Ogoun
5 months ago
parent
aff5c617c5
commit
accc9d0e05
@ -0,0 +1,877 @@
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class GraphEdge {
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/**
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* @param {GraphVertex} startVertex
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* @param {GraphVertex} endVertex
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* @param {number} [weight=1]
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*/
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constructor(startVertex, endVertex, weight = 0) {
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this.startVertex = startVertex;
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this.endVertex = endVertex;
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this.weight = weight;
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}
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/**
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* @return {string}
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*/
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getKey() {
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const startVertexKey = this.startVertex.getKey();
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const endVertexKey = this.endVertex.getKey();
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return `${startVertexKey}_${endVertexKey}`;
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}
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/**
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* @return {GraphEdge}
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*/
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reverse() {
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const tmp = this.startVertex;
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this.startVertex = this.endVertex;
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this.endVertex = tmp;
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return this;
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}
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/**
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* @return {string}
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*/
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toString() {
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return this.getKey();
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}
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}
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class Comparator {
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/**
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* Constructor.
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* @param {function(a: *, b: *)} [compareFunction] - It may be custom compare function that, let's
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* say may compare custom objects together.
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*/
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constructor(compareFunction) {
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this.compare = compareFunction || Comparator.defaultCompareFunction;
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}
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/**
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* Default comparison function. It just assumes that "a" and "b" are strings or numbers.
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* @param {(string|number)} a
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* @param {(string|number)} b
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* @returns {number}
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*/
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static defaultCompareFunction(a, b) {
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if (a === b) {
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return 0;
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}
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return a < b ? -1 : 1;
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}
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/**
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* Checks if two variables are equal.
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* @param {*} a
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* @param {*} b
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* @return {boolean}
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*/
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equal(a, b) {
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return this.compare(a, b) === 0;
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}
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/**
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* Checks if variable "a" is less than "b".
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* @param {*} a
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* @param {*} b
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* @return {boolean}
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*/
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lessThan(a, b) {
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return this.compare(a, b) < 0;
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}
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/**
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* Checks if variable "a" is greater than "b".
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* @param {*} a
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* @param {*} b
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* @return {boolean}
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*/
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greaterThan(a, b) {
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return this.compare(a, b) > 0;
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}
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/**
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* Checks if variable "a" is less than or equal to "b".
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* @param {*} a
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* @param {*} b
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* @return {boolean}
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*/
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lessThanOrEqual(a, b) {
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return this.lessThan(a, b) || this.equal(a, b);
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}
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/**
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* Checks if variable "a" is greater than or equal to "b".
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* @param {*} a
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* @param {*} b
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* @return {boolean}
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*/
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greaterThanOrEqual(a, b) {
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return this.greaterThan(a, b) || this.equal(a, b);
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}
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/**
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* Reverses the comparison order.
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*/
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reverse() {
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const compareOriginal = this.compare;
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this.compare = (a, b) => compareOriginal(b, a);
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}
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}
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class LinkedListNode {
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constructor(value, next = null) {
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this.value = value;
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this.next = next;
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}
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toString(callback) {
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return callback ? callback(this.value) : `${this.value}`;
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}
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}
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class LinkedList {
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/**
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* @param {Function} [comparatorFunction]
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*/
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constructor(comparatorFunction) {
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/** @var LinkedListNode */
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this.head = null;
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/** @var LinkedListNode */
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this.tail = null;
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this.compare = new Comparator(comparatorFunction);
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}
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/**
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* @param {*} value
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* @return {LinkedList}
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*/
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prepend(value) {
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// Make new node to be a head.
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const newNode = new LinkedListNode(value, this.head);
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this.head = newNode;
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// If there is no tail yet let's make new node a tail.
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if (!this.tail) {
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this.tail = newNode;
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}
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return this;
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}
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/**
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* @param {*} value
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* @return {LinkedList}
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*/
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append(value) {
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const newNode = new LinkedListNode(value);
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// If there is no head yet let's make new node a head.
