TweetFollow Us on Twitter

Recursion

Volume Number: 16 (2000)
Issue Number: 11
Column Tag: Mac OS X

Recursion: The Programmer's Friend

by Andrew C. Stone

A programmer's bag of tricks is loaded with heuristics, algorithms and techniques, but of these, few are as powerful as recursion. The Oxford English Dictionary recursively defines recursion as "The application or use of a recursive procedure or definitiion"! Recursive has the definition "Involving or being a repeated procedure such that the required result at each step except the last is given in terms of the result(s) of the next step, until after a finite number of steps a terminus is reached with an outright evaluation of a result."

In software, recursion is when a function or method calls itself, over and over, with slightly differing arguments. Of course this sounds like the perfect recipe for an infinite loop, but we will design in an exit condition so you don't end up in Cupertino! Recursion allows the writing of elegant and terse code once you understand how it works.

Recursion abounds in nature, and can be visualized by thinking of the fractal Mandelbrot set — no matter how deep into the set you continue to go, the same forms appear over and over, in an increasingly minute, yet perfectly replicated form.

Programmers often use a recursive data structure called a tree to represent hierarchical data. A tree is a root (Now that's an oxyomoron!) with zero or more subtrees. Each subtree consists of a root node with zero or more subtrees. A subtree node with no branches or children is a leaf node. (Tree terminology uses both botanical (root/branch) and geneological (parent/child) terms.) A classic use of recursion is for tree traversal, where you want to perform some action on each node in the tree.


Figure 1. A Tree with nodes labeled postorder.

A tree can be implemented in various ways, depending on the structure and use of the tree. It's beyond the scope of this article to cover the implementation of "scales well to large N" trees such as the btree; however for a reasonably small number (e.g. under 1000) of nodes, arrays of arrays will work fine. Let's define a simplistic Node as:

@interface Node {
       id data; // an opaque pointer to some kind of data
       NSArray *_children; 
   // if an internal node, this contains children nodes
   // if this is a leaf node, it contains 0 elements.
}
// query the Node:
- (NSArray *)children;
- (NSData *)data;

// establish the Node:
- (void)setChildren:(NSArray *)newKids;
- (void)setData:(id)data;
@end

And our tree controller object would look like:

@interface TreeController {
      Node * _rootOfTreeNode;   // the root is all you need to get at any Node
}
- (void)visitNode:(Node *)node;
- (void)printData:(Node *)node;
@end

Walking a Tree: Kinds of Traversals

There are three types of tree traversals: preorder, inorder, and postorder - each defines the particulars of whether you work on a node before or after working on its children. In preorder, you work on the parent and then do an inorder traversal of each of the children . In inorder, you do a preorder traversal on the leftmost child, work on the parent, and then do an inorder traversal of each of the remaining children. In postorder, you do a postorder traversal of each of the children and then work on the parent.

Here's the code for a recursive preorder traversal:

- (void)visitNode:(Node *)node {
        NSArray *childrenToVisit = [node children];
        unsigned i, count = [childrenToVisit Count];

        // visit the current node:
       [self printData:[node data]].

       // if there are no children, then recursion ends:
        for (i = 0; i < count; i++)   // make recursive call:
   [self visitNode:[childrenToVisit objectAtIndex:i]];
}

- (void)printData:(Node *)node {
       // this is just an example - in reality you might do something useful!
      NSLog([node description]);
}

To traverse an entire tree, you would simply start the recursive process at the top of the tree by calling our method with the root node as the argument:

      [self visitNode:_rootOfTreeNode];

Note that to perform a postorder traversal, you just move the "printData" (our placeholder for the action we wish to perform on any node) to the bottom of the method:

- visitNodePostorder:(Node *)node {
        NSArray *childrenToVisit = [node children];
        unsigned i, count = [childrenToVisit Count];
        for (i = 0; i < count; i++)
   [self visitNodePostorder:[childrenToVisit objectAtIndex:i]];
        // now visit the current node:
       [self printData:[node data]].
}

Stacks and Stacks of Stacks

So how does this all work? Every programming language that supports recursion (including Objective-C) maintains a stack of information about parameters and local variables for each time a procedure, function, or method is called. When a procedure is called, the information is pushed onto the stack; when the procedure exits, the information is popped from the stack.

