Practice problems: Higher Order Functions

Easy

Question 1

Draw an environment diagram for the following code:

>>> def adder_maker(x):
...     def adder(y):
...         return x + y
...     return adder
>>> add3 = adder_maker(3)
>>> add3(4)
______
7
>>> sub5 = adder_maker(-5)
>>> sub5(6)
______
1
>>> sub5(10) == add3(2)
______
True

Question 2

Draw the environment diagram for the following piece of code

def yak(zebra):
    return 20 // zebra
def llama(alpaca):
    zebra = 0
    def yak(zebra):
        return alpaca(zebra)
    return yak

llama(yak)(4)

Medium

Question 3

>>> def troy():
...     abed = 0
...     while abed < 10:
...         def britta():
...             return abed
...         abed += 1
...     abed = 20
...     return britta
>>> annie = troy()
>>> def shirley():
...     return annie
>>> pierce = shirley()
>>> pierce()
______
20

Question 4

Consider the following implementations of count_factors and count_primes:

def count_factors(n):
    """Return the number of positive factors that n has."""
    i, count = 1, 0
    while i <= n:
        if n % i == 0:
            count += 1
        i += 1
    return count

def count_primes(n):
    """Return the number of prime numbers up to and including n."""
    i, count = 1, 0
    while i <= n:
        if is_prime(i):
            count += 1
        i += 1
    return count

def is_prime(n):
    if n < 2:
        return False
    i = 2
    while i < n:
        if n % i == 0:
            return False
        i += 1
    return True

Generalize this logic by writing a function count_cond, which takes in a two-argument predicate function cond(n, i). count_cond returns a one-argument function that counts all the numbers from 1 to n that satisfy cond.

def count_cond(condition):
    """
    >>> count_factors = count_cond(lambda n, i: n % i)
    >>> count_factors(2)
    2
    >>> count_factors(4)
    3
    >>> count_factors(12)
    6

    >>> count_primes = count_cond(lambda n, i: is_prime(i))
    >>> count_primes(2)
    1
    >>> count_primes(3)
    2
    >>> count_primes(4)
    2
    >>> count_primes(5)
    3
    >>> count_primes(30)
    10
    """
    # BEGIN SOLUTION
    def counter(n):
        i, count = 1, 0
        while i <= n:
            if condition(n, i):
                count += 1
            i += 1
        return count
    return counter
    # BEGIN SOLUTION

def is_prime(n):
    if n < 2:
        return False
    i = 2
    while i < n:
        if n % i == 0:
            return False
        i += 1
    return True

Question 5: Doge

Draw the following environment diagram:

wow = 6
def much(wow):
    if much == wow:
        such = lambda wow: 5
        def wow():
            return such
        return wow
    such = lambda wow: 4
    return wow()
wow = much(much(much))(wow)