1. LECTURE 20: RECURSION CSC 212 – Data Structures

2. Humorous Asides

3. “A journey begins with a single step”

5.  Large problems hard to solve  Thinking about & solving small problems easier  Split large problems into smaller ones  Before you start coding, plan each assignment  Break up large methods with many if s and loops  Action in many methods into small (private) methods Solving Problems

6.  (At least for programming) Smaller is Better CENSORED

7.  Should be boring, monotonous drone  Given its parameters, perform the expected action  Only perform the action defined for its parameters  Should not cure cancer  Do not worry about the larger problem  This greater solution is not this method’s concern  Solving entire programming assignment is hard  Why we divide up tasks in the first place! Goal of a Java Method

8.  re-cur-sion: Method of solving problem by combining solutions to identical, smaller problems Recursion

9.  Keep dividing until base case(s) reached  Base cases are cases that are trivial to solve 4! = 4 * 3! = 4 * (3 * 2!) = 4 * (3 * (2 * 1!))  After base case, combine solutions to complete work = 4 * (3 * (2 * 1)) = 4 * (3 * 2) = 4 * 6 = 24 See Recursion Work

10.  Begin by figuring out what are the base case(s)  Simple subproblem that is solved immediately  A base case will always be reached solving problem  Recursive step can then be generated  Create easier problem(s) which splits original problem  Combine subproblems’ solutions for final answer Writing Recursive Solution

11.  Will your solution work?  Each step moves toward base case  All possible inputs must be considered  Otherwise, get infinite recursion Working Recursive Solutions

12.  A method is recursive if it calls itself: public static int factorial(int i) { if (i <= 1) { return 1; } else { return i * factorial(i - 1); } } Recursion in Java

13.  public method starts the recursive process  Usually only calls recursive method  private recursive method has 1+ parameter  Results should only depend on the parameters  if or switch selects from different cases  Using fields can avoid parameters…  … but not recursive approach to solving the problem  Cheating recursion with fields does not scale Designing Recursion

14.  Should have immediately check for base case(s)  Cannot have recursive calls within this code  Include 1+ method calls in recursive step(s)  Assume recursion works when writing these  Take 1 step toward base case (not 2, 3, or 10482) Writing Recursive Method

15.  Each call gets frame created for it  Within frame, place all local variables & parameters  (Real frames include line being executed)  Trace shows frames solving their single step  N O CURING CANCER Tracing Recursion X

16. private static void rev(int[] a, int j) { int opposite = a.length - (j + 1); if (j < opposite) { rev(a, j + 1); int temp = a[j]; a[j] = a[opposite]; a[opposite] = temp; } } public static void reverse(int[] a) { rev(a,0); } int[] example1 = { 0 }; reverse(example1); Trace This, Buddy!

17. private static void rev(int[] a, int j) { int opposite = a.length - (j + 1); if (j < opposite) { rev(a, j + 1); int temp = a[j]; a[j] = a[opposite]; a[opposite] = temp; } } public static void reverse(int[] a) { rev(a,0); } int[] example2 = { 0, 1, 2, 3, 4 }; reverse(example2); Trace This, Buddy!

18.  Divide array in two parts  First element & everything after  Last element & all preceding elements  Left & right halves of the array  Base case when working with 0 (or 1) entries Recursive Array Handling

19.  Complete week #7 assignment  Due by 5PM next Wednesday  Finish programming assignment #2  Due before next lecture (Wednesday)  Review sections 3.1-3.5 in book before class  How do linked lists, arrays & recursion work together?  How do they work? Before Next Lecture…