Given the tree pictured in Figure 1, let's mentally walk through what's happening. First we call visitNodePostorder: on the root node (node A), placing this method call on the stack. Node A has 3 children so we call visitNodePostorder on the first child (node B), pushing that call on the stack. Node B has 2 children, so we call visitNodePostorder on the first child (node C), placing that call on the stack. We then call the method on node C's first child, node D. Now the stack is 4 deep, but this final node is a leaf, so we call printData on node D. We're back in visitNodePostorder:C and the second child (node E) is called, increasing the stack to 4 again. Since it is also a leaf, we print it, pop the method call, and we're back down to 3. Now node C will print itself, and we're down to 2 deep in the stack. The second child of node B is a leaf, so we go 3 deep, and after printing, we're at 2 deep. Node B is then printed, and then we're back to the first frame in the stack (node A), on the second iteration of its for loop. Since the second child (node G) of the root node is a leaf, it gets printed, and we're on the third child. And so on for the rest of the tree.


Figure 2. Snapshots of the stack during the tree traversal.

So, you can see that the stack will grow to the depth of the tree. If you are working with very deep trees and you're concerned with implementation efficiency and want to avoid the overhead inherent in making method calls, you can remove the recursion by managing your own stack of variables. However, this results in much more complex, less elegant, less maintainable code. I'd avoid it in all but the most extreme situations.

Conclusion

As programming challenges arise, remember this recursive jewel I learned many years ago in Computer Science school: if you cannot tackle a problem, divide it into smaller problems which you can tackle. Eventually you'll have wittled the problem down to something manageable, and applying this recursive problem solving tool will usually result in a readable and maintainable software solution.


Andrew Stone <andrew@stone.com> is founder of Stone Design Corp <http://www.stone.com/> and has spent 12 years writing Cocoa software in its various incarnations.

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

ClamXav 2.10 - Virus checker based on Cl...
ClamXav is a popular virus checker for OS X. I have been working on ClamXav for more than 10 years now, and over those years, I have invested a huge amount of my own time and energy into bringing... Read more
Tweetbot 2.4.4 - Popular Twitter client.
Tweetbot is a full-featured OS X Twitter client with a lot of personality. Whether it's the meticulously-crafted interface, sounds and animation, or features like multiple timelines and column views... Read more
Sierra Cache Cleaner 11.0.1 - Clear cach...
Sierra Cache Cleaner is an award-winning general purpose tool for macOS X. SCC makes system maintenance simple with an easy point-and-click interface to many macOS X functions. Novice and expert... Read more
Things 2.8.8 - Elegant personal task man...
Things is a task management solution that helps to organize your tasks in an elegant and intuitive way. Things combines powerful features with simplicity through the use of tags and its intelligent... Read more
Remotix 4.1 - Access all your computers...
Remotix is a fast and powerful application to easily access multiple Macs (and PCs) from your own Mac. Features Complete Apple Screen Sharing support - including Mac OS X login, clipboard... Read more
Airfoil 5.1.2 - Send audio from any app...
Airfoil allows you to send any audio to AirPort Express units, Apple TVs, and even other Macs and PCs, all in sync! It's your audio - everywhere. With Airfoil you can take audio from any... Read more
Firefox 49.0.1 - Fast, safe Web browser.
Firefox offers a fast, safe Web browsing experience. Browse quickly, securely, and effortlessly. With its industry-leading features, Firefox is the choice of Web development professionals and casual... Read more
Default Folder X 5.0.7 - Enhances Open a...
Default Folder X attaches a toolbar to the right side of the Open and Save dialogs in any OS X-native application. The toolbar gives you fast access to various folders and commands. You just click on... Read more
Safari Technology Preview 10.1 - The new...
Safari Technology Preview contains the most recent additions and improvements to WebKit and the latest advances in Safari web technologies. And once installed, you will receive notifications of... Read more
Pinegrow Web Designer 2.94 - Mockup and...
Pinegrow Web Designer is desktop app that lets you mockup and design webpages faster with multi-page editing, CSS and LESS styling, and smart components for Bootstrap, Foundation, Angular JS, and... Read more

