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

Sound Studio 4.8.6 - Robust audio record...
Sound Studio lets you easily record and professionally edit audio on your Mac. Easily rip vinyls and digitize cassette tapes, or record lectures and voice memos. Prepare for live shows with live... Read more
Capo 3.5.1 - Slow down and learn to play...
Capo lets you slow down your favorite songs so you can hear the notes and learn how they are played. With Capo, you can quickly tab out your songs atop a highly-detailed OpenCL-powered spectrogram... Read more
Google Earth 7.1.8.3036 - View and contr...
Google Earth gives you a wealth of imagery and geographic information. Explore destinations like Maui and Paris, or browse content from Wikipedia, National Geographic, and more. Google Earth combines... Read more
QuickBooks 16.1.11.1556 R12 - Financial...
QuickBooks helps you manage your business easily and efficiently. Organize your finances all in one place, track money going in and out of your business, and spot areas where you can save. Built for... Read more
Google Earth 7.1.8.3036 - View and contr...
Google Earth gives you a wealth of imagery and geographic information. Explore destinations like Maui and Paris, or browse content from Wikipedia, National Geographic, and more. Google Earth combines... Read more
QuickBooks 16.1.11.1556 R12 - Financial...
QuickBooks helps you manage your business easily and efficiently. Organize your finances all in one place, track money going in and out of your business, and spot areas where you can save. Built for... Read more
FileZilla 3.24.0 - Fast and reliable FTP...
FileZilla (ported from Windows) is a fast and reliable FTP client and server with lots of useful features and an intuitive interface. Version 3.24.0: New The context menu for remote file search... Read more
Bookends 12.7.8 - Reference management a...
Bookends is a full-featured bibliography/reference and information-management system for students and professionals. Bookends uses the cloud to sync reference libraries on all the Macs you use.... Read more
Duplicate Annihilator 5.8.3 - Find and d...
Duplicate Annihilator takes on the time-consuming task of comparing the images in your iPhoto library using effective algorithms to make sure that no duplicate escapes. Duplicate Annihilator detects... Read more
BusyContacts 1.1.6 - Fast, efficient con...
BusyContacts is a contact manager for OS X that makes creating, finding, and managing contacts faster and more efficient. It brings to contact management the same power, flexibility, and sharing... Read more

Super Mario Run dashes onto Android in M...
Super Mario Run was one of the biggest mobile launches in 2016 before it was met with a lukewarm response by many. While the game itself plays a treat, it's pretty hard to swallow the steep price for the full game. With that said, Android users... | Read more »
WarFriends Beginner's Guide: How to...
Chillingo's new game, WarFriends, is finally available world wide, and so far it's a refreshing change from common mobile game trends. The game's a mix of tower defense, third person shooter, and collectible card game. There's a lot to unpack here... | Read more »
Super Gridland (Entertainment)
Super Gridland 1.0 Device: iOS Universal Category: Entertainment Price: $1.99, Version: 1.0 (iTunes) Description: Match. Build. Survive. "exquisitely tuned" - Rock Paper Shotgun No in-app purches, and no ads! | Read more »
Red's Kingdom (Games)
Red's Kingdom 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: Mad King Mac has kidnapped your father and stolen your golden nut! Solve puzzles and battle goons as you explore and battle your... | Read more »
Turbo League Guide: How to tame the cont...
| Read more »
Fire Emblem: Heroes coming to Google Pla...
Nintendo gave us our first look at Fire Emblem: Heroes, the upcoming mobile Fire Emblem game the company hinted at last year. Revealed at the Fire Emblem Direct event held today, the game will condense the series' tactical RPG combat into bite-... | Read more »
ReSlice (Music)
ReSlice 1.0 Device: iOS Universal Category: Music Price: $9.99, Version: 1.0 (iTunes) Description: Audio Slice Machine Slice your audio samples with ReSlice and create flexible musical atoms which can be triggered by MIDI notes or... | Read more »
Stickman Surfer rides in with the tide t...
Stickson is back and this time he's taken up yet another extreme sport - surfing. Stickman Surfer is out this Thursday on both iOS and Android, so if you've been following the other Stickman adventures, you might be interested in picking this one... | Read more »
Z-Exemplar (Games)
Z-Exemplar 1.4 Device: iOS Universal Category: Games Price: $3.99, Version: 1.4 (iTunes) Description: | Read more »
5 dastardly difficult roguelikes like th...
Edmund McMillen's popular roguelike creation The Binding of Isaac: Rebirth has finally crawled onto mobile devices. It's a grotesque dual-stick shooter that tosses you into an endless, procedurally generated basement as you, the pitiable Isaac,... | Read more »

