = (a: INode<K, V>, b: INode<K, V>) => number;
|
|
|
+
|
|
|
+class Node<K, V> implements INode<K, V> {
|
|
|
+ public key: K;
|
|
|
+ public value: V | undefined;
|
|
|
+ public prev: Node<K, V>;
|
|
|
+ public next: Node<K, V>;
|
|
|
+ public parent: Node<K, V> | null = null;
|
|
|
+ public child: Node<K, V> | null = null;
|
|
|
+
|
|
|
+ public degree: number = 0;
|
|
|
+ public isMarked: boolean = false;
|
|
|
+
|
|
|
+ constructor(key: K, value?: V) {
|
|
|
+ this.key = key;
|
|
|
+ this.value = value;
|
|
|
+ this.prev = this;
|
|
|
+ this.next = this;
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+class NodeListIterator<K, V> {
|
|
|
+ private _index: number;
|
|
|
+ private _items: Node<K, V>[];
|
|
|
+ private _len: number;
|
|
|
+ /**
|
|
|
+ * Creates an Iterator used to simplify the consolidate() method. It works by
|
|
|
+ * making a shallow copy of the nodes in the root list and iterating over the
|
|
|
+ * shallow copy instead of the source as the source will be modified.
|
|
|
+ * @param start A node from the root list.
|
|
|
+ */
|
|
|
+ constructor(start?: Node<K, V>) {
|
|
|
+ this._index = -1;
|
|
|
+ this._items = [];
|
|
|
+ this._len = 0;
|
|
|
+ if (start) {
|
|
|
+ let current = start, l = 0;
|
|
|
+ do {
|
|
|
+ this._items[l++] = current;
|
|
|
+ current = current.next;
|
|
|
+ } while (start !== current);
|
|
|
+ this._len = l;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * @return Whether there is a next node in the iterator.
|
|
|
+ */
|
|
|
+ public hasNext(): boolean {
|
|
|
+ return this._index < this._len - 1;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * @return The next node.
|
|
|
+ */
|
|
|
+ public next(): Node<K, V> {
|
|
|
+ return this._items[++this._index];
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * @return Resets iterator to reuse it.
|
|
|
+ */
|
|
|
+ public reset(start: Node<K, V>) {
|
|
|
+ this._index = -1;
|
|
|
+ this._len = 0;
|
|
|
+ let current = start, l = 0;
|
|
|
+ do {
|
|
|
+ this._items[l++] = current;
|
|
|
+ current = current.next;
|
|
|
+ } while (start !== current);
|
|
|
+ this._len = l;
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+const tmpIt = new NodeListIterator<any, any>();
|
|
|
+/**
|
|
|
+ * A Fibonacci heap data structure with a key and optional value.
|
|
|
+*/
|
|
|
+export class FibonacciHeap<K, V> {
|
|
|
+ private _minNode: Node<K, V> | null = null;
|
|
|
+ private _nodeCount: number = 0;
|
|
|
+ private _compare: CompareFunction<K, V>;
|
|
|
+
|
|
|
+ constructor(
|
|
|
+ compare?: CompareFunction<K, V>
|
|
|
+ ) {
|
|
|
+ this._compare = compare ? compare : this._defaultCompare;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Clears the heap's data, making it an empty heap.
|
|
|
+ */
|
|
|
+ public clear(): void {
|
|
|
+ this._minNode = null;
|
|
|
+ this._nodeCount = 0;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Decreases a key of a node.
|
|
|
+ * @param node The node to decrease the key of.
|
|
|
+ * @param newKey The new key to assign to the node.
|
|
|
+ */
|
|
|
+ public decreaseKey(node: Node<K, V>, newKey: K): void {
|
|
|
+ if (!node) {
|
|
|
+ throw new Error('Cannot decrease key of non-existent node');
|
|
|
+ }
|
|
|
+ if (this._compare({ key: newKey }, { key: node.key }) > 0) {
|
|
|
+ throw new Error('New key is larger than old key');
|
|
|
+ }
|
|
|
+
|
|
|
+ node.key = newKey;
|
|
|
+ const parent = node.parent;
|
|
|
+ if (parent && this._compare(node, parent) < 0) {
|
|
|
+ this._cut(node, parent, <Node<K, V>> this._minNode);
|
|
|
+ this._cascadingCut(parent, <Node<K, V>> this._minNode);
|
|
|
+ }
|
|
|
+ if (this._compare(node, <Node<K, V>> this._minNode) < 0) {
|
|
|
+ this._minNode = node;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Deletes a node.
|
|
|
+ * @param node The node to delete.
|
|
|
+ */
|
|
|
+ public delete(node: Node<K, V>): void {
|
|
|
+ // This is a special implementation of decreaseKey that sets the argument to
|
|
|
+ // the minimum value. This is necessary to make generic keys work, since there
|
|
|
+ // is no MIN_VALUE constant for generic types.