3 reasons you need to play Kingdom: New...
Developed by a tag team of indie developers - Thomas "Noio" van den Berg and Marco "Licorice" Bancale - Kingdom is a vibrant medieval fantasy adventure that casts players as a king or queen who must expand their empire by exploring the vasts lands... | Read more »
JoyCity have launched a brand new King o...
Great news for all of you Game of Dice fans out there - JoyCity have just released a brand new limited edition pack with a really cool twist. The premise of Game of Dice is fairly straightforward, asking you to roll dice to navigate your way around... | Read more »
Burly Men at Sea (Games)
Burly Men at Sea 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: Burly Men at Sea is a folktale about a trio of large, bearded fishermen who step away from the ordinary to seek adventure. | Read more »
3 tips for catching the gnarliest waves...
Like a wave breaking on the shore, Tidal Rider swept its way onto the App Store charts this week settling firmly in the top 10. It’s a one-touch high score-chaser in which you pull surfing stunts while dodging seagulls and collecting coins. The... | Read more »
The beginner's guide to destroying...
Age of Heroes: Conquest is 5th Planet Games’ all new turn-based multiplayer RPG, full of fantasy exploration, guild building, and treasure hunting. It’s pretty user-friendly as far as these games go, but when you really get down to it, you’ll find... | Read more »
Infinite Tanks (Games)
Infinite Tanks 1.0.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0.0 (iTunes) Description: | Read more »
Agatha Christie - The ABC Murders (FULL)...
Agatha Christie - The ABC Murders (FULL) 1.0 Device: iOS Universal Category: Games Price: $6.99, Version: 1.0 (iTunes) Description: Agatha Christie: The ABC Murders Your weapon is your knowledge. Your wits will be put to the ultimate... | Read more »
HeadlessD (Games)
HeadlessD 1.0 Device: iOS Universal Category: Games Price: $.99, Version: 1.0 (iTunes) Description: HeadlessD is hand-painted dungeon crawler with intuitive touch controls and NO in-app purchases. | Read more »
Leaf for Twitter (Social Networking)
Leaf for Twitter 1.0.1 Device: iOS iPhone Category: Social Networking Price: $4.99, Version: 1.0.1 (iTunes) Description: | Read more »
Banner Saga 2 (Games)
Banner Saga 2 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: The epic award winning story-based role-playing game continues its emotional journey across a breaking world. Lead your Viking... | Read more »

Price Scanner via MacPrices.net

MacBook Airs on sale for up to $100 off MSRP
B&H Photo has 13″ and 11″ MacBook Airs on sale for up to $100 off MSRP. Shipping is free, and B&H charges NY sales tax only: - 11″ 1.6GHz/128GB MacBook Air: $799 $100 MSRP - 11″ 1.6GHz/256GB... Read more
Apple refurbished 12-inch 128GB iPad Pros ava...
Apple has Certified Refurbished 12″ Apple iPad Pros available for up to $160 off the cost of new iPads. An Apple one-year warranty is included with each model, and shipping is free: - 32GB 12″ iPad... Read more
Phone2Action Unveils New Voter Turnout Techno...
Phone2Action, a leading digital advocacy platform, today launched its Tech to Vote Civic Action Center digital advocacy and communications platform on National Voter Registration Day September 27.... Read more
Apple & Deloitte Team Up to Help Business...
Apple and international professional services firm Deloitte have announced a partnership to help companies quickly and easily transform their workflow dynamics by maximizing the power, ease-of-use,... Read more
Chop Commute – See Traffic and Drive Times on...
Shrewsbury, Massachusetts based Indie developer, InchWest has released Chop Commute 1.61, a Mac app that takes the guesswork out of daily commute by showing real-time traffic and drive times right on... Read more
12-inch 32GB WiFi iPad Pros on sale for $50 o...
B&H Photo has 12″ 32GB WiFi Apple iPad Pros on sale for $50 off MSRP, each including free shipping. B&H charges sales tax in NY only: - 12″ Space Gray 32GB WiFi iPad Pro: $749 $50 off MSRP -... Read more
Recent price drops on refurbished iPad minis...
Apple recently dropped prices on several Certified Refurbished iPad mini 4s and 2s as well as iPad Air 2s. An Apple one-year warranty is included with each model, and shipping is free: - 16GB iPad... Read more
Apple refurbished Mac minis available startin...
Apple has Certified Refurbished Mac minis available starting at $419. Apple’s one-year warranty is included with each mini, and shipping is free: - 1.4GHz Mac mini: $419 $80 off MSRP - 2.6GHz Mac... Read more
13-inch 2.5GHz MacBook Pro available for $928...
Overstock has the 13″ 2.5GHz MacBook Pro available for $927.99 including free shipping. Their price is $171 off MSRP. Read more
Buying McLaren Would Give Apple Instant Car C...
Apple “iCar” rumors have waxed and waned over the years, piquing interest and speculation as to whether Apple is seriously interested in getting into the automotobile business, either in a joint... Read more

Jobs Board

Lead *Apple* Solutions Consultant - Apple (...
# Lead Apple Solutions Consultant Job Number: 51829230 Detroit, Michigan, United States Posted: Sep. 19, 2016 Weekly Hours: 40.00 **Job Summary** The Lead ASC is an Read more
US- *Apple* Store Leader Program - Apple (Un...
…Summary Learn and grow as you explore the art of leadership at the Apple Store. You'll master our retail business inside and out through training, hands-on Read more
*Apple* Retail - Multiple Positions- Chicago...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
*Apple* Retail - Multiple Positions- Raleigh...
Job Description:SalesSpecialist - Retail Customer Service and SalesTransform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
User Support Specialist *Apple* Product Spe...
…Description:Ciber, Inc. is seeking a User Support Specialist - Apple Product Support in Nashville, TN!Responsibilities:Support, implementation, and upgrade of Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.