Understanding Recursive Solutions in Programming

1. Problem of the Day • At what times do the minute and hour hands on an analog clock line up?

2. Problem of the Day • At what times do the minute and hour hands on an analog clock line up?

3. Lecture 21:Writing Recursive Solutions

4. Recursion re-cur-sion:Solving problems by breaking into identical, smaller problems andcombining solutions after base case(s) reached.

5. See Recursion Work • Recursive stepsimplifies problem to base case(s) • Recast using slightly easier version in recursive step4! = 4 *3! = 4 *(3 * 2!) = 4 * (3 * (2 * 1!)) • Base case(s) handle and solve obvious cases = 4 * (3 * (2 * 1)) • Solve in recursive step using results from base case= 4 * (3 * 2) = 4 * 6 = 24

6. Writing Recursive Code • No different than usual coding had been doing • At some point, recursive method calls itself • Parameters & locals in frame & so specific to each call • Once complete, execution returns to calling frame NOT

7. Starting Recursive Solution • Identify obvious solution needing little/no work • Should only need one or two operations to identify • Simple return statement(s) with literal or no value • Consider every input: can have many base case(s) • If you cannot determine, stop immediately • There are many problems without recursive solutions

8. Example Base Case(s) • Range of indices leaves 0 or 1 entries in array • If specific item searched for in array, stop at 0 entries • 1 entry used as base casewhen each item will be used • At last Node or null reference in Linked List • Just like with arrays, base case(s)are comparable • int reaches 0if working linearly through data • If multiplying int each pass, base caseat 1 • 0 or 1 characters left in a String

9. Starting Recursive Step • Determine state calling each of the base case(s) • These cases also easy to solve using base case result • Must be one step away from reaching base case(s) • Stand-alone base case may not have prior state • Identify single step advancing toward base case • Coding much easier when same step used in all cases • Know when each is used if different steps needed

10. Consider All Possible Inputs • Determine how to solve within recursive steps • Must check that solution works for all possible inputs • For each input you examine, must consider • Check that recursive call moves toward base case • No conflicting recursive steps that cycle within space

11. Consider All Possible Inputs • Determine how to solve within recursive steps • Must check that solution works for all possible inputs • For each input you examine, must consider • Check that recursive call moves toward base case • No conflicting recursive steps that cycle within space

12. Next to Last Step • Examine how method combines recursive result • No result for somerecursive solutions, so can skip this • Some other recursive solutions just return result • Others require even more work to be performed • When using recursion, fairly simple actions required • If many or complex actions required, then… • First ask yourself: is this solution actually recursive? • Could it be more recursive & simpler is next question

13. Last Step • Do not want to be locked into recursive solution • May need extra parameter to work correctly • Public method only has required parameters • Linked list instance or array to be processed • User is interested in testing some value • Use private method to hold the extra variable • Value or array index where method currently working • Node in linked listto be processed by method • Range or indices where method starts & stops

14. Check It Out public static intfindSum(int[] a) { }

15. Check It Out publicstatic intfindSum(int[] a) {return findSum(a, 0); } privatestatic intfindSum(int[] a, int j) { }

16. Check It Out publicstatic intfindSum(int[] a) {return findSum(a, 0); } privatestatic intfindSum(int[] a, int j) { if (j == a.length - 1) { return a[j];} }

17. Check It Out publicstatic intfindSum(int[] a) {return findSum(a, 0); } privatestatic intfindSum(int[] a, int j) { if (j == a.length - 1) { return a[j];} else {intnextJ = j + 1;} }

18. Check It Out publicstatic intfindSum(int[] a) {return findSum(a, 0); } privatestatic intfindSum(int[] a, int j) { if (j == a.length - 1) { return a[j];} else {intnextJ = j + 1;intsumRemain = findSum(a, nextJ);} }

19. Check It Out publicstatic intfindSum(int[] a) {return findSum(a, 0); } privatestatic intfindSum(int[] a, int j) { if (j == a.length - 1) { return a[j];} else {intnextJ = j + 1;intsumRemain = findSum(a, nextJ);intmyData = a[j]; return myData + sumRemain;} }

20. Your Turn • Get into your groups and complete activity

21. For Next Lecture • Read GT5.1 – 5.1.1, 5.1.4, 5.1.5 for next class • What is an ADT and how are they defined? • How does a Stack work? • Also available is week #8 weekly assignment • Programming assignment #1 also on Angel • Pulls everything together and shows off your stuff • Better get moving on it, since will be due within week