ActionScript 3 Design Patterns

The Recursive Vice

After our post on the binary search algorithm, I found that no one had cooked up an example of a Recursive Binary Search. So, I did. In a recent post, we looked at linked lists and used a recursive algorithm to move through the list. The algorithm is simple, and I hope explains both binary search and how to use recursion with such a search. As with the other posts in this recent series, we’re working our way to skip lists, and I hope this will aid in understanding how skip lists work.

Divide and Conquer

The binary search algorithm uses a divide and conquer approach that works like a vice. With each division in half, the bottom range gets higher and the top range gets lower and the search object is either squeezed out or not found. This saves a lot of poking around an array (or other list) to find what you’re looking for.

When using recursion, the function containing the search algorithm keeps calling itself until a match occurs or it runs out of places to look. In order to provide a visual representation of what’s going on, I used trace statements with each call to a recursive function. As you will see, with each recursive call, the search function displays the call and the values. The first parameter is the search value (44 in this case) and the second two parameters represent the beginning and ending values of the search fields. When you run the program, you will see something like the following:

recursive call to: recursiveBinarySearch(44,0,49);
recursive call to: recursiveBinarySearch(44,25,49);
recursive call to: recursiveBinarySearch(44,38,49);
recursive call to: recursiveBinarySearch(44,38,42);
recursive call to: recursiveBinarySearch(44,41,42);
recursive call to: recursiveBinarySearch(44,42,42);
Your number is at position 42

The beginning search of 100 elements is 49 for the top and 0 for the bottom. It then moves up through the numeric elements of the array until it finally squeezes out the found item in array element 42. (The array is randomly populated from 1 to 100 and then sorted—binary searches require sorted lists.)

Normally in these posts I don’t use a lot of comments in the code because the text in the post is supposed to explain everything. (Also, comments often get in the way of the flow of the programming logic and good agile programming shouldn’t need comments.) However, for this algorithm, I found that it probably helps to see each step in detail so I put in quite a few comments.

I also put the algorithm in a class. Because,

…an algorithm without a class is like a child without a mother…

That reminds me, Happy Mothers Day to all of you mothers out there.

(I suppose a corollary would be,

…a class without a design pattern is like a child without a father…

but I’d never say that because people might get the wrong idea about the latter piece of wisdom.)

Okay, so let’s take a look at the class containing the algorithm:

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package 
{
	import flash.display.Sprite;
 
	public class Binary extends Sprite
	{
		private var searchArray:Array=new Array();
		private var sizeNow:uint;
		private var mid:uint;
		private var poke:uint;
		private var begin:uint;
		private var end:uint;
		private var flagUp:Boolean=true;
 
		public function Binary()
		{
			for (var stuff:uint=0; stuff<100; stuff++)
			{
				searchArray.push(uint(Math.random()*100));
			}
			searchArray.sort();
			sizeNow=searchArray.length;
		}
 
		public function recursiveBinarySearch(valueN:uint,begin:uint,end:uint):uint
		{
			/*Only on the first time through use the array
			length as the end value. The Algorithm keeps
			changing the end value so you don't want to use
			the array length more than once.    */
			if (flagUp)
			{
				end=sizeNow;
				flagUp=false;
			}
 
			/*If the end value is smaller than the begin value
			the search is over and item was not found.    */
			if (end<begin)
			{
				return -1;
			}
 
			/*Find the midway point between begin and end
			and use it as the numeric key for the current search
			value—guess (poke).     */
			mid=uint((begin + end)/2);
			poke=searchArray[mid];
 
			/*If a match occurs return
			the value of the numeric key.  Search ends here.  */
			if (poke==valueN)
			{
				return mid;
			}
 
			/*If no match; guess larger than value; the end value
			becomes the midway value minus 1. Otherwise, the begin
			value becomes the midway value plus 1.     */
			else
			{
				if (poke>valueN)
				{
					end=mid-1;
				}
				else
				{
					if (poke<valueN)
					{
						begin=mid+1;
					}
				}
			}
 
			/* Keep making the recursive call until value is found
			or all possible values are searched */
			trace("recursive call to: recursiveBinarySearch("+valueN+","+begin+","+end+");");
			return recursiveBinarySearch(valueN,begin,end);
		}
	}
}

