Mastering Recursion: Programming Fundamentals in Java

1. COP 3503 FALL 2012ShayanJavedLecture 17 Programming Fundamentals using Java

2. Recursion

3. Definition • Method where: Solution to a problem depends on solutions of smaller instances of the same problem.

4. Example: Merge Sort Split Now Sort and Merge

5. Recursive Function • A function which calls itself to solve a problem. • Alternative to iterative solutions • Most programming languages support recursion • Some only support recursion (Functional languages)

6. Problems solved by Recursion • Mathematical problems (Factorial, Fibonacci sequence, etc.) • Searching and sorting algorithms (binary search, merge sort, etc.) • Traversing file systems • Traversing data structures (linked lists, trees) • Etc…

7. Defining a Recursive Function 1. When does the recursion stop? • Have to stop at some point otherwise you’ll run into problems • Also known as the “base case” 2. Repeat the process by calling the function again

8. Defining a Recursive Function Example: intrecursiveMethod(parameters) { if (baseCase) returnsomeValue; else returnrecursiveMethod(modifiedParameters); }

9. Fibonacci sequence A sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … How would you implement this recursively?

10. Fibonacci sequence intfibonacci(int n) { if (n == 0) return 0; else if (n == 1) return 1; else returnfibonacci(n-1) + fibonacci(n-2); }

11. Fibonacci sequence How would you implement this iteratively? (Using loops) intfibonacci(int n) { int fn1 = 0, fn2 = 1; intprev; for(inti = 0; i < num; i++) { prev = fn1; fn1 = fn2; fn2 = fn2 + prev; } return fn1; } Let’s run both

12. Fibonacci sequence • Recursive version seems to be much slower. • Why? • What happens when a function call is made?

13. Function calls • When a method is called: • The method reference and arguments/parameters are pushed onto the calling method’s operand stack • A new stack frame is created for the method which is called. Contains variables, operand stack, etc. for it. • Stack frame is pushed onto the Java Stack. • When method is done, it is popped from the Java Stack.

14. Function calls Java Stack Approximation after calling fibonacci(2): 1 is returned to Main fib(2) Main Main fib(0) 0 1 1 fib(1) fib(2) fib(2) fib(2) 1 Main Main Main Main

15. Function calls • Program counters have to be updated, local variables, stacks, method references, etc. • So a lot of work is done when methods are called. • Imagine calling fibonacci(1000). • Results in “stack overflow” (no available memory on the call stack)

16. Recursion • Advantages: • Very simple to write • Programs are short • Sometimes recursion is the only option • Disadvantages: • Extra storage required • Slow

17. More Examples Iterative version of Binary Search: intbinarySearch(int[] array, int key, int left, int right){ while (left <= right) { int middle = (left + right)/2; // Compute mid point if (key < array[mid]) { right = mid-1; // repeat search in bottom half } else if (key > array[mid]) { left = mid + 1; // Repeat search in top half } else { return mid; // found! } } return -1; // Not found } How would you implement recursively?

18. Binary Search • Identify base case first • When do we stop? • When do you repeat?

19. Binary Search intbinarySearch(int[] array, int key, int left, int right) { if (left > right) // base case 1: not found return -1; int mid = (left + right)/2; // Compute mid point if (key == array[mid]) // base case 2: found! return middle; else if (key < array[mid]) // repeat search in upper half returnbinarySearch(array, key, left, mid-1); else // lower half returnbinarySearch(array, key, mid, right); }

20. File Systems • What happens when you run this command in Linux? rm –r * • Recursively (“-r”) goes through every file in the directory and sub-directories and deletes it. • Has to use recursion

21. File Systems • How do you think the program “rm” is implemented? • Probably something like this (pseudocode): function rm(directory): File[] files = directory.getAllFiles(); for each file in files: if (file is directory) rm(file); else delete file;

22. Summary • Recursion is useful for writing simple programs. • Alternative to iterative solutions, but slower and requires more space. • Some solutions require recursion (file directory traversal)