|
|
|
+ const parent = node.parent;
|
|
|
+ if (parent) {
|
|
|
+ this._cut(node, parent, <Node<K, V>> this._minNode);
|
|
|
+ this._cascadingCut(parent, <Node<K, V>> this._minNode);
|
|
|
+ }
|
|
|
+ this._minNode = node;
|
|
|
+
|
|
|
+ this.extractMinimum();
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Extracts and returns the minimum node from the heap.
|
|
|
+ * @return The heap's minimum node or null if the heap is empty.
|
|
|
+ */
|
|
|
+ public extractMinimum(): Node<K, V> | null {
|
|
|
+ const extractedMin = this._minNode;
|
|
|
+ if (extractedMin) {
|
|
|
+ // Set parent to null for the minimum's children
|
|
|
+ if (extractedMin.child) {
|
|
|
+ let child = extractedMin.child;
|
|
|
+ do {
|
|
|
+ child.parent = null;
|
|
|
+ child = child.next;
|
|
|
+ } while (child !== extractedMin.child);
|
|
|
+ }
|
|
|
+
|
|
|
+ let nextInRootList = null;
|
|
|
+ if (extractedMin.next !== extractedMin) {
|
|
|
+ nextInRootList = extractedMin.next;
|
|
|
+ }
|
|
|
+ // Remove min from root list
|
|
|
+ this._removeNodeFromList(extractedMin);
|
|
|
+ this._nodeCount--;
|
|
|
+
|
|
|
+ // Merge the children of the minimum node with the root list
|
|
|
+ this._minNode = this._mergeLists(nextInRootList, extractedMin.child);
|
|
|
+ if (this._minNode) {
|
|
|
+ this._minNode = this._consolidate(this._minNode);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ return extractedMin;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Returns the minimum node from the heap.
|
|
|
+ * @return The heap's minimum node or null if the heap is empty.
|
|
|
+ */
|
|
|
+ public findMinimum(): Node<K, V> | null {
|
|
|
+ return this._minNode;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Inserts a new key-value pair into the heap.
|
|
|
+ * @param key The key to insert.
|
|
|
+ * @param value The value to insert.
|
|
|
+ * @return node The inserted node.
|
|
|
+ */
|
|
|
+ public insert(key: K, value?: V): Node<K, V> {
|
|
|
+ const node = new Node(key, value);
|
|
|
+ this._minNode = this._mergeLists(this._minNode, node);
|
|
|
+ this._nodeCount++;
|
|
|
+ return node;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * @return Whether the heap is empty.
|
|
|
+ */
|
|
|
+ public isEmpty(): boolean {
|
|
|
+ return this._minNode === null;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * @return The size of the heap.
|
|
|
+ */
|
|
|
+ public size(): number {
|
|
|
+ if (this._minNode === null) {
|
|
|
+ return 0;
|
|
|
+ }
|
|
|
+ return this._getNodeListSize(this._minNode);
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Joins another heap to this heap.
|
|
|
+ * @param other The other heap.
|
|
|
+ */
|
|
|
+ public union(other: FibonacciHeap<K, V>): void {
|
|
|
+ this._minNode = this._mergeLists(this._minNode, other._minNode);
|
|
|
+ this._nodeCount += other._nodeCount;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Compares two nodes with each other.
|
|
|
+ * @param a The first key to compare.
|
|
|
+ * @param b The second key to compare.
|
|
|
+ * @return -1, 0 or 1 if a < b, a == b or a > b respectively.
|
|
|
+ */
|
|
|
+ private _defaultCompare(a: INode<K, V>, b: INode<K, V>): number {
|
|
|
+ if (a.key > b.key) {
|
|
|
+ return 1;
|
|
|
+ }
|
|
|
+ if (a.key < b.key) {
|
|
|
+ return -1;
|
|
|
+ }
|
|
|
+ return 0;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Cut the link between a node and its parent, moving the node to the root list.
|
|
|
+ * @param node The node being cut.
|
|
|
+ * @param parent The parent of the node being cut.
|
|
|
+ * @param minNode The minimum node in the root list.
|
|
|
+ * @return The heap's new minimum node.
|
|
|
+ */
|
|
|
+ private _cut(node: Node<K, V>, parent: Node<K, V>, minNode: Node<K, V>): Node<K, V> | null {
|
|
|
+ node.parent = null;
|
|
|
+ parent.degree--;
|
|
|
+ if (node.next === node) {
|
|
|
+ parent.child = null;
|
|
|
+ } else {
|
|
|
+ parent.child = node.next;
|
|
|
+ }
|
|
|
+ this._removeNodeFromList(node);
|
|
|
+ const newMinNode = this._mergeLists(minNode, node);
|
|
|
+ node.isMarked = false;
|
|
|
+ return newMinNode;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Perform a cascading cut on a node; mark the node if it is not marked,
|
|
|
+ * otherwise cut the node and perform a cascading cut on its parent.
|
|
|
+ * @param node The node being considered to be cut.
|
|
|
+ * @param minNode The minimum node in the root list.
|
|
|
+ * @return The heap's new minimum node.
