1. 1 Foundations of Software Design Fall 2002 Marti Hearst Lecture 14: Intro to Recursion

2. 2 Recursion An algorithmic technique in which a function, in order to accomplish a task, calls itself with some part of the task.

3. 3 Recursion A method that invokes itself Examples: –GNU stands for: GNU’s Not Unix (part of its own definition!) –A dog is a Collie if its name is Lassie or its mother was a Collie. Start with a given dog. Is its name Lassie? If so, done. Else is its mother a Collie? –Is the mother named Lassie? If so, done. –Else is its mother a Collie? –… and so on.

4. 4 Recursion Example Let’s illustrate with a mother-child relationship. Definition: A dog is a collie if its name is Lassie or if its mother is Lassie, or if its mother’s mother is Lassie, or … if any of its female ancestors is Lassie. public class Dog { public String name; public Dog mother; Dog () { name = “Lassie”; mother = null; } Dog (String s, Dog d) { name = s; mother = d; } public static void main(String s[]) { Dog lassie = new Dog(); Dog fido = new Dog(“Fido”,lassie); Dog fifi = new Dog(“Fifi”, fido); Dog rover = new Dog(“Fover”, fifi); Dog grover = new Dog(“Grover”, fifi); if (grover.isCollie(grover)) { System.out.println(grover.name + “ is a collie.”); } else { System.out.println(grover.name + “ is not a collie.”); }

5. 5 Recursion public boolean isCollie (Dog d) { if (d == null) { return false; } if (d.name == “Lassie”) { return true; } return isCollie(d.mother); } base cases recursive call: note that the argument to the function has to refine the problem A method that calls itself –A kind of iteration – Recursive methods need: A base case / terminating condition (or else it doesn’t halt) A body (containing the recursive call)

6. 6 Recursion & the Runtime Stack Each call of the recursive method is placed on the stack. When we finally reach the base case, all the frames are popped off of the stack. –Say Grover’s mother is Fifi Rover’s mother is Fifi too Fifi’s mother is Fido Fido’s mother is Lassie –Call the isCollie() method starting with Grover Push the frame associated with each dog’s method call on the stack When we reach Lassie, we return “true” This value gets passed as the result from the 4 th frame to the 3 rd frame The 3 rd frame passes this to the 2 nd frame The 2 nd frame passes this to the 1 st frame And “true” is the final result.

7. 7 From Goodrich & Tamassia

8. 8 Recursion vs. Iteration adding up consecutive integers

9. 9 Illustrated Output

10. 10 Methods and the Java VM Stack Each time a method is called –A new copy of the method’s data is pushed on the JVM stack This data includes local variables –This applies to all methods, not only recursive ones The “return” command does two things: –Pops the data for the method off the stack Local variables disappear –Passes the return value to the calling method If there is no return statement –The method is popped –Nothing is passed to the calling method

11. 11 Recursion & the Java VM Stack First time called –Push a stack frame with n=12 –This won’t complete until after the recursive call returns Second time called –Push a stack frame with n=11 –… and so on

12. 12 Recursion & the Java VM Stack When a frame is pushed with n==0 –The frame is popped –The value returned is 0 –This is sent to the frame in which n==1 –It can now add the 0 to n –… and so on

13. 13 Recursion vs. Loops We could use recursion as an alternative to a loop for our various summation problems. This does not reduce (or increase) the O(g(n)) of the problem. public static int gaussianSum (int n) { if (n <= 1) return 1; else return n + gaussianSum(n-1); }

14. 14 Recursion Example: Drawing Fractals This is from Main CH. 8 Main Idea: –Drawing a line of a given length –Divide the line in half, and Recursively draw the line in a certain way –Boring version: Draw the half as a horizontal line –Interesting version: Choose random numbers to determine the Y coordinates, but ensure that the halves all hook up.

15. 15 Setting up Boring Fractal

16. 16 Recursive Part of Boring Fractal

17. 17 Output of Boring Fractal

18. 18 Setting up Random Fractal (nearly the same as for Boring Fractal)

19. 19 Recursive Part of Random Fractal

20. 20 Output of Random Fractal (1)

21. 21 Output of Random Fractal (2)

22. 22 Summary: Recursion Recursion is a useful problem-solving technique –We will see it again when we study trees and sorting But it takes some getting used to. To help: –Study the Main chapter (quite well-written) –Remember that each method call gets put on the stack until the base case is found; then the calls are popped off the stack. –You HAVE TO understand basic programming concepts like Method calls Returning from methods Passing parameters (formal vs actual parameters)