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Midterm 1

Midterm 1. You did great If you need a regrade, see the person that graded that question Solutions available on the portal soon. Schedule. Number Spelling. Read Simply Scheme , page 233, which has hints Another hint (principle): don't force "everything" into the recursion.

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Midterm 1

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  1. Midterm 1 • You did great • If you need a regrade, see the person that graded that question • Solutions available on the portal soon.

  2. Schedule

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

  4. Problem: find all the even numbers insentence of numbers (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))) ) )) (define (find-evens sent) (cond ( ;base case ) ( ;rec case 1: odd ) ( ;rec case 2: even ) ))

  5. > (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)

  6. 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 don’t often use it.

  7. 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

  8. What recursions aren’t covered by these patterns? • Weird ones like reverse, or downup • Ones that don’t 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

  9. Advanced recursion Pascal’s Triangle • How many ways can you choose C things from R choices? • Coefficients of the (x+y)^R: look in row R • etc.

  10. 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)

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