|
|
|
+ */
|
|
|
+ private _cascadingCut(node: Node<K, V>, minNode: Node<K, V> | null): Node<K, V> | null {
|
|
|
+ const parent = node.parent;
|
|
|
+ if (parent) {
|
|
|
+ if (node.isMarked) {
|
|
|
+ minNode = this._cut(node, parent, <Node<K, V>>minNode);
|
|
|
+ minNode = this._cascadingCut(parent, minNode);
|
|
|
+ } else {
|
|
|
+ node.isMarked = true;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ return minNode;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Merge all trees of the same order together until there are no two trees of
|
|
|
+ * the same order.
|
|
|
+ * @param minNode The current minimum node.
|
|
|
+ * @return The new minimum node.
|
|
|
+ */
|
|
|
+ private _consolidate(minNode: Node<K, V>): Node<K, V> | null {
|
|
|
+
|
|
|
+ const aux = [];
|
|
|
+ tmpIt.reset(minNode);
|
|
|
+ while (tmpIt.hasNext()) {
|
|
|
+ let current = tmpIt.next();
|
|
|
+
|
|
|
+ // If there exists another node with the same degree, merge them
|
|
|
+ let auxCurrent = aux[current.degree];
|
|
|
+ while (auxCurrent) {
|
|
|
+ if (this._compare(current, auxCurrent) > 0) {
|
|
|
+ const temp = current;
|
|
|
+ current = auxCurrent;
|
|
|
+ auxCurrent = temp;
|
|
|
+ }
|
|
|
+ this._linkHeaps(auxCurrent, current);
|
|
|
+ aux[current.degree] = null;
|
|
|
+ current.degree++;
|
|
|
+ auxCurrent = aux[current.degree];
|
|
|
+ }
|
|
|
+
|
|
|
+ aux[current.degree] = current;
|
|
|
+ }
|
|
|
+
|
|
|
+ let newMinNode = null;
|
|
|
+ for (let i = 0; i < aux.length; i++) {
|
|
|
+ const node = aux[i];
|
|
|
+ if (node) {
|
|
|
+ // Remove siblings before merging
|
|
|
+ node.next = node;
|
|
|
+ node.prev = node;
|
|
|
+ newMinNode = this._mergeLists(newMinNode, node);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ return newMinNode;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Removes a node from a node list.
|
|
|
+ * @param node The node to remove.
|
|
|
+ */
|
|
|
+ private _removeNodeFromList(node: Node<K, V>): void {
|
|
|
+ const prev = node.prev;
|
|
|
+ const next = node.next;
|
|
|
+ prev.next = next;
|
|
|
+ next.prev = prev;
|
|
|
+ node.next = node;
|
|
|
+ node.prev = node;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Links two heaps of the same order together.
|
|
|
+ *
|
|
|
+ * @private
|
|
|
+ * @param max The heap with the larger root.
|
|
|
+ * @param min The heap with the smaller root.
|
|
|
+ */
|
|
|
+ private _linkHeaps(max: Node<K, V>, min: Node<K, V>): void {
|
|
|
+ this._removeNodeFromList(max);
|
|
|
+ min.child = this._mergeLists(max, min.child);
|
|
|
+ max.parent = min;
|
|
|
+ max.isMarked = false;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Merge two lists of nodes together.
|
|
|
+ *
|
|
|
+ * @private
|
|
|
+ * @param a The first list to merge.
|
|
|
+ * @param b The second list to merge.
|
|
|
+ * @return The new minimum node from the two lists.
|
|
|
+ */
|
|
|
+ private _mergeLists(a: Node<K, V> | null, b: Node<K, V> | null): Node<K, V> | null {
|
|
|
+ if (!a) {
|
|
|
+ if (!b) {
|
|
|
+ return null;
|
|
|
+ }
|
|
|
+ return b;
|
|
|
+ }
|
|
|
+ if (!b) {
|
|
|
+ return a;
|
|
|
+ }
|
|
|
+
|
|
|
+ const temp = a.next;
|
|
|
+ a.next = b.next;
|
|
|
+ a.next.prev = a;
|
|
|
+ b.next = temp;
|
|
|
+ b.next.prev = b;
|
|
|
+
|
|
|
+ return this._compare(a, b) < 0 ? a : b;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Gets the size of a node list.
|
|
|
+ * @param node A node within the node list.
|
|
|
+ * @return The size of the node list.
|
|
|
+ */
|
|
|
+ private _getNodeListSize(node: Node<K, V>): number {
|
|
|
+ let count = 0;
|
|
|
+ let current = node;
|
|
|
+
|
|
|
+ do {
|
|
|
+ count++;
|
|
|
+ if (current.child) {
|
|
|
+ count += this._getNodeListSize(current.child);
|
|
|
+ }
|
|
|
+ current = current.next;
|
|
|
+ } while (current !== node);
|
|
|
+
|
|
|
+ return count;
|
|
|
+ }
|
|
|
+}
|
Alexander Rose