CS3 Week 8: Recursion

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CS3Week 8 Recursion
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Midterm 1

• You did great
• If you need a re-grade, see the person that
  graded that question
• Solutions are available on the portal (check
  announcements).

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Question 1

• Shotgun questions
• ( 3 x 5) may not cause an error
• ( 3 'fred 5) will

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Question 2

• add-em
• (add-em '(1 4 2 0 934 -3 5)) ? 7
• The conditional was tricky here
• Needed to check for 3 things to get sent to the
  base case

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Question 3

• ranking cards
• Scores are all over the place (hallmark of a bad
  question)
• Accessors!

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Question 4

• day-span
• Question 4c the short answers was a good one
  (I think).
• Some had trouble deciding between
• conditional ,
• the base case,
• making the problem smaller,
• calling the function recursively
• combining the recursive calls.

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Question 5

• coins
• Nice!

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Schedule
Oct 3 Midterm 1
Oct 10 Advanced recursion
Oct 17 Number-spelling Miniproject
Oct 24 Higher order procedures
Oct 31 More HOF Lists! (instead of sentences and words)
Nov 7 Recursion (advanced)
Nov 14 Midterm 2
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Problem find all the even numbers insentence of
numbers

• (define (find-evens sent)
• (cond ( base case
• )
• ( rec case 1 odd
• )
• ( rec case 2 even
• )
• ))

(define (find-evens sent) (cond ((empty? sent)
base case '() )
((odd? (first sent)) rec case 1
(find-evens (bf sent)) ) (else
rec case 2 even (se (first sent)
(find-evens (bf sent))) ) ))
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gt (find-evens '(2 3 4 5 6))
sent ( 2 3 4 5 6 )
(se 2
sent ( 3 4 5 6 )
sent ( 4 5 6 )
(se 4
sent ( 5 6 )
sent ( 6 )
(se 6
sent ( )
()

• (se 2 (se 4 (se 6 ())
• (2 4 6)

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Why is recursion hard?

• ONE function
• replicates itself,
• knows how to stop,
• knows how to combine the replications
• There are many ways to think about recursion you
  absolutely do not need to understand all of them.
• "down-up" recursion as an extension of writing
  many specific functions
• "many base cases" recursion as using a clone,
  once you have many base cases

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Patterns in recursion

• Most recursions fall into a kind of patterns
• Students say that this helps them
• As a corollary, some recursions dont!

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• Mapping
• does something to every part of the input
  sentence
• E.g., square-all
• Counting
• Counts the number of elements that satisfy a
  predicate
• E.g., count-vowels, count-evens
• Finding
• Return the first element that satisfies predicate
  (or, return rest of sentence)
• E.g., member, member-even

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• Filtering
• Keep or discard elements of input sentence
• E.g., keep-evens
• Testing
• A predicate that checks that every or any element
  of input satistfies a test
• E.g., all-even?
• Combining
• Combines the elements in some way
• E.g., sentence-sum

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What recursions arent covered by these patterns?

• Weird ones like reverse, or downup
• ... bowling ...
• "Advanced" recursions
• when it does more than one thing at a time
• Ones that dont traverse a single sentence
• E.g., mad-libs takes a sentence of replacement
  words e.g., (fat Henry three) and a sentence
  to mutate e.g., (I saw a horse named
  with legs)
• Tree recursion multiple recursive calls in a
  single recursive step

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Advanced recursion
  columns (C)   columns (C)   columns (C)   columns (C)   columns (C)   columns (C)   columns (C)   columns (C)
rows(R) 0 1 2 3 4 5 ...
rows(R) 0 1           ...
rows(R) 1 1 1         ...
rows(R) 2 1 2 1       ...
rows(R) 3 1 3 3 1     ...
rows(R) 4 1 4 6 4 1   ...
rows(R) 5 1 5 10 10 5 1 ...
rows(R) ...  ... ... ... ... ... ... ...
Pascals Triangle

• How many ways can you choose C things from R
  choices?
• Coefficients of the (xy)R look in row R
• etc.

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pair-all

• Write pair-all, which takes a sentence of
  prefixes and a sentence of suffixes and returns a
  sentence pairing all prefixes to all suffixes.
• (pair-all (a b c) (1 2 3)) ? (a1 b1 c1 a2 b2
  c2 a3 b3 c3)
• (pair-all (spr s k) (ite at ing ong)) ?(sprite
  sprat spring sprong site sat sing song kite kat
  king kong)