CSC 151 2019S, Class 22: Recursion with helper procedures

Overview

• Preliminaries
  • Notes and news
  • Upcoming work
  • Extra credit
  • Spring break PSA
  • Questions
• Quiz
• Lab

Preliminaries

News / Etc.

• Mentor sessions Wednesday 8-9 p.m., Thursday 8-9 p.m., Sunday 5-6 p.m.
  • No mentor session the Sunday at the end of break.
• I was sorry to see so few of you at Convocation yesterday. It was one of the best ones that I’ve been to in recent years.
• I expect to have grading completed by the end of spring break.

Upcoming work

• No reading for Monday after break.
• Lab writeup: TBD.

Extra Credit

I would certainly appreciate suggestions of other extra credit activities (preferably via email).

Extra credit (Academic/Artistic)

Extra credit (Peer)

• Grinnell Singers, St. Paul Saturday, Rochester Sunday, …
• Women’s Golf, Amelia Island, last Sunday of spring break.
• Track and Field, Emory University, last weekend of spring break.

Extra credit (Wellness)

• Sub-free spring break

Extra credit (Wellness, Regular)

• 30 Minutes of Mindfulness at SHACS every Monday 4:15-4:45
• Any organized exercise. (See previous eboards for a list.)
• 60 minutes of some solitary self-care activities that are unrelated to academics or work. Your email reflection must explain how the activity contributed to your wellness.
• 60 minutes of some shared self-care activity with friends. Your email reflection must explain how the activity contributed to your wellness.

Extra credit (Misc)

Other good things

Spring break PSA

• Relax. Enjoy time away from Grinnell.
• Moderation in everything (or almost everthing; catching up on sleep is fine)
• Consent is essential.

Questions

A few of us traded names this morning. Will that effect the quiz?

For the quiz, you must use the name you have been using for the earlier part of the semester.

Quiz

Quick summary of the reading

We’ve been talking about recursion and have a basic model of recursion.

• You have your base case (and a base-case test)
• You also have a recursive case which consists of
  • A simplification procedure (e.g., cdr)
  • A recursive call
  • A combination/postprocessing

(define proc
  (lambda (lst)
    (if (null? lst)
        base-case
        (combine (car lst) (proc (cdr lst))))))

(define product
  (lambda (lst)
    (if (null? lst)
        1
        (* (car lst) (product (cdr lst))))))

(define product 
  (lambda (lst)
    (if (singleton? lst)
        (car lst)
        (* (car lst) (product (cdr lst))))))

Detour: What’s going on with nested tick marks (nested quotes)?

• 'thing is a shorthand for (quote thing)
• (quote thing) is a keyword that says “take this thing as is, without evaluating it”
• (quote 5) is 5
• (quote sam) is 'sam
• (quote '(1 2 3)) is a three-element list

> (quote 5)
5
> (quote sam)
'sam
> (quote (1 2 3))
'(1 2 3)
> (quote (1 (+ 2 3) 4))
'(1 (+ 2 3) 4)
> (list? (list-ref (quote (1 (+ 2 3) 4)) 1))
#t
> (list? (list-ref (quote (1 (quote a) 2)) 1))
#t
>  (list-ref (quote (1 (quote a) 2)) 1)
''a
> '(quote a)
''a
> (list-ref '(1 'a 2) 1)
''a
> (quote (and a))
'(and a)
> (quote (quote a))
''a
> (list? (quote (quote a)))
#t

The moral? Don’t nest tick marks. It makes everbody’s brain hurt.

</detour>

Back to recursion.

Observation: Sometimes we want to keep track of extra values while recursing. E.g., reversing a list.

remaining       so-far
---------       ------
'(a b c)        '()
  cdr             cons
'(b c)          '(a)
  cdr             cons
'(c)            '(b a)
  cdr             cons
'()             '(c b a)

Let’s try expressing that in Scheme. Is this correct?

(define rev
  (lambda (lst)
    (if (null? lst)
        null
        (cons (car lst) (rev (cdr lst))))))

This does not work. In fact, our model of thinking through the problem suggests we need two parameters, rather than one. But reverse should only have one parameter.

(define rev
  (lambda (lst)
    (rev-kernel lst '())))

(define rev-kernel
  (lambda (remaining reversed-so-far)
    (if (null? remaining)
        reversed-so-far
        (rev-kernel (cdr remaining)
                    (cons (car remaining) reversed-so-far)))))

It can be helpful to put in a call to display.

(define rev
  (lambda (lst)
    (rev-kernel lst '())))

(define rev-kernel
  (lambda (remaining reversed-so-far)
    (display (list 'kernel remaining reversed-so-far)) (newline)
    (if (null? remaining)
        reversed-so-far
        (rev-kernel (cdr remaining)
                    (cons (car remaining) reversed-so-far)))))

Lab

No writeup! It’s break.