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Commit 6a80dc7

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Added Prim's Algoritm (TheAlgorithms#227)
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‎Graphs/PrimMST.js‎

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// Priority Queue Helper functions
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function getParentPosition (position) {
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// Get the parent node of the current node
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return Math.floor((position - 1) / 2)
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}
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function getChildrenPosition (position) {
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// Get the children nodes of the current node
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return [2 * position + 1, 2 * position + 2]
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}
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class PriorityQueue {
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// Priority Queue class using Minimum Binary Heap
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constructor () {
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this._heap = []
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this.keys = {}
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}
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isEmpty () {
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// Checking if the heap is empty
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return this._heap.length === 0
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}
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push (key, priority) {
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// Adding element to the queue (equivalent to add)
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this._heap.push([key, priority])
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this.keys[key] = this._heap.length - 1
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this._shiftUp(this.keys[key])
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}
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pop () {
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// Removing the element with least priority (equivalent to extractMin)
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this._swap(0, this._heap.length - 1)
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const [key] = this._heap.pop()
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delete this.keys[key]
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this._shiftDown(0)
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return key
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}
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contains (key) {
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// Check if a given key is present in the queue
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return (key in this.keys)
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}
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update (key, priority) {
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// Update the priority of the given element (equivalent to decreaseKey)
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const currPos = this.keys[key]
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this._heap[currPos][1] = priority
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const parentPos = getParentPosition(currPos)
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const currPriority = this._heap[currPos][1]
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let parentPriority = Infinity
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if (parentPos >= 0) {
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parentPriority = this._heap[parentPos][1]
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}
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const [child1Pos, child2Pos] = getChildrenPosition(currPos)
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let [child1Priority, child2Priority] = [Infinity, Infinity]
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if (child1Pos < this._heap.length) {
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child1Priority = this._heap[child1Pos][1]
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}
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if (child2Pos < this._heap.length) {
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child2Priority = this._heap[child2Pos][1]
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}
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if (parentPos >= 0 && parentPriority > currPriority) {
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this._shiftUp(currPos)
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} else if (child2Pos < this._heap.length &&
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(child1Priority < currPriority || child2Priority < currPriority)) {
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this._shiftDown(currPos)
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}
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}
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_shiftUp (position) {
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// Helper function to shift up a node to proper position (equivalent to bubbleUp)
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let currPos = position
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let parentPos = getParentPosition(currPos)
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let currPriority = this._heap[currPos][1]
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let parentPriority = Infinity
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if (parentPos >= 0) {
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parentPriority = this._heap[parentPos][1]
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}
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while (parentPos >= 0 && parentPriority > currPriority) {
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this._swap(currPos, parentPos)
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currPos = parentPos
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parentPos = getParentPosition(currPos)
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currPriority = this._heap[currPos][1]
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try {
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parentPriority = this._heap[parentPos][1]
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} catch (error) {
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parentPriority = Infinity
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}
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}
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this.keys[this._heap[currPos][0]] = currPos
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}
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_shiftDown (position) {
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// Helper function to shift down a node to proper position (equivalent to bubbleDown)
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let currPos = position
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let [child1Pos, child2Pos] = getChildrenPosition(currPos)
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let [child1Priority, child2Priority] = [Infinity, Infinity]
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if (child1Pos < this._heap.length) {
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child1Priority = this._heap[child1Pos][1]
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}
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if (child2Pos < this._heap.length) {
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child2Priority = this._heap[child2Pos][1]
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}
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let currPriority
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try {
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currPriority = this._heap[currPos][1]
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} catch {
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return
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}
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while (child2Pos < this._heap.length &&
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(child1Priority < currPriority || child2Priority < currPriority)) {
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if (child1Priority < currPriority && child1Priority < child2Priority) {
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this._swap(child1Pos, currPos)
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currPos = child1Pos
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} else {
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this._swap(child2Pos, currPos)
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currPos = child2Pos
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}
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[child1Pos, child2Pos] = getChildrenPosition(currPos)
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try {
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[child1Priority, child2Priority] = [this._heap[child1Pos][1], this._heap[child2Pos][1]]
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} catch (error) {
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[child1Priority, child2Priority] = [Infinity, Infinity]
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}
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currPriority = this._heap[currPos][1]
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}
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this.keys[this._heap[currPos][0]] = currPos
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if (child1Pos < this._heap.length && child1Priority < currPriority) {
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this._swap(child1Pos, currPos)
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this.keys[this._heap[child1Pos][0]] = child1Pos
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}
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}
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_swap (position1, position2) {
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// Helper function to swap 2 nodes
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[this._heap[position1], this._heap[position2]] = [this._heap[position2], this._heap[position1]]
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this.keys[this._heap[position1][0]] = position1
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this.keys[this._heap[position2][0]] = position2
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}
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}
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class GraphWeightedUndirectedAdjacencyList {
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// Weighted Undirected Graph class
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constructor () {
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this.connections = {}
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}
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addNode (node) {
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// Function to add a node to the graph (connection represented by set)
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this.connections[node] = {}
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}
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addEdge (node1, node2, weight) {
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// Function to add an edge (adds the node too if they are not present in the graph)
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if (!(node1 in this.connections)) { this.addNode(node1) }
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if (!(node2 in this.connections)) { this.addNode(node2) }
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this.connections[node1][node2] = weight
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this.connections[node2][node1] = weight
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}
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PrimMST (start) {
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// Kruskal's Algorithm to generate a Minimum Spanning Tree (MST) of a graph
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// Details: https://en.wikipedia.org/wiki/Prim%27s_algorithm
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const distance = {}
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const parent = {}
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const priorityQueue = new PriorityQueue()
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// Initialization
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for (const node in this.connections) {
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distance[node] = (node === start.toString() ? 0 : Infinity)
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parent[node] = null
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priorityQueue.push(node, distance[node])
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}
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// Updating 'distance' object
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while (!priorityQueue.isEmpty()) {
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const node = priorityQueue.pop()
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Object.keys(this.connections[node]).forEach(neighbour => {
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if (priorityQueue.contains(neighbour) && distance[node] + this.connections[node][neighbour] < distance[neighbour]) {
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distance[neighbour] = distance[node] + this.connections[node][neighbour]
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parent[neighbour] = node
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priorityQueue.update(neighbour, distance[neighbour])
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}
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})
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}
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// MST Generation from the 'parent' object
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const graph = new GraphWeightedUndirectedAdjacencyList()
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Object.keys(parent).forEach(node => {
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if (node && parent[node]) {
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graph.addEdge(node, parent[node], this.connections[node][parent[node]])
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}
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})
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return graph
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}
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}
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function main () {
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const graph = new GraphWeightedUndirectedAdjacencyList()
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graph.addEdge(1, 2, 1)
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graph.addEdge(2, 3, 2)
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graph.addEdge(3, 4, 1)
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graph.addEdge(3, 5, 100) // Removed in MST
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graph.addEdge(4, 5, 5)
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console.log(graph.PrimMST(1))
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}
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main()

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