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if (!this.head) {
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this.head = newNode;
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this.tail = newNode;
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return this;
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}
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// Attach new node to the end of linked list.
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this.tail.next = newNode;
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this.tail = newNode;
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return this;
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}
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/**
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* @param {*} value
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* @param {number} index
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* @return {LinkedList}
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*/
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insert(value, rawIndex) {
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const index = rawIndex < 0 ? 0 : rawIndex;
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if (index === 0) {
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this.prepend(value);
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} else {
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let count = 1;
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let currentNode = this.head;
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const newNode = new LinkedListNode(value);
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while (currentNode) {
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if (count === index) break;
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currentNode = currentNode.next;
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count += 1;
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}
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if (currentNode) {
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newNode.next = currentNode.next;
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currentNode.next = newNode;
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} else {
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if (this.tail) {
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this.tail.next = newNode;
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this.tail = newNode;
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} else {
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this.head = newNode;
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this.tail = newNode;
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}
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}
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}
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return this;
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}
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/**
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* @param {*} value
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* @return {LinkedListNode}
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*/
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delete(value) {
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if (!this.head) {
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return null;
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}
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let deletedNode = null;
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// If the head must be deleted then make next node that is different
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// from the head to be a new head.
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while (this.head && this.compare.equal(this.head.value, value)) {
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deletedNode = this.head;
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this.head = this.head.next;
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}
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let currentNode = this.head;
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if (currentNode !== null) {
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// If next node must be deleted then make next node to be a next next one.
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while (currentNode.next) {
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if (this.compare.equal(currentNode.next.value, value)) {
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deletedNode = currentNode.next;
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currentNode.next = currentNode.next.next;
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} else {
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currentNode = currentNode.next;
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}
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}
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}
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// Check if tail must be deleted.
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if (this.compare.equal(this.tail.value, value)) {
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this.tail = currentNode;
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}
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return deletedNode;
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}
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/**
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* @param {Object} findParams
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* @param {*} findParams.value
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* @param {function} [findParams.callback]
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* @return {LinkedListNode}
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*/
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find({
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value = undefined,
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callback = undefined
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}) {
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if (!this.head) {
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return null;
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}
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let currentNode = this.head;
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while (currentNode) {
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// If callback is specified then try to find node by callback.
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if (callback && callback(currentNode.value)) {
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return currentNode;
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}
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// If value is specified then try to compare by value..
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if (value !== undefined && this.compare.equal(currentNode.value, value)) {
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return currentNode;
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}
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currentNode = currentNode.next;
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}
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return null;
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}
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/**
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* @return {LinkedListNode}
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*/
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deleteTail() {
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const deletedTail = this.tail;
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if (this.head === this.tail) {
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// There is only one node in linked list.
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this.head = null;
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this.tail = null;
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return deletedTail;
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}
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// If there are many nodes in linked list...
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// Rewind to the last node and delete "next" link for the node before the last one.
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let currentNode = this.head;
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while (currentNode.next) {
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if (!currentNode.next.next) {
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currentNode.next = null;
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} else {
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currentNode = currentNode.next;
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}
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}
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this.tail = currentNode;
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return deletedTail;
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}
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/**
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* @return {LinkedListNode}
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*/
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deleteHead() {
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if (!this.head) {
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return null;
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}
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const deletedHead = this.head;
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if (this.head.next) {
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this.head = this.head.next;
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} else {
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this.head = null;
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this.tail = null;
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}
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return deletedHead;
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}
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/**
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* @param {*[]} values - Array of values that need to be converted to linked list.
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* @return {LinkedList}
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*/
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fromArray(values) {
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values.forEach((value) => this.append(value));
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return this;
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}
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/**
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* @return {LinkedListNode[]}
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*/
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toArray() {
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const nodes = [];
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let currentNode = this.head;
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while (currentNode) {
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nodes.push(currentNode);
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currentNode = currentNode.next;
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}
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return nodes;
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}
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/**
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* @param {function} [callback]
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* @return {string}
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*/
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toString(callback) {
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return this.toArray().map((node) => node.toString(callback)).toString();
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}
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/**
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* Reverse a linked list.
