fix: refactor PrimMST and fix bug in PriorityQueue (#1300)

* ref: KeyPriorityQueue in separate  file #1298

* feat: add tests for KeyPriorityQueue #1298

* fix: _shiftDown refactored and corrected #1298

* fix: use KeyPriorityQueue in PrimMST #1298

* feat: add test for PrimMST #1298

* fix: format files #1298

* fix: minor coding style changes

* fix: use map for keys and priorities #1298

Data-Structures/Heap/KeyPriorityQueue.js

@@ -0,0 +1,153 @@
+/**
+ * KeyPriorityQueue is a priority queue based on a Minimum Binary Heap.
+ *
+ * Minimum Binary Heaps are binary trees which are filled level by level
+ * and then from left to right inside a depth level.
+ * Their main property is that any parent node has a smaller or equal priority to all of its children,
+ * hence the root of the tree always has the smallest priority of all nodes.
+ *
+ * This implementation of the Minimum Binary Heap allows for nodes to be associated to both a key,
+ * which can be any datatype, and a priority.
+ *
+ * The heap is represented by an array with nodes ordered
+ * from root-to-leaf, left-to-right.
+ * Therefore, the parent-child node relationship is such that
+ *      * the children nodes positions relative to their parent are: (parentPos * 2 + 1) and (parentPos * 2 + 2)
+ *      * the parent node position relative to either of its children is: Math.floor((childPos - 1) / 2)
+ *
+ * More information and visuals on Binary Heaps can be found here: https://www.geeksforgeeks.org/binary-heap/
+ */
+
+// Priority Queue Helper functions
+const getParentPosition = position => Math.floor((position - 1) / 2)
+const getChildrenPositions = position => [2 * position + 1, 2 * position + 2]
+
+class KeyPriorityQueue {
+  // Priority Queue class using Minimum Binary Heap
+  constructor () {
+    this._heap = []
+    this.priorities = new Map()
+  }
+
+  /**
+   * Checks if the heap is empty
+   * @returns boolean
+   */
+  isEmpty () {
+    return this._heap.length === 0
+  }
+
+  /**
+   * Adds an element to the queue
+   * @param {*} key
+   * @param {number} priority
+   */
+  push (key, priority) {
+    this._heap.push(key)
+    this.priorities.set(key, priority)
+    this._shiftUp(this._heap.length - 1)
+  }
+
+  /**
+   * Removes the element with least priority
+   * @returns the key of the element with least priority
+   */
+  pop () {
+    this._swap(0, this._heap.length - 1)
+    const key = this._heap.pop()
+    this.priorities.delete(key)
+    this._shiftDown(0)
+    return key
+  }
+
+  /**
+   * Checks whether a given key is present in the queue
+   * @param {*} key
+   * @returns boolean
+   */
+  contains (key) {
+    return this.priorities.has(key)
+  }
+
+  /**
+   * Updates the priority of the given element.
+   * Adds the element if it is not in the queue.
+   * @param {*} key the element to change
+   * @param {number} priority new priority of the element
+   */
+  update (key, priority) {
+    const currPos = this._heap.indexOf(key)
+    // if the key does not exist yet, add it
+    if (currPos === -1) return this.push(key, priority)
+    // else update priority
+    this.priorities.set(key, priority)
+    const parentPos = getParentPosition(currPos)
+    const currPriority = this._getPriorityOrInfinite(currPos)
+    const parentPriority = this._getPriorityOrInfinite(parentPos)
+    const [child1Pos, child2Pos] = getChildrenPositions(currPos)
+    const child1Priority = this._getPriorityOrInfinite(child1Pos)
+    const child2Priority = this._getPriorityOrInfinite(child2Pos)
+
+    if (parentPos >= 0 && parentPriority > currPriority) {
+      this._shiftUp(currPos)
+    } else if (child1Priority < currPriority || child2Priority < currPriority) {
+      this._shiftDown(currPos)
+    }
+  }
+
+  _getPriorityOrInfinite (position) {
+    // Helper function, returns priority of the node, or Infinite if no node corresponds to this position
+    if (position >= 0 && position < this._heap.length) return this.priorities.get(this._heap[position])
+    else return Infinity
+  }
+
+  _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._getPriorityOrInfinite(currPos)
+    let parentPriority = this._getPriorityOrInfinite(parentPos)
+
+    while (parentPos >= 0 && parentPriority > currPriority) {
+      this._swap(currPos, parentPos)
+      currPos = parentPos
+      parentPos = getParentPosition(currPos)
+      currPriority = this._getPriorityOrInfinite(currPos)
+      parentPriority = this._getPriorityOrInfinite(parentPos)
+    }
+  }
+
+  _shiftDown (position) {
+    // Helper function to shift down a node to proper position (equivalent to bubbleDown)
+    let currPos = position
+    let [child1Pos, child2Pos] = getChildrenPositions(currPos)
+    let child1Priority = this._getPriorityOrInfinite(child1Pos)
+    let child2Priority = this._getPriorityOrInfinite(child2Pos)
+    let currPriority = this._getPriorityOrInfinite(currPos)
+
+    if (currPriority === Infinity) {
+      return
+    }
+
+    while (child1Priority < currPriority || child2Priority < currPriority) {
+      if (child1Priority < currPriority && child1Priority < child2Priority) {
+        this._swap(child1Pos, currPos)
+        currPos = child1Pos
+      } else {
+        this._swap(child2Pos, currPos)
+        currPos = child2Pos
+      }
+      [child1Pos, child2Pos] = getChildrenPositions(currPos)
+      child1Priority = this._getPriorityOrInfinite(child1Pos)
+      child2Priority = this._getPriorityOrInfinite(child2Pos)
+      currPriority = this._getPriorityOrInfinite(currPos)
+    }
+  }
+
+  _swap (position1, position2) {
+    // Helper function to swap 2 nodes
+    [this._heap[position1], this._heap[position2]] = [this._heap[position2], this._heap[position1]]
+  }
+}
+
+export { KeyPriorityQueue }