Held: Tuesday, 27 October 2015

Back to Outline 30 - Other Forms of List Recursion. On to Outline 32 - Naming Local Procedures.

Summary

We visit a slightly different kind of recursion, numeric recursion. In this technique, we once again have procedures call themselves. However, the parameter that we "simplify" at every step is a number, rather than a list.

Related Pages

• Reading: Numeric Recursion
• Lab: Numeric Recursion
• EBoard 31 (Source 31)

Overview

• Recursion, generalized.
• Numeric recursion.

Administrivia

• Continue partners.
• Still some pre-lab stuff this week.
• Review sessions this week
  • Wednesday 8pm (Caleb)
  • Thursday 10am (SamR)
  • Thursday 8pm (Erin)
• If you don't finish a lab or lab writeup in class, you do not need to finish lab writeups with your partners (but it's nice to try to do so).

Upcoming Work

• Reading for Wednesday: Naming Local Procedures
• Quiz Friday: Recursion, Recursion, and more Recursion
• HW 6 is ready.
  • We'll look at a few issues.
  • Pick your own partners (or work alone)!
• Today's Lab writeup (due before class Friday)
  • Email to grader-151-01@cs.grinnell.edu
  • Subject: CSC 151 Lab Writeup Class 31 (Your Names)
  • Exercises:

Extra Credit Opportunities

• If possible, send me these in advance.

Academic

• Any visit to the current show in the Faulconer gallery.
• Any of the Grinnell Prize Week Activities this week.
• CS Table Tuesday: Hear about the Grace Hopper Celebration of Women in Computing.
• Grinnell Town Hall Wednesday at noon: Self-Gov.
• Conversation about Study Abroad at AIT in Hungary: Wednesday at 4:15 in 3821.
• Convocation Thursday at 11: Contesting Muhammad: Contermporary Controversies in Historical Perspective
• CS Extras Thursday at 4:15pm in 3821: Algorithms for Assembling the Tree of Life.
• What's the Deal with the Digital Liberal Arts? Thursday at 4:15 in the D-Lab. With Autumnal snacks!
• Sexual Misconduct at Grinnell College: Results from the 2013 and 2015 Sexual Conduct Surveys. 1-3 pm, November 8, JRC 101.
• R.L. Stephens II events Thursday and Friday.

Peer Support

• YZ on "Rainbow Ramsey Theory" Tuesday at 11 a.m. 2517.
• Thursday at 7pm, Womens BBall (scrimmage)
• Spark Tank, Wednesday, 7pm in Roberts Theatre in Bucksbaum.
• Pals of PALS, pals@grinnell.edu, normally Saturday at 7:45 am (breakfast included), Sunday at 4:45, and Mondays at 4:45. Requires sign up in advance.
• Pun Club, Saturdays, 4pm, Way over Younker.

Upcoming Peer Support

• Women's Basketball Opening Game, 1pm, Nov. 15, vs. Silver Lake.
• One-act Festival Dec. 5 & 6.

Good Things to Do, No EC

• 8:30 p.m. tonight in Loose Lounge: Campus Conversation on Healthy and Unhealthy Relationship Dynamics

Patterns of Recursion

While we've seen and written a variety of examples of direct recursion, they typically have the following form:

(define RECURSIVE-PROC
  (lambda (PARAMS)
    (if (BASE-CASE-TEST)
        (BASE-CASE PARAMS)
        (COMBINE (PART-OF PARAMS)
                 (RECURSIVE-PROC (SIMPLIFY PARAMS))))))

For lists, the simplification was almost always "take the cdr" and the "part-of" was almost always "take the car".

Recursion with Numbers

• While most of the recursion we've been doing has used lists as the structure to recurse over, you can recurse with many different kinds of values.
• It is fairly common to recurse using numbers.
• The natural base cases for integers are when you hit 0 or when you hit 1.
• The natural simplification step for recursive procedure using numbers calls typically involves subtracting 1 from the argument.
  • Other simplifications, such as dividing in half, are also possible.

Lab

• Do the lab