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* @returns {LinkedList}
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*/
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reverse() {
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let currNode = this.head;
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let prevNode = null;
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let nextNode = null;
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while (currNode) {
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// Store next node.
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nextNode = currNode.next;
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// Change next node of the current node so it would link to previous node.
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currNode.next = prevNode;
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// Move prevNode and currNode nodes one step forward.
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prevNode = currNode;
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currNode = nextNode;
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}
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// Reset head and tail.
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this.tail = this.head;
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this.head = prevNode;
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return this;
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}
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}
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class GraphVertex {
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/**
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* @param {*} value
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*/
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constructor(value) {
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if (value === undefined) {
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throw new Error('Graph vertex must have a value');
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}
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/**
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* @param {GraphEdge} edgeA
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* @param {GraphEdge} edgeB
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*/
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const edgeComparator = (edgeA, edgeB) => {
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if (edgeA.getKey() === edgeB.getKey()) {
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return 0;
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}
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return edgeA.getKey() < edgeB.getKey() ? -1 : 1;
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};
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// Normally you would store string value like vertex name.
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// But generally it may be any object as well
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this.value = value;
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this.edges = new LinkedList(edgeComparator);
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}
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/**
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* @param {GraphEdge} edge
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* @returns {GraphVertex}
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*/
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addEdge(edge) {
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this.edges.append(edge);
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return this;
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}
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/**
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* @param {GraphEdge} edge
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*/
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deleteEdge(edge) {
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this.edges.delete(edge);
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}
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/**
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* @returns {GraphVertex[]}
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*/
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getNeighbors() {
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const edges = this.edges.toArray();
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/** @param {LinkedListNode} node */
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const neighborsConverter = (node) => {
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return node.value.startVertex === this ? node.value.endVertex : node.value.startVertex;
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};
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// Return either start or end vertex.
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// For undirected graphs it is possible that current vertex will be the end one.
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return edges.map(neighborsConverter);
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}
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/**
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* @return {GraphEdge[]}
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*/
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getEdges() {
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return this.edges.toArray().map((linkedListNode) => linkedListNode.value);
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}
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/**
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* @return {number}
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*/
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getDegree() {
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return this.edges.toArray().length;
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}
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/**
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* @param {GraphEdge} requiredEdge
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* @returns {boolean}
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*/
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hasEdge(requiredEdge) {
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const edgeNode = this.edges.find({
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callback: (edge) => edge === requiredEdge,
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});
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return !!edgeNode;
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}
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/**
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* @param {GraphVertex} vertex
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* @returns {boolean}
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*/
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hasNeighbor(vertex) {
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const vertexNode = this.edges.find({
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callback: (edge) => edge.startVertex === vertex || edge.endVertex === vertex,
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});
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return !!vertexNode;
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}
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/**
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* @param {GraphVertex} vertex
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* @returns {(GraphEdge|null)}
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*/
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findEdge(vertex) {
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const edgeFinder = (edge) => {
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return edge.startVertex === vertex || edge.endVertex === vertex;
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};
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const edge = this.edges.find({
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callback: edgeFinder
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});
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return edge ? edge.value : null;
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}
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/**
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* @returns {string}
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*/
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getKey() {
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return this.value;
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}
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/**
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* @return {GraphVertex}
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*/
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deleteAllEdges() {
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this.getEdges().forEach((edge) => this.deleteEdge(edge));
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return this;
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}
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/**
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* @param {function} [callback]
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* @returns {string}
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*/
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toString(callback) {
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return callback ? callback(this.value) : `${this.value}`;
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}
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}
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class Graph {
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/**
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* @param {boolean} isDirected
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*/
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constructor(isDirected = false) {
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this.vertices = {};
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this.edges = {};
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this.isDirected = isDirected;
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}
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/**
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* @param {GraphVertex} newVertex
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* @returns {Graph}
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*/
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addVertex(newVertex) {
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this.vertices[newVertex.getKey()] = newVertex;
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return this;
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}
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/**
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* @param {string} vertexKey
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* @returns GraphVertex
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*/
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getVertexByKey(vertexKey) {
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return this.vertices[vertexKey];
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}
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/**
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* @param {GraphVertex} vertex
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* @returns {GraphVertex[]}
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*/
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getNeighbors(vertex) {
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return vertex.getNeighbors();
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}
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/**
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* @return {GraphVertex[]}
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*/
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getAllVertices() {
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return Object.values(this.vertices);
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}
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/**
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* @return {GraphEdge[]}
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*/
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getAllEdges() {
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return Object.values(this.edges);
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}
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/**
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* @param {GraphEdge} edge
|
||||
* @returns {Graph}
|
||||
*/
|
||||
addEdge(edge) {
|
||||
// Try to find and end start vertices.
