Heap, Priority Queue
Tags: heap, priorityqueue
Published: 2020-11-01 23:55:52

####Heap (data-structure)

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property described below.

In a min heap, if P is a parent node of C, then the key (the value) of P is less than or equal to the key of C.

In a max heap, the key of P is greater than or equal to the key of C

The node at the "top" of the heap with no parents is called the root node.

```javascript
import Comparator from '../../utils/comparator/Comparator';

/**
 * Parent class for Min and Max Heaps.
 */
export default class Heap {
  /**
   * @constructs Heap
   * @param {Function} [comparatorFunction]
   */
  constructor(comparatorFunction) {
    if (new.target === Heap) {
      throw new TypeError('Cannot construct Heap instance directly');
    }

    // Array representation of the heap.
    this.heapContainer = [];
    this.compare = new Comparator(comparatorFunction);
  }

  /**
   * @param {number} parentIndex
   * @return {number}
   */
  getLeftChildIndex(parentIndex) {
    return (2 * parentIndex) + 1;
  }

  /**
   * @param {number} parentIndex
   * @return {number}
   */
  getRightChildIndex(parentIndex) {
    return (2 * parentIndex) + 2;
  }

  /**
   * @param {number} childIndex
   * @return {number}
   */
  getParentIndex(childIndex) {
    return Math.floor((childIndex - 1) / 2);
  }

  /**
   * @param {number} childIndex
   * @return {boolean}
   */
  hasParent(childIndex) {
    return this.getParentIndex(childIndex) >= 0;
  }

  /**
   * @param {number} parentIndex
   * @return {boolean}
   */
  hasLeftChild(parentIndex) {
    return this.getLeftChildIndex(parentIndex) < this.heapContainer.length;
  }

  /**
   * @param {number} parentIndex
   * @return {boolean}
   */
  hasRightChild(parentIndex) {
    return this.getRightChildIndex(parentIndex) < this.heapContainer.length;
  }

  /**
   * @param {number} parentIndex
   * @return {*}
   */
  leftChild(parentIndex) {
    return this.heapContainer[this.getLeftChildIndex(parentIndex)];
  }

  /**
   * @param {number} parentIndex
   * @return {*}
   */
  rightChild(parentIndex) {
    return this.heapContainer[this.getRightChildIndex(parentIndex)];
  }

  /**
   * @param {number} childIndex
   * @return {*}
   */
  parent(childIndex) {
    return this.heapContainer[this.getParentIndex(childIndex)];
  }

  /**
   * @param {number} indexOne
   * @param {number} indexTwo
   */
  swap(indexOne, indexTwo) {
    const tmp = this.heapContainer[indexTwo];
    this.heapContainer[indexTwo] = this.heapContainer[indexOne];
    this.heapContainer[indexOne] = tmp;
  }

  /**
   * @return {*}
   */
  peek() {
    if (this.heapContainer.length === 0) {
      return null;
    }

    return this.heapContainer[0];
  }

  /**
   * @return {*}
   */
  poll() {
    if (this.heapContainer.length === 0) {
      return null;
    }

    if (this.heapContainer.length === 1) {
      return this.heapContainer.pop();
    }

    const item = this.heapContainer[0];

    // Move the last element from the end to the head.
    this.heapContainer[0] = this.heapContainer.pop();
    this.heapifyDown();

    return item;
  }

  /**
   * @param {*} item
   * @return {Heap}
   */
  add(item) {
    this.heapContainer.push(item);
    this.heapifyUp();
    return this;
  }

  /**
   * @param {*} item
   * @param {Comparator} [comparator]
   * @return {Heap}
   */
  remove(item, comparator = this.compare) {
    // Find number of items to remove.
    const numberOfItemsToRemove = this.find(item, comparator).length;

    for (let iteration = 0; iteration < numberOfItemsToRemove; iteration += 1) {
      // We need to find item index to remove each time after removal since
      // indices are being changed after each heapify process.
      const indexToRemove = this.find(item, comparator).pop();

      // If we need to remove last child in the heap then just remove it.
      // There is no need to heapify the heap afterwards.
      if (indexToRemove === (this.heapContainer.length - 1)) {
        this.heapContainer.pop();
      } else {
        // Move last element in heap to the vacant (removed) position.
        this.heapContainer[indexToRemove] = this.heapContainer.pop();

        // Get parent.
        const parentItem = this.parent(indexToRemove);

        // If there is no parent or parent is in correct order with the node
        // we're going to delete then heapify down. Otherwise heapify up.
        if (
          this.hasLeftChild(indexToRemove)
          && (
            !parentItem
            || this.pairIsInCorrectOrder(parentItem, this.heapContainer[indexToRemove])
          )
        ) {
          this.heapifyDown(indexToRemove);
        } else {
          this.heapifyUp(indexToRemove);
        }
      }
    }

    return this;
  }

  /**
   * @param {*} item
   * @param {Comparator} [comparator]
   * @return {Number[]}
   */
  find(item, comparator = this.compare) {
    const foundItemIndices = [];

    for (let itemIndex = 0; itemIndex < this.heapContainer.length; itemIndex += 1) {
      if (comparator.equal(item, this.heapContainer[itemIndex])) {
        foundItemIndices.push(itemIndex);
      }
    }

    return foundItemIndices;
  }

  /**
   * @return {boolean}
   */
  isEmpty() {
    return !this.heapContainer.length;
  }

  /**
   * @return {string}
   */
  toString() {
    return this.heapContainer.toString();
  }

  /**
   * @param {number} [customStartIndex]
   */
  heapifyUp(customStartIndex) {
    // Take the last element (last in array or the bottom left in a tree)
    // in the heap container and lift it up until it is in the correct
    // order with respect to its parent element.
    let currentIndex = customStartIndex || this.heapContainer.length - 1;

    while (
      this.hasParent(currentIndex)
      && !this.pairIsInCorrectOrder(this.parent(currentIndex), this.heapContainer[currentIndex])
    ) {
      this.swap(currentIndex, this.getParentIndex(currentIndex));
      currentIndex = this.getParentIndex(currentIndex);
    }
  }

  /**
   * @param {number} [customStartIndex]
   */
  heapifyDown(customStartIndex = 0) {
    // Compare the parent element to its children and swap parent with the appropriate
    // child (smallest child for MinHeap, largest child for MaxHeap).
    // Do the same for next children after swap.
    let currentIndex = customStartIndex;
    let nextIndex = null;

    while (this.hasLeftChild(currentIndex)) {
      if (
        this.hasRightChild(currentIndex)
        && this.pairIsInCorrectOrder(this.rightChild(currentIndex), this.leftChild(currentIndex))
      ) {
        nextIndex = this.getRightChildIndex(currentIndex);
      } else {
        nextIndex = this.getLeftChildIndex(currentIndex);
      }

      if (this.pairIsInCorrectOrder(
        this.heapContainer[currentIndex],
        this.heapContainer[nextIndex],
      )) {
        break;
      }

      this.swap(currentIndex, nextIndex);
      currentIndex = nextIndex;
    }
  }

  /**
   * Checks if pair of heap elements is in correct order.
   * For MinHeap the first element must be always smaller or equal.
   * For MaxHeap the first element must be always bigger or equal.
   *
   * @param {*} firstElement
   * @param {*} secondElement
   * @return {boolean}
   */
  /* istanbul ignore next */
  pairIsInCorrectOrder(firstElement, secondElement) {
    throw new Error(`
      You have to implement heap pair comparision method
      for ${firstElement} and ${secondElement} values.
    `);
  }
}

