the building blocks of functional computing data, sequences conditionals recursion cs 121 today list...
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The building blocks of
functional computing
data, sequences
conditionals
recursion
CS 121 today
List Comprehensions
map and applications
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 concisenot maximally efficient for
the computer…vs.
return to recursion
Composing functions into specific applications
Creating general functions that will be useful everywhere (or almost…)
return to recursion
Composing functions into specific applications
Creating general functions that will be useful everywhere (or almost…)
building blocks with which to compose…
sum, range
def sum(L):
""" input: a list of numbers, L
output: L's sum
"""
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 Caseif 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…
sum, range
def range(low,hi):
""" input: two ints, low and hi
output: int list from low up to hi
"""
excluding hi
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
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
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!
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
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!
Map: a higher-order function
In Python, functions can take other functions as input…
def map( f, L ):
KeyConcep
t Functions ARE data!
Why use map?
Why use map?
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)
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
output
output
input
input
input
name that takes on the value of each element
in turnthe list (or string)
any name is OK!
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]
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
List Comprehensions
LC = [1 for x in L] return sum( LC )
len(L)
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
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 )
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 stringoutput: 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
Remember True == 1 and False == 0
Extra! Write
def divs(N):
input: N, an int >= 2output: the number of positive divisors of Nexample: divs(12) == 6 (1,2,3,4,6,12)
LC = [x==e for x in L] return sum( LC )
count(e,L)
lotto(Y,W)LC = [c in Y for c in W]return sum( LC )
divs(N)LC = [ N%c==0 for c in range(1,N+1)] return sum( LC )
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 )