|
||||
let startVertex = this.getVertexByKey(edge.startVertex.getKey());
|
||||
let endVertex = this.getVertexByKey(edge.endVertex.getKey());
|
||||
|
||||
// Insert start vertex if it wasn't inserted.
|
||||
if (!startVertex) {
|
||||
this.addVertex(edge.startVertex);
|
||||
startVertex = this.getVertexByKey(edge.startVertex.getKey());
|
||||
}
|
||||
|
||||
// Insert end vertex if it wasn't inserted.
|
||||
if (!endVertex) {
|
||||
this.addVertex(edge.endVertex);
|
||||
endVertex = this.getVertexByKey(edge.endVertex.getKey());
|
||||
}
|
||||
|
||||
// Check if edge has been already added.
|
||||
if (this.edges[edge.getKey()]) {
|
||||
throw new Error('Edge has already been added before');
|
||||
} else {
|
||||
this.edges[edge.getKey()] = edge;
|
||||
}
|
||||
|
||||
// Add edge to the vertices.
|
||||
if (this.isDirected) {
|
||||
// If graph IS directed then add the edge only to start vertex.
|
||||
startVertex.addEdge(edge);
|
||||
} else {
|
||||
// If graph ISN'T directed then add the edge to both vertices.
|
||||
startVertex.addEdge(edge);
|
||||
endVertex.addEdge(edge);
|
||||
}
|
||||
|
||||
return this;
|
||||
}
|
||||
|
||||
/**
|
||||
* @param {GraphEdge} edge
|
||||
*/
|
||||
deleteEdge(edge) {
|
||||
// Delete edge from the list of edges.
|
||||
if (this.edges[edge.getKey()]) {
|
||||
delete this.edges[edge.getKey()];
|
||||
} else {
|
||||
throw new Error('Edge not found in graph');
|
||||
}
|
||||
|
||||
// Try to find and end start vertices and delete edge from them.
|
||||
const startVertex = this.getVertexByKey(edge.startVertex.getKey());
|
||||
const endVertex = this.getVertexByKey(edge.endVertex.getKey());
|
||||
|
||||
startVertex.deleteEdge(edge);
|
||||
endVertex.deleteEdge(edge);
|
||||
}
|
||||
|
||||
/**
|
||||
* @param {GraphVertex} startVertex
|
||||
* @param {GraphVertex} endVertex
|
||||
* @return {(GraphEdge|null)}
|
||||
*/
|
||||
findEdge(startVertex, endVertex) {
|
||||
const vertex = this.getVertexByKey(startVertex.getKey());
|
||||
|
||||
if (!vertex) {
|
||||
return null;
|
||||
}
|
||||
|
||||
return vertex.findEdge(endVertex);
|
||||
}
|
||||
|
||||
/**
|
||||
* @return {number}
|
||||
*/
|
||||
getWeight() {
|
||||
return this.getAllEdges().reduce((weight, graphEdge) => {
|
||||
return weight + graphEdge.weight;
|
||||
}, 0);
|
||||
}
|
||||
|
||||
/**
|
||||
* Reverse all the edges in directed graph.
