Recursion: Making Big Problems Smaller

Recursion is a key concept in programming, and can be used to simplify code and create elegant solutions. It's also has a reputation of being a little hard to learn. I will show you that it is not as difficult as you think, and that you can take a formulaic approach to writing recursive functions. Doing so will allow you to solve big problems, by dividing them up into smaller, easier ones.

Transcript

1. Recursion Making Big Problems Smaller By Jeremy Lindblom @jeremeamia
2. – some sarcastic jerkface “ “ To understand recursion, you must understand recursion.
3. Why Should You Care? 1.  You’re Here! – You’re already here, so I’m guessing you are interested. 2.  Academics – Recursion is a key concept in computer science and mathematics. 3.  Career – Technical interviews often contain questions where recursive solutions are a good answer.
4. Why Should You Care? 4.  Open Source – A survey of 14 major PHP projects yielded more than 300 examples of recursive functions. 5.  Other Languages – Some languages in the functional programming paradigm rely solely on recursion for loops. 6.  Parallelization – Recursive functions are stateless and can be parallelized easier.
5. Takeaways ① Using recursion (when appropriate) can result in shorter, simpler code. ② Recursion allows you to solve the whole problem, by only solving part of the problem. Recursion: Making Big Problems Smaller
6. Hello! I'm @jeremeamia PHP Software Engineer at Co-author of the AWS SDK for PHP Co-organizer of the Seattle PHP User Group Zend Education Advisory Board for 5.5 exam
7. What exactly is recursion?
9. O RLY? K, THX!
10. O RLY? K, THX! And yes, I do see what you did there.
11. Recursion is easier to visualize, IMO.
16. Fractals Images created with math and recursion Mandelbrot
17. Sierpinski’s Triangle
18. Sierpinski’s Triangle
22. “I eat recursion for breakfast!”
23. PHP Hypertext Preprocessor
24. PHP Hypertext Preprocessor PHP Hypertext Preprocessor Hypertext Preprocessor
25. PHP Hypertext Preprocessor PHP Hypertext Preprocessor Hypertext Preprocessor PHP Hypertext Preprocessor Hypertext Preprocessor Hypertext Preprocessor
26. So… how about some code! (well, a little math first, actually)
27. Factorial — n!   20!  =  20  ×  19  ×  18  …  ×  2  ×  1   6!  =  720   5!  =  120   4!  =    24   3!  =      6  
28. Factorial — n!   20!  =  20  ×  19  ×  18  …  ×  2  ×  1  
29. Factorial — n!   20!  =  20  ×  19!  
30. Factorial — n!   20!  =  20  ×  19!   Hey look! Recursion!
31. Factorial — n!   n!  =  n  ×  (n-­‐1)!  
32. Factorial — n! n  ×      (n-­‐1)!  
35. Recursive Function Anatomy •  Base Case(s) •  Recursive Call(s) •  Problem Size Reduction
36. Anatomy: Base Case
37. Anatomy: Recursive Call
38. Anatomy: Reduce Problem Size
39. OK, but can’t you do that without recursion?
40. Anything you can do with recursion, you can also do without recursion. FYI
41. Iterative Factorial
42. Iterative solutions typically are faster and require less memory than recursive solutions. FYI
43. Iteration vs. Recursion Iterative Factorial Benchmark: ~4.25  µs   Result w/ large input: INF  
44. Iteration vs. Recursion Iterative Factorial Benchmark: ~4.25  µs   Result w/ large input: INF   Recursive Factorial Benchmark: ~10.50  µs   Result w/ large input: Seg  fault:  11  
45. Iteration vs. Recursion Iterative Factorial Benchmark: ~4.25  µs   Result w/ large input: INF   Recursive Factorial Benchmark: ~10.50  µs   Result w/ large input: Seg  fault:  11   Yep, that's a stack overflow
46. Not Impressed with Recursion?
47. How about another example?
48. Tree Traversal ABCDEFGH
49. Tree Traversal
50. Traversal: Base Case
51. Traversal: Recursive Call
52. Traversal: Reduce Size
53. OK, but can’t you do that without recursion?
54. Iterative Tree Traversal
55. Iteration vs. Recursion Iterative Traversal Benchmark: ~54  µs   Recursive Traversal Benchmark: ~39  µs   w00t!  FTW!  
56. Making Big Problems Smaller ① Using recursion (when appropriate) can result in shorter, simpler code. (that is sometimes faster, too) vs. Iterative (20 LOC) Recursive (9 LOC)
57. Making Big Problems Smaller ② Recursion allows you to solve the whole problem, by only solving part of the problem. This logic only prints 1 node!
58. Making Big Problems Smaller ② Recursion allows you to solve the whole problem, by only solving part of the problem. =
59. Recursion is… The Adjustable Crescent Wrench. No matter what the problem (nut/bolt) size is, you perform the same action.
60. Alright, I'm impressed now. Recursion is pretty cool, but…
61. Alright, I'm impressed now. Recursion is pretty cool, but… Do you have any practical examples?
62. General Examples •  Mathematical and geometric Series •  Tree/graph traversal – DOM/XML/array traversing/building – Directory structure traversing (-r) – Parsing computer languages – Resolving dependency graphs (DIC) •  “Divide-and-conquer” algorithms
63. Let's Use "Recursed"
64. Recursive Methods in Your Phavorite Projects •  ZF2: 50+ •  Symfony: 75+ •  Laravel 4: 8+ •  Guzzle 3: 8+ •  Wordpress: 100+ •  Drupal 8: 25+ •  Joomla: 50+ •  Monolog: 2 •  Twig: 10+ •  SwiftMailer: 7+ •  PHPParser: 10+ •  AWS PHP SDK: 1+ •  Doctrine: 7+ •  CodeIgniter: 35+
65. Example 1 – WordPress
66. Example 2 – ZF2 Mail
67. Example 3 – Laravel Container
68. Takeaways ① Using recursion (when appropriate) can result in shorter, simpler code. ② Recursion allows you to solve the whole problem, by only solving part of the problem. Recursion: Making Big Problems Smaller
69. Recursion Making Big Problems Smaller By Jeremy Lindblom @jeremeamia https://joind.in/10803