#### Prim MST

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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) {
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
}
}

// Weighted Undirected Graph class
constructor () {
this.connections = {}
}

// Function to add a node to the graph (connection represented by set)
this.connections[node] = {}
}

// 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
Object.keys(parent).forEach(node => {
if (node && parent[node]) {
}
})
return graph
}
}