|
||||
* @return {Graph}
|
||||
*/
|
||||
reverse() {
|
||||
/** @param {GraphEdge} edge */
|
||||
this.getAllEdges().forEach((edge) => {
|
||||
// Delete straight edge from graph and from vertices.
|
||||
this.deleteEdge(edge);
|
||||
|
||||
// Reverse the edge.
|
||||
edge.reverse();
|
||||
|
||||
// Add reversed edge back to the graph and its vertices.
|
||||
this.addEdge(edge);
|
||||
});
|
||||
|
||||
return this;
|
||||
}
|
||||
|
||||
/**
|
||||
* @return {object}
|
||||
*/
|
||||
getVerticesIndices() {
|
||||
const verticesIndices = {};
|
||||
this.getAllVertices().forEach((vertex, index) => {
|
||||
verticesIndices[vertex.getKey()] = index;
|
||||
});
|
||||
|
||||
return verticesIndices;
|
||||
}
|
||||
|
||||
/**
|
||||
* @return {*[][]}
|
||||
*/
|
||||
getAdjacencyMatrix() {
|
||||
const vertices = this.getAllVertices();
|
||||
const verticesIndices = this.getVerticesIndices();
|
||||
|
||||
// Init matrix with infinities meaning that there is no ways of
|
||||
// getting from one vertex to another yet.
|
||||
const adjacencyMatrix = Array(vertices.length).fill(null).map(() => {
|
||||
return Array(vertices.length).fill(Infinity);
|
||||
});
|
||||
|
||||
// Fill the columns.
|
||||
vertices.forEach((vertex, vertexIndex) => {
|
||||
vertex.getNeighbors().forEach((neighbor) => {
|
||||
const neighborIndex = verticesIndices[neighbor.getKey()];
|
||||
adjacencyMatrix[vertexIndex][neighborIndex] = this.findEdge(vertex, neighbor).weight;
|
||||
});
|
||||
});
|
||||
|
||||
return adjacencyMatrix;
|
||||
}
|
||||
|
||||
/**
|
||||
* @return {string}
|
||||
*/
|
||||
toString() {
|
||||
return Object.keys(this.vertices).toString();
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* @param {number[][]} adjacencyMatrix
|
||||
* @param {object} verticesIndices
|
||||
* @param {GraphVertex[]} cycle
|
||||
* @param {GraphVertex} vertexCandidate
|
||||
* @return {boolean}
|
||||
*/
|
||||
function isSafe(adjacencyMatrix, verticesIndices, cycle, vertexCandidate) {
|
||||
const endVertex = cycle[cycle.length - 1];
|
||||
|
||||
// Get end and candidate vertices indices in adjacency matrix.
|
||||
const candidateVertexAdjacencyIndex = verticesIndices[vertexCandidate.getKey()];
|
||||
const endVertexAdjacencyIndex = verticesIndices[endVertex.getKey()];
|
||||
|
||||
// Check if last vertex in the path and candidate vertex are adjacent.
|
||||
if (adjacencyMatrix[endVertexAdjacencyIndex][candidateVertexAdjacencyIndex] === Infinity) {
|
||||
return false;
|
||||
}
|
||||
|
||||
// Check if vertexCandidate is being added to the path for the first time.
|
||||
const candidateDuplicate = cycle.find((vertex) => vertex.getKey() === vertexCandidate.getKey());
|
||||
|
||||
return !candidateDuplicate;
|
||||
}
|
||||
|
||||
/**
|
||||
* @param {number[][]} adjacencyMatrix
|
||||
* @param {object} verticesIndices
|
||||
* @param {GraphVertex[]} cycle
|
||||
* @return {boolean}
|
||||
*/
|
||||
function isCycle(adjacencyMatrix, verticesIndices, cycle) {
|
||||
// Check if first and last vertices in hamiltonian path are adjacent.
|
||||
|
||||
// Get start and end vertices from the path.
