fix: refactor PrimMST and fix bug in PriorityQueue

Data-Structures/Heap/KeyPriorityQueue.js

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+/**
+ * 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 contain both a key and a priority.
+ * WARNING: keys must be Integers as they are used as array indices.
+ *
+ * In this implementation, 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
+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 KeyPriorityQueue {
+  // Priority Queue class using Minimum Binary Heap
+  constructor () {
+    this._heap = []
+    this.keys = {}
+  }
+
+  /**
+   * Checks if the heap is empty
+   * @returns boolean
+   */
+  isEmpty () {
+    return this._heap.length === 0
+  }
+
+  /**
+   * Adds an element to the queue
+   * @param {number} key
+   * @param {number} priority
+   */
+  push (key, priority) {
+    this._heap.push([key, priority])
+    this.keys[key] = this._heap.length - 1
+    this._shiftUp(this.keys[key])
+  }
+
+  /**
+   * 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()
+    delete this.keys[key]
+    this._shiftDown(0)
+    return key
+  }
+
+  /**
+   * Checks whether a given key is present in the queue
+   * @param {number} key
+   * @returns boolean
+   */
+  contains (key) {
+    return (key in this.keys)
+  }
+
+  /**
+   * Updates the priority of the given element
+   * @param {number} key the element to change
+   * @param {number} priority new priority of the element
+   */
+  update (key, priority) {
+    const currPos = this.keys[key]
+    this._heap[currPos][1] = priority
+    const parentPos = getParentPosition(currPos)
+    const currPriority = this._getPriorityOrInfinite(currPos)
+    const parentPriority = this._getPriorityOrInfinite(parentPos)
+    const [child1Pos, child2Pos] = getChildrenPosition(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._heap[position][1]
+    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)
+    }
+    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 = 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] = getChildrenPosition(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]]
+    this.keys[this._heap[position1][0]] = position1
+    this.keys[this._heap[position2][0]] = position2
+  }
+}
+
+export { KeyPriorityQueue }

Data-Structures/Heap/test/KeyPriorityQueue.test.js

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+import { KeyPriorityQueue } from '../KeyPriorityQueue.js'
+
+describe('Method isEmpty', () => {
+  test('Check heap is empty', () => {
+    const queue = new KeyPriorityQueue()
+    const res = queue.isEmpty()
+    expect(res).toEqual(true)
+  })
+
+  test('Check heap is not empty', () => {
+    const queue = new KeyPriorityQueue()
+    queue.push(0, 2)
+    const res = queue.isEmpty()
+    expect(res).toEqual(false)
+  })
+})
+
+describe('Methods push and pop', () => {
+  test('Test Case 1', () => {
+    // create queue
+    const queue = new KeyPriorityQueue()
+    queue.push(0, 3)
+    queue.push(1, 7)
+    queue.push(2, 9)
+    queue.push(3, 13)
+    // create expected queue
+    const expectedQueue = new KeyPriorityQueue()
+    expectedQueue.push(1, 7)
+    expectedQueue.push(3, 13)
+    expectedQueue.push(2, 9)
+    // result from popping element from the queue
+    queue.pop()
+    expect(queue).toEqual(expectedQueue)
+  })
+
+  test('Test Case 2', () => {
+    // create queue
+    const queue = new KeyPriorityQueue()
+    queue.push(0, 3)
+    queue.push(1, 9)
+    queue.push(2, 7)
+    queue.push(3, 13)
+    // create expected queue
+    const expectedQueue = new KeyPriorityQueue()
+    expectedQueue.push(2, 7)
+    expectedQueue.push(1, 9)
+    expectedQueue.push(3, 13)
+    // result from popping element from the queue
+    queue.pop()
+    expect(queue).toEqual(expectedQueue)
+  })
+
+  test('Test Case 3', () => {
+    // create queue
+    const queue = new KeyPriorityQueue()
+    queue.push(0, 3)
+    queue.push(1, 7)
+    queue.push(2, 9)
+    queue.push(3, 12)
+    queue.push(4, 13)
+    // create expected queue
+    const expectedQueue = new KeyPriorityQueue()
+    expectedQueue.push(1, 7)
+    expectedQueue.push(3, 12)
+    expectedQueue.push(2, 9)
+    expectedQueue.push(4, 13)
+    // result from popping element from the queue
+    queue.pop()
+    expect(queue).toEqual(expectedQueue)
+  })
+})
+
+describe('Method contains', () => {
+  test('Check heap does not contain element', () => {
+    const queue = new KeyPriorityQueue()
+    const res = queue.contains(0)
+    expect(res).toEqual(false)
+  })
+
+  test('Check heap contains element', () => {
+    const queue = new KeyPriorityQueue()
+    queue.push(0, 2)
+    const res = queue.contains(0)
+    expect(res).toEqual(true)
+  })
+})
+
+describe('Method update', () => {
+  test('Update without change in position', () => {
+    // create queue
+    const queue = new KeyPriorityQueue()
+    queue.push(0, 3)
+    queue.push(1, 5)
+    queue.push(2, 7)
+    queue.push(3, 11)
+    // create expected queue
+    const expectedQueue = new KeyPriorityQueue()
+    expectedQueue.push(0, 2)
+    expectedQueue.push(1, 5)
+    expectedQueue.push(2, 7)
+    expectedQueue.push(3, 11)
+    // result from updating to similar priority
+    queue.update(0, 2)
+    expect(queue).toEqual(expectedQueue)
+  })
+
+  test('Update with change in position', () => {
+    // create queue
+    const queue = new KeyPriorityQueue()
+    queue.push(0, 3)
+    queue.push(1, 5)
+    queue.push(2, 7)
+    queue.push(3, 11)
+    // create expected queue
+    const expectedQueue = new KeyPriorityQueue()
+    expectedQueue.push(1, 5)
+    expectedQueue.push(3, 11)
+    expectedQueue.push(2, 7)
+    expectedQueue.push(0, 9)
+    // result from updating to similar priority
+    queue.update(0, 9)
+    expect(queue).toEqual(expectedQueue)
+  })
+})