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Recursion CSSE 221 Fundamentals of Software Development Honors Rose-Hulman Institute of Technology Announcements Exam Wednesday, Oct 23 & Friday, Oct 25 Sample exam is posted on Moodle We think Markov Chains are used in the

  1. Recursion CSSE 221 Fundamentals of Software Development Honors Rose-Hulman Institute of Technology

  2. Announcements • Exam Wednesday, Oct 23 & Friday, Oct 25 – Sample exam is posted on Moodle • We think Markov Chains are used in the SwiftKey smartphone app. – http://www.swiftkey.net/

  3. If you don't have a base case for your recursion, it can become a nightmare!

  4. Recursion • What is a recursive method? • A method that calls itself, but on a simpler problem • Used for any situation where parts of a whole look like mini versions of the whole: – Folders within folders on computers – Some computer languages (Scheme) – Trees in general • Cons: Takes more space (but time can be roughly equal; it depends) • Pros: Can gives code that’s very easy to understand

  5. Recursion template • For a method that calculates a value: int foo(int n) { if (n <=1) { //Base case return (some easy expression); } else { return (some expr. with foo(n-1); //not just foo(n)) so progress } Of course, you can write void recursive methods, and ones that recurse on values other than n-1

  6. Four Rules of Recursion 1. Base case – You need at least 1 base case that can be solved without recursing 2. Progress – You can only recurse on a simpler problem 3. “You gotta believe” – Otherwise, you’ll try to solve the problem both recursively and non-recursively. This is bad. 4. Compound interest rule – Ef fi ciency: Don’t duplicate work by solving the same instance of the problem in separate recursive calls – Later

  7. Demo

  8. Let’s watch in the debugger • Checkout Recursion project • Navigate to memoization package. • Let's look at stack trace for Fibonacci. fi b() • What if missing base case?

  9. What else can we do recursively? • gcd(a,b): //assumes a > b – if a is a multiple of b, return b – Otherwise, return gcd(b, a % b) (guaranteed to be smaller) • myPow(x, a) • Program this now • Contest: Which table can write a version with the shallowest call stack?

  10. Break

  11. “Memoization” • What if I wish to speedup the calculation of fi b(n)? • Can I do this any faster with recursion? • What is memoization? • How can I use memoization to speedup calculation?

  12. Mutual Recursion • Two or more methods that call each other repeatedly – For example, Hofstadter Female and Male Sequences – Burning Questions for you to fi gure out now by coding: • How often are the sequences different in the fi rst 50 positions? fi rst 500? fi rst 5,000? fi rst 5,000,000? • This is part of the homework

  13. Two Mirrors If you actually do this, what really happens is Douglas Hofstadter appears and talks to you for eight hours about strange loops.

  14. A graphical exercise on recursion • Sierpinski’s Triangle… – http://www.shodor.org/interactivate/activities/ SierpinskiTriangle/ • See starting code in the repository. • How can you use recursion to solve this problem? – Discuss with a partner • You may pair-program this if you want • Fun extensions: – Add color – Play with non-equilateral triangles

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