|
||||
const startVertex = cycle[0];
|
||||
const endVertex = cycle[cycle.length - 1];
|
||||
|
||||
// Get start/end vertices indices in adjacency matrix.
|
||||
const startVertexAdjacencyIndex = verticesIndices[startVertex.getKey()];
|
||||
const endVertexAdjacencyIndex = verticesIndices[endVertex.getKey()];
|
||||
|
||||
// Check if we can go from end vertex to the start one.
|
||||
return adjacencyMatrix[endVertexAdjacencyIndex][startVertexAdjacencyIndex] !== Infinity;
|
||||
}
|
||||
|
||||
/**
|
||||
* @param {number[][]} adjacencyMatrix
|
||||
* @param {GraphVertex[]} vertices
|
||||
* @param {object} verticesIndices
|
||||
* @param {GraphVertex[][]} cycles
|
||||
* @param {GraphVertex[]} cycle
|
||||
*/
|
||||
function hamiltonianCycleRecursive({
|
||||
adjacencyMatrix,
|
||||
vertices,
|
||||
verticesIndices,
|
||||
cycles,
|
||||
cycle,
|
||||
}) {
|
||||
// Clone cycle in order to prevent it from modification by other DFS branches.
|
||||
const currentCycle = [...cycle].map((vertex) => new GraphVertex(vertex.value));
|
||||
|
||||
if (vertices.length === currentCycle.length) {
|
||||
// Hamiltonian path is found.
|
||||
// Now we need to check if it is cycle or not.
|
||||
if (isCycle(adjacencyMatrix, verticesIndices, currentCycle)) {
|
||||
// Another solution has been found. Save it.
|
||||
cycles.push(currentCycle);
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
for (let vertexIndex = 0; vertexIndex < vertices.length; vertexIndex += 1) {
|
||||
// Get vertex candidate that we will try to put into next path step and see if it fits.
|
||||
const vertexCandidate = vertices[vertexIndex];
|
||||
|
||||
// Check if it is safe to put vertex candidate to cycle.
|
||||
if (isSafe(adjacencyMatrix, verticesIndices, currentCycle, vertexCandidate)) {
|
||||
// Add candidate vertex to cycle path.
|
||||
currentCycle.push(vertexCandidate);
|
||||
|
||||
// Try to find other vertices in cycle.
|
||||
hamiltonianCycleRecursive({
|
||||
adjacencyMatrix,
|
||||
vertices,
|
||||
verticesIndices,
|
||||
cycles,
|
||||
cycle: currentCycle,
|
||||
});
|
||||
|
||||
// BACKTRACKING.
|
||||
// Remove candidate vertex from cycle path in order to try another one.
|
||||
currentCycle.pop();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* @param {Graph} graph
|
||||
* @return {GraphVertex[][]}
|
||||
*/
|
||||
function hamiltonianCycle(graph) {
|
||||
// Gather some information about the graph that we will need to during
|
||||
// the problem solving.
|
||||
const verticesIndices = graph.getVerticesIndices();
|
||||
const adjacencyMatrix = graph.getAdjacencyMatrix();
|
||||
const vertices = graph.getAllVertices();
|
||||
|
||||
// Define start vertex. We will always pick the first one
|
||||
// this it doesn't matter which vertex to pick in a cycle.
|
||||
// Every vertex is in a cycle so we can start from any of them.
|
||||
const startVertex = vertices[0];
|
||||
|
||||
// Init cycles array that will hold all solutions.
|
||||
const cycles = [];
|
||||
|
||||
// Init cycle array that will hold current cycle path.
|
||||
const cycle = [startVertex];
|
||||
|
||||
// Try to find cycles recursively in Depth First Search order.
|
||||
hamiltonianCycleRecursive({
|
||||
adjacencyMatrix,
|
||||
vertices,
|
||||
verticesIndices,
|
||||
cycles,
|
||||
cycle,
|
||||
});
|
||||
|
||||
// Return found cycles.
|
||||
return cycles;
|
||||
}
|
||||
Loading…
Reference in new issue