Price Scanner via MacPrices.net

12-inch 1.2GHz Space Gray Retina MacBook on s...
Amazon has the 2016 12″ 1.2GHz/512GB Space Gray Retina MacBook (Apple model #MLH82LL/A) on sale for $1299.99 including free shipping. Their price is $300 off MSRP. Read more
Twelve South Releases RelaxedLeather Cases fo...
Inspired by the laid-back luxury of burnished leather boots and crafted in rich tones of taupe, herb and marsala, RelaxedLeather cases deliver smart, easy protection for the iPhone 7. Each genuine... Read more
Week’s Best Deal: New 2016 13-inch 2.0GHz Mac...
Amazon has the new 2016 13″ 2.0GHz non-Touch Bar MacBook Pros on sale for a limited time for $225 off MSRP including free shipping: - 13″ 2.0GHz MacBook Pro, Space Gray (MLL42LL/A): $1274.99 $225 off... Read more
Back in stock: Apple refurbished Mac minis fr...
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
Apple Ranked ‘Most Intimate Brand’
The top ranked ‘”intimate” brands continued to outperform the S&P and Fortune 500 indices in revenue and profit over the past 10 years, according to MBLM’s Brand Intimacy 2017 Report, the largest... Read more
B-Eng introduces SSD Health Check for Mac OS
Fehraltorf, Switzerland based independant Swiss company- B-Eng has announced the release and immediate availability of SSD Health Check 1.0, the company’s new hard drive utility for Mac OS X. As the... Read more
Apple’s Education discount saves up to $300 o...
Purchase a new Mac or iPad using Apple’s Education Store and take up to $300 off MSRP. All teachers, students, and staff of any educational institution qualify for the discount. Shipping is free: -... Read more
4-core 3.7GHz Mac Pro on sale for $2290, save...
Guitar Center has the 3.7GHz 4-core Mac Pro (MD253LL/A) on sale for $2289.97 including free shipping or free local store pickup (if available). Their price is a $710 savings over standard MSRP for... Read more
128GB Apple iPad Air 2, refurbished, availabl...
Apple has Certified Refurbished 128GB iPad Air 2s WiFis available for $419 including free shipping. That’s an $80 savings over standard MSRP for this model. A standard Apple one-year warranty is... Read more
13-inch 2.7GHz Retina MacBook Pro on sale for...
B&H Photo has the 2015 13″ 2.7GHz/128GB Retina Apple MacBook Pro on sale for $100 off MSRP. Shipping is free, and B&H charges NY tax only: - 13″ 2.7GHz/128GB Retina MacBook Pro (MF839LL/A): $... Read more

Jobs Board

*Apple* macOS Systems Integration Administra...
…most exceptional support available in the industry. SCI is seeking an Junior Apple macOS systems integration administrator that will be responsible for providing Read more
*Apple* Retail - Multiple Positions- Deer Pa...
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 - Apple,...
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* Technician - nfrastructure (United S...
Let’s Work Together Apple Technician This position is based in Portland, ME Life at nfrastructure At nfrastructure, we understand that our success results from our Read more
*Apple* Mobile Master - Best Buy (United Sta...
**467692BR** **Job Title:** Apple Mobile Master **Location Number:** 000602-Columbia MO-Store **Job Description:** **What does a Best Buy Apple Mobile Master Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.