Administrivia

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Midterm 1

• You did great
• If you need a regrade, see the person that graded
  that question
• Solutions available on the portal soon.

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Schedule
Feb 28 Midterm 1
March 7 Tree recursion, etc. Number-spelling Miniproject
March 14 Higher order procedures
March 21 Spring Break
March 28 More HOF Lists! (instead of sentences and words)
April 4 Recursion (advanced)
April 11 Midterm 2
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Number Spelling

• Read Simply Scheme, page 233, which has hints
• Another hint (principle) don't force
  "everything" into the recursion.

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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.
• Knowing recursion WILL help with all sorts of
  ways while programming, even if you dont often
  use it.

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Recursive patterns

• Most recursive functions that operate on a
  sentence fall into
• Mapping square-all
• Counting count-vowels, count-evens
• Finding member, first-even
• Filtering keep-evens
• Testing all-even?
• Combining sum-evens

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What recursions arent covered by these patterns?

• Weird ones like reverse, or downup
• 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)