1. EECS 110: Lec 5: List Comprehensions Aleksandar Kuzmanovic Northwestern University http://networks.cs.northwestern.edu/EECS110-s15/

2. The building blocks of functional computing data, sequences conditionals recursion EECS 110 today List Comprehensions map and applications Homework 1 - submitted Homework 2 - this coming Sunday…! 3 problems 1 lab problem Tuesday 2 python problems

3. "Quiz" on recursion def power(b,p): Names: Handle negative values of p, as well. """ returns b to the p power using recursion, not ** inputs: ints b and p output: a float """ Want more power ? power(5,2) == 25.0 For example, power(5,-1) == 0.2 (or so) def sajak(s): sajak('wheel of fortune') == 6 """ returns the number of vowels in the input string, s """

4. def power(b,p): """ inputs: base b and power p (an int) implements: b**p = b*b**(p-1) """ if p == 0: return if p > 0: return else: # p < 0 return

5. def power(b,p): """ inputs: base b and power p (an int) implements: b**p = b*b**(p-1) """ if p == 0: return 1 if p > 0: return else: # p < 0 return

6. def power(b,p): """ inputs: base b and power p (an int) implements: b**p = b*b**(p-1) """ if p == 0: return 1 if p > 0: return b*power(b,p-1) else: # p < 0 return

7. def power(b,p): """ inputs: base b and power p (an int) implements: b**p = b*b**(p-1) """ if p == 0: return 1 if p > 0: return b*power(b,p-1) else: # p < 0 return 1/power(b,-1*p)

8. behind the curtain power(2,3)

9. def sajak(s): Base case? when there are no letters, there are ZERO vowels if it is NOT a vowel, the answer is Rec. step? Look at the initial character. if it IS a vowel, the answer is

10. def sajak(s): Base case? when there are no letters, there are ZERO vowels if it is NOT a vowel, the answer is just the number of vowels in the rest of s Rec. step? Look at the initial character. if it IS a vowel, the answer is 1 + the number of vowels in the rest of s

11. def sajak(s): if len(s) == 0: return 0 else: Checking for a vowel: Try #1 Base Case

12. def sajak(s): if len(s) == 0: return 0 else: Checking for a vowel: Try #1 and or not same as in English! but each side has to be a complete boolean value! Base Case

13. def sajak(s): if len(s) == 0: return 0 else: Checking for a vowel: Try #1 and or not same as in English! but each side has to be a complete boolean value! if s[0] == 'a' or s[0] == 'e' or… Base Case

14. in Checking for a vowel: Try #2 def sajak(s): if len(s) == 0: return 0 else: Base Case

15. def sajak(s): if len(s) == 0: return 0 else: if s[0] not in 'aeiou': return sajak(s[1:]) else: return 1+sajak(s[1:]) if it is NOT a vowel, the answer is just the number of vowels in the rest of s if it IS a vowel, the answer is 1 + the number of vowels in the rest of s Base Case Rec. Step

16. sajak('eerier') behind the curtain

17. The key to understanding recursion is to first understand recursion… - advice from a student

18. functional programming >>> 'fun' in 'functional' True Key ideas in functional programming create small building blocks (functions) leverage self-similarity (recursion) representation via list structures (data) Compose these together to solve or investigate problems. elegant and concise not maximally efficient for the computer… vs.

19. return to recursion Composing functions into specific applications Creating general functions that will be useful everywhere (or almost…)

20. return to recursion Composing functions into specific applications Creating general functions that will be useful everywhere (or almost…) building blocks with which to compose…

21. sum, range def sum(L): """ input: a list of numbers, L output: L's sum """

22. sum, range def sum(L): """ input: a list of numbers, L output: L's sum """ if len(L) == 0: return 0.0 else: return L[0] + sum(L[1:]) Base Case if the input has no elements, its sum is zero Recursive Case if L does have an element, add that element's value to the sum of the REST of the list… This input to the recursive call must be "smaller" somehow…

23. sum, range def range(low,hi): """ input: two ints, low and hi output: int list from low up to hi """ excluding hi

24. sum, range def range(low,hi): """ input: two ints, low and hi output: int list from low up to hi """ if hi <= low: return [] else: return excluding hi

25. sum, range def range(low,hi): """ input: two ints, low and hi output: int list from low up to hi """ if hi <= low: return [] else: return [low] + range(low+1,hi) excluding hi

26. sum and range >>> sum(range(101)) Looks sort of scruffy for a 7-year old… ! and 100 more…

27. Recursion: Good News/Bad News Recursion is common (fundamental) in functional programming def dblList(L): """ Doubles all the values in a list. input: L, a list of numbers """ if L == []: return L else: return [L[0]*2] + dblList(L[1:]) But you can sometimes hide it away!

