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2. Slide 2 Midterm 1 You did great If you need a regrade, see the person that graded that question Solutions available on the portal soon.

3. Slide 3 Schedule Feb 28Midterm #1 March 7Tree recursion, etc. Number-spelling Miniproject March 14Higher order procedures March 21Spring Break March 28More HOF Lists! (instead of sentences and words) April 4Recursion (advanced) April 11Midterm #2

4. Slide 4 Number Spelling Read Simply Scheme, page 233, which has hints Another hint (principle): don't force "everything" into the recursion.

5. Slide 5 Problem: find all the even numbers in sentence 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))) ) ))

6. Slide 6 > (find-evens '(2 3 4 5 6))  (se 2 (se 4 (se 6 ())  (2 4 6) (se 2 (se 4 (se 6 () sent = ( 2 3 4 5 6 ) sent = ( 3 4 5 6 ) sent = ( 4 5 6 ) sent = ( 5 6 ) sent = ( 6 ) sent = ( )

7. Slide 7 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.

8. Slide 8 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

9. Slide 9 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

10. Slide 10 Advanced recursion columns (C) r o w s (R) 012345... 01 111 2121 31331 414641 51510 51... 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.

11. Slide 11 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)