Like I said, there are a lot of comments there so that you can see the steps through the algorithm. Now, a second class acts like a client and calls the method in the Binary class:

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package 
{
	import flash.display.Sprite;
	public class Searcher extends Sprite
	{
		private var searching:Binary=new Binary();
		private var searchElement:Number;
		private var searchNow:Number;
 
		public function Searcher()
		{
			searchNow=searching.recursiveBinarySearch(44,0,0);
			if (searchNow>=0 && searchNow != 4294967295)
			{
				trace("Your number is at position " + searchNow );
			}
			else
			{
				trace("Not found");
			}
		}
	}
}

Keep in mind that all of the searches are searching the numeric element keys of the array—not the values. Therefore, you shouldn’t expect the found value to be the same as the numeric key value. Also, since the values are generated randomly, the value you place in the first parameter of the line:

searchNow=searching.recursiveBinarySearch(44,0,0);

may not be found at all. I put in 44 for the search value, but you can add any value you want between 1 and 100. Alternatively, you can fix it up so that you can dynamically enter different values or even change it to make it look for string values. However, the point is simply to demonstrate how to create and use a recursive binary search.

As always, your comments, corrections and wisdom are always welcomed.

A while back a comment by Timo Hannelin suggested that I use a skip list in one of the design patterns. (I looked but couldn’t find the comment, but I remember it was a good idea.) Anyway, I read the original article on skip lists by William Pugh. After reading the article and a few more articles on skip lists, I saw Timo’s point. However, since I’ve got my hands full with design patterns, and I dislike design pattern discussions degenerating into a chat about algorithms, I didn’t bring it up.

Algorithms in Participants

Having a little time right now, I thought I’d return to skip lists and see where they’d be valuable for participants in one of the design patterns. So, to warm up for working with skip lists I thought I’d whip up a Binary Search algorithm in ActionScript 3.0. Further, I wanted to entertain myself, and so I decided not to peek at any solutions on the Web.

After a few hours of trying to strong arm a solution I gave up and decided to peek. This is what I found:

Although the basic idea of binary search is comparatively straightforward, the details can be surprisingly tricky… — Professor Donald Knuth (Professor emeritus, Stanford University)

Further, I learned that only five out of twenty textbooks had accurate code for a binary search! Well, at least I didn’t feel like an idiot, but still, the concept is pretty simple, and it’s easy to do in your head. It’s just difficult (or tricky) to whip one up in code.

The Binary Search

The concept behind the binary search is to search by dividing an ordered list in consecutive halves. If the search guess is higher (in the ordered list) than the one being searched for, the bottom of a range is the search guess. If the search guess is lower; then the top of the range is the search guess. Each consecutive search is the halfway point between the top and bottom of the range. The solution is found by closing in like a vice taking chunks in halves rather than iterating through an entire list. It’s very fast and efficient for searches.

To get started, I created a function to generate a quick and dirty ordered array with 100 random numbers. (The variables were declared elsewhere in the class.)

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private function generate():Array
{
	//Generates 100 numbers 
	//Places them in a sorted array
	while (pack < 100)
	{
		ranInt=Math.random()*100;
		arrayPack.push(ranInt);
		pack++;
	}
	arrayPack.sort();
	return arrayPack;
}

Then I started writing the algorithm for the binary search. After locking up my computer with infinite loops a couple of times and rerouting the power grid of Bloomfield, Connecticut to Timbuktu, I gave up. Using numbers, I kept mixing up array numeric keys with the search values.

Your Turn to Have Some Fun

Anyway, since a lot of our readers like algorithms, I thought this might be a fun one for you to solve. You can find a lot of discussions of the binary search concept online as well as solutions (in the form of code and generic algorithms). However, see what you can come up with before you give up and peek (like I did). I can tell you this, though. One general solution uses recursive coding and the other uses iterative. Remember, though—only about a quarter of the computer science textbooks had it right. So, give it a go on your own knowing that if you come up with a solution, you’re smarter than 75% of the CS textbooks! We’ll use the Comments Section of this post for your solutions and look at skip lists in a future post.