Below is what I believe to be a truly efficient version of a PriorityQueue which uses an array-based binary heap (where the root is at index 0, and the children of a node at index i are at indices 2i + 1 and 2i + 2, respectively).

This implementation includes the classical priority queue methods like push, peek, pop, and size, as well as convenience methods isEmpty and replace (the latter being a more efficient substitute for a pop followed immediately by a push). Values are stored not as [value, priority] pairs, but simply as values; this allows for automatic prioritization of types that can be natively compared using the > operator. A custom comparator function passed to the PriorityQueue constructor can be used to emulate the behavior of pairwise semantics, however, as shown in the example below.

Heap-based Implementation:

const top = 0;

const parent = i => ((i + 1) >>> 1) - 1;

const left = i => (i << 1) + 1;

const right = i => (i + 1) << 1;



class PriorityQueue {

  constructor(comparator = (a, b) => a > b) {

    this._heap = [];

    this._comparator = comparator;

  }

  size() {

    return this._heap.length;

  }

  isEmpty() {

    return this.size() == 0;

  }

  peek() {

    return this._heap[top];

  }

  push(...values) {

    values.forEach(value => {

      this._heap.push(value);

      this._siftUp();

    });

    return this.size();

  }

  pop() {

    const poppedValue = this.peek();

    const bottom = this.size() - 1;

    if (bottom > top) {

      this._swap(top, bottom);

    }

    this._heap.pop();

    this._siftDown();

    return poppedValue;

  }

  replace(value) {

    const replacedValue = this.peek();

    this._heap[top] = value;

    this._siftDown();

    return replacedValue;

  }

  _greater(i, j) {

    return this._comparator(this._heap[i], this._heap[j]);

  }

  _swap(i, j) {

    [this._heap[i], this._heap[j]] = [this._heap[j], this._heap[i]];

  }

  _siftUp() {

    let node = this.size() - 1;

    while (node > top && this._greater(node, parent(node))) {

      this._swap(node, parent(node));

      node = parent(node);

    }

  }

  _siftDown() {

    let node = top;

    while (

      (left(node) < this.size() && this._greater(left(node), node)) ||

      (right(node) < this.size() && this._greater(right(node), node))

    ) {

      let maxChild = (right(node) < this.size() && this._greater(right(node), left(node))) ? right(node) : left(node);

      this._swap(node, maxChild);

      node = maxChild;

    }

  }

}

Example:

{const top=0,parent=c=>(c+1>>>1)-1,left=c=>(c<<1)+1,right=c=>c+1<<1;class PriorityQueue{constructor(c=(d,e)=>d>e){this._heap=[],this._comparator=c}size(){return this._heap.length}isEmpty(){return 0==this.size()}peek(){return this._heap[top]}push(...c){return c.forEach(d=>{this._heap.push(d),this._siftUp()}),this.size()}pop(){const c=this.peek(),d=this.size()-1;return d>top&&this._swap(top,d),this._heap.pop(),this._siftDown(),c}replace(c){const d=this.peek();return this._heap[top]=c,this._siftDown(),d}_greater(c,d){return this._comparator(this._heap[c],this._heap[d])}_swap(c,d){[this._heap[c],this._heap[d]]=[this._heap[d],this._heap[c]]}_siftUp(){for(let c=this.size()-1;c>top&&this._greater(c,parent(c));)this._swap(c,parent(c)),c=parent(c)}_siftDown(){for(let d,c=top;left(c)<this.size()&&this._greater(left(c),c)||right(c)<this.size()&&this._greater(right(c),c);)d=right(c)<this.size()&&this._greater(right(c),left(c))?right(c):left(c),this._swap(c,d),c=d}}window.PriorityQueue=PriorityQueue}



// Default comparison semantics

const queue = new PriorityQueue();

queue.push(10, 20, 30, 40, 50);

console.log('Top:', queue.peek()); //=> 50

console.log('Size:', queue.size()); //=> 5

console.log('Contents:');

while (!queue.isEmpty()) {

  console.log(queue.pop()); //=> 40, 30, 20, 10

}



// Pairwise comparison semantics

const pairwiseQueue = new PriorityQueue((a, b) => a[1] > b[1]);

pairwiseQueue.push(['low', 0], ['medium', 5], ['high', 10]);

console.log('nContents:');

while (!pairwiseQueue.isEmpty()) {

  console.log(pairwiseQueue.pop()[0]); //=> 'high', 'medium', 'low'

}

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