```

####Priority Queue

In computer science, a priority queue is an abstract data type which is like a regular queue or stack data structure, but where additionally each element has a "priority" associated with it. In a priority queue, an element with high priority is served before an element with low priority. If two elements have the same priority, they are served according to their order in the queue.

While priority queues are often implemented with heaps, they are conceptually distinct from heaps. A priority queue is an abstract concept like "a list" or "a map"; just as a list can be implemented with a linked list or an array, a priority queue can be implemented with a heap or a variety of other methods such as an unordered array.

```javascript

import MinHeap from '../heap/MinHeap';
import Comparator from '../../utils/comparator/Comparator';

// It is the same as min heap except that when comparing two elements
// we take into account its priority instead of the element's value.
export default class PriorityQueue extends MinHeap {
  constructor() {
    // Call MinHip constructor first.
    super();

    // Setup priorities map.
    this.priorities = new Map();

    // Use custom comparator for heap elements that will take element priority
    // instead of element value into account.
    this.compare = new Comparator(this.comparePriority.bind(this));
  }

  /**
   * Add item to the priority queue.
   * @param {*} item - item we're going to add to the queue.
   * @param {number} [priority] - items priority.
   * @return {PriorityQueue}
   */
  add(item, priority = 0) {
    this.priorities.set(item, priority);
    super.add(item);
    return this;
  }

  /**
   * Remove item from priority queue.
   * @param {*} item - item we're going to remove.
   * @param {Comparator} [customFindingComparator] - custom function for finding the item to remove
   * @return {PriorityQueue}
   */
  remove(item, customFindingComparator) {
    super.remove(item, customFindingComparator);
    this.priorities.delete(item);
    return this;
  }

  /**
   * Change priority of the item in a queue.
   * @param {*} item - item we're going to re-prioritize.
   * @param {number} priority - new item's priority.
   * @return {PriorityQueue}
   */
  changePriority(item, priority) {
    this.remove(item, new Comparator(this.compareValue));
    this.add(item, priority);
    return this;
  }

  /**
   * Find item by ite value.
   * @param {*} item
   * @return {Number[]}
   */
  findByValue(item) {
    return this.find(item, new Comparator(this.compareValue));
  }

  /**
   * Check if item already exists in a queue.
   * @param {*} item
   * @return {boolean}
   */
  hasValue(item) {
    return this.findByValue(item).length > 0;
  }

  /**
   * Compares priorities of two items.
   * @param {*} a
   * @param {*} b
   * @return {number}
   */
  comparePriority(a, b) {
    if (this.priorities.get(a) === this.priorities.get(b)) {
      return 0;
    }
    return this.priorities.get(a) < this.priorities.get(b) ? -1 : 1;
  }

  /**
   * Compares values of two items.
   * @param {*} a
   * @param {*} b
   * @return {number}
   */
  compareValue(a, b) {
    if (a === b) {
      return 0;
    }
    return a < b ? -1 : 1;
  }
}
```

*References*
https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/heap
https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/priority-queue