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{Priority Queue}

The Question

 Breakdown

1. Define the structure of the priority queue
2. Define the insert function
3. Define the peek and popMax functions

1. Define the Priority Queue

    
    function Node(data, priority) {
    	this.data = data;
    	this.priority = priority;
    	this.next;
    }
    
    function PriorityQueue() {
    	this.first;
    }

2. Define the insert function

    PriorityQueue.prototype.insert = function(data, priority) {
    	if (!this.first || this.first.priority < priority) {
    		// First case handles both empty PQ and higher priority than anything else
    		var prevFirst = this.first;
    		this.first = new Node(data, priority);
    		this.first.next = prevFirst;
    	} else {
    		// Second case finds the place to insert the new item and inserts it
    		var pointer = this.first;
    		while (pointer.next && pointer.next.priority >= priority) {
    			pointer = pointer.next;
    		}
    		var newItem = new Node(data, priority);
    		newItem.next = pointer.next;
    		pointer.next = newItem;
    	}
    }

3. Define the peek and popMax functions

    PriorityQueue.prototype.peek = function() {
    	return this.first.data;
    }
    
    PriorityQueue.prototype.popMax = function() {
    	var retVal = this.first.data;
    	this.first = this.first.next;
    	return retVal;
    }

Performance  

How fast is each function?

insert

peek

popMax

Conclusion  

The other way to do this would be to just insert the new elements at the front and search for the highest whenever you need it.  (Overall this is slower since you'd be searching for its location once when you use popMax plus every time you peek rather than just once when you insert)