public void binarySearch(int key, int start, int end, List array){
		System.out.println("key: "+key);
		System.out.println("start: "+start);
		System.out.println("end: "+end+"\n");
		
		int position;
		int comparisonCount = 0;
		
		position = (start + end) / 2;
		
		while(list.get(position) != key && start <= end){
			++comparisonCount;
			
			if(list.get(position) > key){
				end = position - 1;
			}else{
				start = position + 1;
			}
			
			position = (start + end) / 2;
		}
		
		if(start <= end){
			System.out.println("The number was found in array index: " + position);
			System.out.println("The binary search found the number after " + comparisonCount + " comparisons.");
		} else
	          System.out.println("Sorry, the number is not in this array.  The binary search made "+comparisonCount  + " comparisons.");
	  
		System.out.println();
		for(int i : list)
			System.out.print(i + " ,");
	}