Added Prim's Algoritm (#227)

Graphs/PrimMST.js

@@ -0,0 +1,210 @@
+// 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) {
+    // Kruskal'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
+  }
+}
+
+function main () {
+  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)
+  console.log(graph.PrimMST(1))
+}
+
+main()