28. Map: The recursion "alternative" def dbl(x): return 2*x def sq(x): return x**2 def isana(x): return x=='a’ >>> map( dbl, [0,1,2,3,4,5] ) [0, 2, 4, 6, 8, 10] >>> map( sq, range(6) ) [0, 1, 4, 9, 16, 25] >>> map( isana, 'go away!' ) [0, 0, 0, 1, 0, 1, 0, 0] Hey… this looks a bit False to me! (1) map always returns a list (2) map(f,L) calls f on each item in L

29. Map ! def dblList(L): """ Doubles all the values in a list. input: L, a list of numbers """ if L == []: return L else: return [L[0]*2] + dblList(L[1:]) Without map def dbl(x): return x*2 def dblList(L): """ Doubles all the values in a list. input: L, a list of numbers """ return map(dbl, L) With map!

30. Map: a higher-order function In Python, functions can take other functions as input… def map( f, L ): Key Concep t Functions ARE data!

31. Why use map ?

32. Faster execution in Python – map optimized for operations in lists More elegant / shorter code, “functional in style” Avoid rewriting list recursion (build once, use lots)

33. Mapping without map : List Comprehensions >>> [ dbl(x) for x in [0,1,2,3,4,5] ] [0, 2, 4, 6, 8, 10] >>> [ x**2 for x in range(6) ] [0, 1, 4, 9, 16, 25] >>> [ c == 'a' for c in 'go away!' ] [0, 0, 0, 1, 0, 1, 0, 0] Anything you want to happen to each element of a list output input name that takes on the value of each element in turn the list (or string) any name is OK!

34. Mapping without map : List Comprehensions >>> [ dbl(x) for x in [0,1,2,3,4,5] ] [0, 2, 4, 6, 8, 10] >>> [ x**2 for x in range(6) ] [0, 1, 4, 9, 16, 25] >>> [ c == 'a' for c in 'go away!' ] [0, 0, 0, 1, 0, 1, 0, 0] def dbl(x): return 2*x def sq(x): return x**2 def isana(x): return x=='a’ >>> map( dbl, [0,1,2,3,4,5] ) [0, 2, 4, 6, 8, 10] >>> map( sq, range(6) ) [0, 1, 4, 9, 16, 25] >>> map( isana, 'go away!' ) [0, 0, 0, 1, 0, 1, 0, 0]

35. List Comprehensions def len(L): if L == []: return 0 else: return 1 + len(L[1:]) len(L) implemented via raw recursion sScore(s) sajak(s) def sajak(s): if len(s) == 0: return 0 else: if s[0] not in 'aeiou': return sajak(s[1:]) else: return 1+sajak(s[1:]) def sScore(s): if len(s) == 0: return 0 else: return letScore(s[0]) + \ sScore(s[1:]) scrabble score

36. List Comprehensions LC = [1 for x in L] return sum( LC ) len(L)

37. List Comprehensions LC = [1 for x in L] return sum( LC ) len(L) sajak(s) LC = [c in 'aeiou' for c in s] return sum( LC ) # of vowels

38. List Comprehensions LC = [1 for x in L] return sum( LC ) len(L) sScore(s) sajak(s) LC = [c in 'aeiou' for c in s] return sum( LC ) scrabble score # of vowels LC = [ letScore(c) for c in s] return sum( LC )

39. Quiz Write each of these functions concisely using list comprehensions… Write def count(e,L): Write def lotto(Y,W): input: e, any element L, any list or string output: the # of times L contains e example: count('f', 'fluff') == 3 input: Y and W, two lists of lottery numbers (ints) output: the # of matches between Y & W example: lotto([5,7,42,44],[3,5,7,44]) == 3 Y are your numbers W are the winning numbers Name(s): Remember True == 1 and False == 0 Extra! Write def divs(N): input: N, an int >= 2 output: the number of positive divisors of N example: divs(12) == 6 (1,2,3,4,6,12)

40. Quiz

41. LC = [x==e for x in L] return sum( LC ) count(e,L)

42. Quiz lotto(Y,W) LC = [c in Y for c in W] return sum( LC )

43. Quiz divs(N) LC = [ N%c==0 for c in range(1,N+1)] return sum( LC )

44. Quiz LC = [x==e for x in L] return sum( LC ) count(e,L) divs(N) lotto(Y,W) LC = [c in Y for c in W] return sum( LC ) LC = [ N%c==0 for c in range(1,N+1)] return sum( LC )

45. See you at Lab!