University of California, Berkeley
EECS Department - Computer Science Division

CS3 Lecture 8
Recursion ­ Patterns (cont'd)

Thanks to Oliver Grillmeyer and Brendan Ferguson for many of the ideas for these notes

Overview of today's lecture

• Answers to questions that have come up
• Review
• Recursion and Patterns (cont'd)
  • Tracing is a great tool to understand the process:
  • Continuation of patterns
  • That's not all the patterns you'll see
• Summary
• Next Time
• Puzzle : Socks in Drawers
• Game : Achi

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Answers to questions that have come up

• Didn't you once say "You almost never need to explicitly put #t or #f in your code so far"...what's the deal?
  • Recursion is one of the only class of problems where you need to put #t or #f explicitly into your code.

Review

• sum-0-to-n, which was our first instance of recursion not on sentences
• Resursive patterns : Can you see the similarities among several different problems?
• Mapping
  • square-all, which squares all the elements of a sentence?
  • Using HOFs: (define (square-all s)(every square s))
• Finding
  • member-even, which returns the rest of the sentence starting with the first even number, #f ottherwise.

Recursion and Patterns (cont'd)

Tracing is a great tool to understand the process:

• Usage: (trace function)
  • Trace a function (print out when it's called and what it returns)
• Usage: (untrace function)
  • Turn off the tracing of a function
• Examples:

: (define (my-count s)
    (if (empty? s)
        0
        (+ 1 (my-count (bf s)))))
my-count

: (trace my-count)
my-count

: (my-count '(cs3 is the best class))
Entry (my-count '(cs3 is the best class))
|Entry (my-count '(is the best class))
| Entry (my-count '(the best class))
|  Entry (my-count '(best class))
|  |Entry (my-count '(class))
|  | Entry (my-count '())
|  | ==> 0
|  |==> 1
|  ==> 2
| ==> 3
|==> 4
==> 5
5

: (untrace my-count)
my-count

: (my-count '(cs3 is the best class))
5

Continuation of patterns

• Counting (like count)
• Filtering (like keep)
• Testing (like all?)
• Combining (like accumulate)

That's not all the patterns you'll see

Almost all the recursive patterns which operate on sentences also operate on words, with slight to no modifications.

• You'll also see problems which don't really fall into one of the these patterns. E.g.:
• (downup 'scheme) ;; slowly eat away at the last of the sentence
  • ==> (scheme schem sche sch sc s sh sch sche schem scheme)
• (reverse 'scheme) ;; reverse the word / sentence
  • ==> emehcs
• Recursion that generates a sentence from a number, takes two sentences and combines them, etc.
• Numerical recursion (e.g., fib)

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Summary

• We finished up looking at recursion patterns, which are extremely useful when you are given a new recursion problem and have no idea where to begin.

Next Time

• As Ray Charles says (paraphrasing): Come on lemme see you shake your tail recursion

Puzzle : Socks in Drawers

• The lights are off in your bedroom, and you walk to your sock drawer which contains 10 black and 10 white socks.
• Your goal is to walk out of your pitch-dark room with a pair of matching socks to wear for the day.
• What is the fewest number of socks you must remove so that when you reach the light you will have a matching pair (of either white or black)?
• What if you wanted a matching pair of black socks, what's the minimum in that case?

Game : Achi ["Pentagames" by Pentagram, Fireside Publishing, 1990]

• Two players each have four counters and take it in turn to place one of them on any vacant point where the lines intersect.
• When all eight counters are on the grid, each player in turn moves one of his counters along a line to a vacant point in an attempt to get three in a row.
• The first player to do so is the winner.

WWW Maven: Dan Garcia (ddgarcia@cs.berkeley.edu) Send me feedback