# Find the running median with 2 heaps

I wrote code to solve the running median challenge using 2 heaps, and I'd appreciate any and all feedback.

Here is the problem:

You have a list of numbers and are scanning them one by one. Calculate and print the median every time you get a new number.

My code:

//program code

var minHeap;
var maxHeap;

function main() {
// n == how many numbers there will be
var a = [];
for(var a_i = 0; a_i < n; a_i++){
}

minHeap = new MinHeap();
maxHeap = new MaxHeap();

for(var i = 0; i < n; i ++){
balanceHeaps();
getMedian();
}
}

if(!minHeap.size() || item >= minHeap.top()){
}
else if(!maxHeap.size() || item <= maxHeap.top()){
}
else{
}
}

function balanceHeaps(){
if(Math.abs(minHeap.size() - maxHeap.size()) > 1){
if(minHeap.size() > maxHeap.size()){
}
else{
}
}
}

function getMedian(){
var median = 0;
if(Math.abs(minHeap.size() - maxHeap.size()) === 1){
if(minHeap.size() > maxHeap.size()){
median = minHeap.top();
}
else{
median = maxHeap.top();
}
}
else{
median = (minHeap.top() + maxHeap.top()) / 2;
}
console.log(median.toFixed(1));
}

//heap class
var Heap = function(){
this._heap = [];
this._size = 0;
};
Heap.prototype.switchItems = function(pos1, pos2){
var _heap = this._heap;
var temp = _heap[pos1];
_heap[pos1] = _heap[pos2];
_heap[pos2] = temp;
};
Heap.prototype.size = function(){
return this._size;
};
Heap.prototype.top = function(){
return this._heap[0];
};
Heap.prototype.incrementSize = function(){
this._size++;
};
Heap.prototype.decrementSize = function(){
this._size--;
};
var _heap = this._heap;
_heap[this.size()] = item;
this.incrementSize();
this.heapifyUp();
};
Heap.prototype.removeTop = function(){
var _heap = this._heap;
if(this.size() === 0){
return null;
}
if(this.size() === 1){
this.decrementSize();
return _heap[0];
}
var tempTop = _heap[0];
_heap[0] = _heap[this.size() - 1];
this.decrementSize();
this.heapifyDown();
return tempTop;
};
Heap.prototype.getLeftChildIndex = function(pos){
return pos * 2 + 1;
};
Heap.prototype.getRightChildIndex = function(pos){
return pos * 2 + 2;
};
Heap.prototype.getParentIndex = function(pos){
return Math.floor((pos - 1) / 2);
};
Heap.prototype.hasLeftChild = function(pos){
return this.size() > this.getLeftChildIndex(pos);
};
Heap.prototype.hasRightChild = function(pos){
return this.size() > this.getRightChildIndex(pos);
};
Heap.prototype.hasParent = function(pos){
return this.getParentIndex(pos) >= 0;
};
Heap.prototype.leftChild = function(pos){
return this._heap[this.getLeftChildIndex(pos)];
};
Heap.prototype.rightChild = function(pos){
return this._heap[this.getRightChildIndex(pos)];
};
Heap.prototype.parent = function(pos){
return this._heap[this.getParentIndex(pos)];
};

var MinHeap = function(){
Heap.call(this);
};
MinHeap.prototype = Object.create(Heap.prototype);
MinHeap.prototype.constructor = MinHeap;
MinHeap.prototype.heapifyUp = function(){
var pos = this.size() - 1;
while(this.hasParent(pos)){
if(this._heap[pos] >= this.parent(pos)){
break;
}
else{
this.switchItems(pos, this.getParentIndex(pos), this.name);
pos = this.getParentIndex(pos);
}
}
};
MinHeap.prototype.heapifyDown = function(){
var pos = 0;
var _heap = this._heap;
while(pos < this.size() && this.hasLeftChild(pos)){
var minChildIndex = this.getLeftChildIndex(pos);
if(this.hasRightChild(pos) && this.rightChild(pos) < _heap[minChildIndex]){
minChildIndex = this.getRightChildIndex(pos);
}
if(_heap[pos] <= _heap[minChildIndex]){
break;
}
else{
this.switchItems(pos, minChildIndex, this.name);
pos = minChildIndex;
}
}
};

var MaxHeap = function(){
Heap.call(this);
};
MaxHeap.prototype = Object.create(Heap.prototype);
MaxHeap.prototype.constructor = MaxHeap;
MaxHeap.prototype.heapifyUp = function(){
var pos = this.size() - 1;
while(this.hasParent(pos)){
if(this._heap[pos] <= this.parent(pos)){
break;
}
else{
this.switchItems(pos, this.getParentIndex(pos), this.name);
pos = this.getParentIndex(pos);
}
}
};
MaxHeap.prototype.heapifyDown = function(){
var pos = 0;
var _heap = this._heap;
while(pos < this.size() && this.hasLeftChild(pos)){
var maxChildIndex = this.getLeftChildIndex(pos);
if(this.hasRightChild(pos) && this.rightChild(pos) > _heap[maxChildIndex]){
maxChildIndex = this.getRightChildIndex(pos);
}
if(_heap[pos] >= _heap[maxChildIndex]){
break;
}
else{
this.switchItems(pos, maxChildIndex, this.name);
pos = maxChildIndex;
}
}
};


Overall, nicely done, and a clever idea for the running median.

### DRY

Don't repeat yourself ;-)

It's a pity that the heapify and siftUp logic is not implemented in Heap, but reimplemented in MinHeap and MaxHeap with a different comparison logic. It would be better to introduce a compare(x, y) function that returns -1, 0, 1 when x < y, x === y, x > y, respectively. heapify and siftUp could be implemented using that, and then the difference between the MinHeap and MaxHeap implementations will be just the implementation of compare, maximizing code reuse.

Even more importantly, encapsulating the comparison logic would open up the possibility of using the heap to order more than just simple numbers, but objects by some property. For example, you could order words by their length, or cities by their population, or processes by their priority.

### Terminology

Instead of heapifyUp and heapifyDown, the common terms are siftUp and heapify. I suggest to follow the common terminology on the wikipedia page of heaps.

### Good practices

It's a bad practice in JavaScript to use var in a loop like this:

for(var i = 0; i < n; i ++){
balanceHeaps();
getMedian();
}


This writing style gives the illusion that the loop variable i is visible only in the scope of the loop. But that's not true and can lead to confusion. The recommended practice is to declare all variables at the top of the function. It's sad but true.

### Writing style

I suggest to add spaces around parentheses for better readability, like this:

for (var i = 0; i < n; i++) {

• You may want to rephrase "The recommended practice is to declare all variables at the top of the function." as variables declared with let and const are block scoped and can not be hoisted or they change their scope. Commented Nov 23, 2016 at 12:05
• Thanks for pointing that out @Blindman67. Is that part of the standard though? These keywords are not mentioned in JavaScript The Good Parts book. Commented Nov 23, 2016 at 12:40
• yes it is. Teh word your looking for though is closure. They are not specific to just javascript Commented Apr 15, 2020 at 9:05