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// Priority Queue Helper functions

function getParentPosition (position) {

// Get the parent node of the current node

return Math.floor((position - 1) / 2)

}

function getChildrenPosition (position) {

// Get the children nodes of the current node

return [2 * position + 1, 2 * position + 2]

}

class PriorityQueue {

// Priority Queue class using Minimum Binary Heap

constructor () {

this._heap = []

this.keys = {}

}

isEmpty () {

// Checking if the heap is empty

return this._heap.length === 0

}

push (key, priority) {

// Adding element to the queue (equivalent to add)

this._heap.push([key, priority])

this.keys[key] = this._heap.length - 1

this._shiftUp(this.keys[key])

}

pop () {

// Removing the element with least priority (equivalent to extractMin)

this._swap(0, this._heap.length - 1)

const [key] = this._heap.pop()

delete this.keys[key]

this._shiftDown(0)

return key

}

contains (key) {

// Check if a given key is present in the queue

return (key in this.keys)

}

update (key, priority) {

// Update the priority of the given element (equivalent to decreaseKey)

const currPos = this.keys[key]

this._heap[currPos][1] = priority

const parentPos = getParentPosition(currPos)

const currPriority = this._heap[currPos][1]

let parentPriority = Infinity

if (parentPos >= 0) {

parentPriority = this._heap[parentPos][1]

}

const [child1Pos, child2Pos] = getChildrenPosition(currPos)

let [child1Priority, child2Priority] = [Infinity, Infinity]

if (child1Pos < this._heap.length) {

child1Priority = this._heap[child1Pos][1]

}

if (child2Pos < this._heap.length) {

child2Priority = this._heap[child2Pos][1]

}

if (parentPos >= 0 && parentPriority > currPriority) {

this._shiftUp(currPos)

} else if (child2Pos < this._heap.length &&

(child1Priority < currPriority || child2Priority < currPriority)) {

this._shiftDown(currPos)

}

}

_shiftUp (position) {

// Helper function to shift up a node to proper position (equivalent to bubbleUp)

let currPos = position

let parentPos = getParentPosition(currPos)

let currPriority = this._heap[currPos][1]

let parentPriority = Infinity

if (parentPos >= 0) {

parentPriority = this._heap[parentPos][1]

}

while (parentPos >= 0 && parentPriority > currPriority) {

this._swap(currPos, parentPos)

currPos = parentPos

parentPos = getParentPosition(currPos)

currPriority = this._heap[currPos][1]

try {

parentPriority = this._heap[parentPos][1]

} catch (error) {

parentPriority = Infinity

}

}

this.keys[this._heap[currPos][0]] = currPos

}

_shiftDown (position) {

// Helper function to shift down a node to proper position (equivalent to bubbleDown)

let currPos = position

let [child1Pos, child2Pos] = getChildrenPosition(currPos)

let [child1Priority, child2Priority] = [Infinity, Infinity]

if (child1Pos < this._heap.length) {

child1Priority = this._heap[child1Pos][1]

}

if (child2Pos < this._heap.length) {

child2Priority = this._heap[child2Pos][1]

}

let currPriority

try {

currPriority = this._heap[currPos][1]

} catch {

return

}

while (child2Pos < this._heap.length &&

(child1Priority < currPriority || child2Priority < currPriority)) {

if (child1Priority < currPriority && child1Priority < child2Priority) {

this._swap(child1Pos, currPos)

currPos = child1Pos

} else {

this._swap(child2Pos, currPos)

currPos = child2Pos

}

[child1Pos, child2Pos] = getChildrenPosition(currPos)

try {

[child1Priority, child2Priority] = [this._heap[child1Pos][1], this._heap[child2Pos][1]]

} catch (error) {

[child1Priority, child2Priority] = [Infinity, Infinity]

}

currPriority = this._heap[currPos][1]

}

this.keys[this._heap[currPos][0]] = currPos

if (child1Pos < this._heap.length && child1Priority < currPriority) {

this._swap(child1Pos, currPos)

this.keys[this._heap[child1Pos][0]] = child1Pos

}

}

_swap (position1, position2) {

// Helper function to swap 2 nodes

[this._heap[position1], this._heap[position2]] = [this._heap[position2], this._heap[position1]]

this.keys[this._heap[position1][0]] = position1

this.keys[this._heap[position2][0]] = position2

}

}

class GraphWeightedUndirectedAdjacencyList {

// Weighted Undirected Graph class

constructor () {

this.connections = {}

}

addNode (node) {

// Function to add a node to the graph (connection represented by set)

this.connections[node] = {}

}

addEdge (node1, node2, weight) {

// Function to add an edge (adds the node too if they are not present in the graph)

if (!(node1 in this.connections)) { this.addNode(node1) }

if (!(node2 in this.connections)) { this.addNode(node2) }

this.connections[node1][node2] = weight

this.connections[node2][node1] = weight

}

PrimMST (start) {

// Prim's Algorithm to generate a Minimum Spanning Tree (MST) of a graph

// Details: https://en.wikipedia.org/wiki/Prim%27s_algorithm

const distance = {}

const parent = {}

const priorityQueue = new PriorityQueue()

// Initialization

for (const node in this.connections) {

distance[node] = (node === start.toString() ? 0 : Infinity)

parent[node] = null

priorityQueue.push(node, distance[node])

}

// Updating 'distance' object

while (!priorityQueue.isEmpty()) {

const node = priorityQueue.pop()

Object.keys(this.connections[node]).forEach(neighbour => {

if (priorityQueue.contains(neighbour) && distance[node] + this.connections[node][neighbour] < distance[neighbour]) {

distance[neighbour] = distance[node] + this.connections[node][neighbour]

parent[neighbour] = node

priorityQueue.update(neighbour, distance[neighbour])

}

})

}

// MST Generation from the 'parent' object

const graph = new GraphWeightedUndirectedAdjacencyList()

Object.keys(parent).forEach(node => {

if (node && parent[node]) {

graph.addEdge(node, parent[node], this.connections[node][parent[node]])

}

})

return graph

}

}

export { GraphWeightedUndirectedAdjacencyList }

// const graph = new GraphWeightedUndirectedAdjacencyList()

// graph.addEdge(1, 2, 1)

// graph.addEdge(2, 3, 2)

// graph.addEdge(3, 4, 1)

// graph.addEdge(3, 5, 100) // Removed in MST

// graph.addEdge(4, 5, 5)

// graph.PrimMST(1)