Midterm

Q1: Exam Check-In

Note to academic interns: ask students how they feel about the midterm, and what they plan to do to do better on the final. Refer to Piazza @83 for how to have “the talk.”

Recursion

Q2: Recursive Hailstone

Recall the hailstone function from hw01:

>>> def hailstone(n):
...     length = 1
...     while n != 1:
...         print(n)
...         if n % 2 == 0:
...             n = n // 2
...         else:
...             n = n * 3 + 1
...         length = length + 1
...     print(n)
...     return length   
...
>>> a = hailstone(10)
10
5
16
8
4
2
1
>>> a
7

Ask students how they would make this a recursive function (on a high level--they'll probably need to do this recursively on a future assignment anyway).

Solution:

1. Instead of incrementing length in a while-loop, make a recursive call 1 + hailstone(n * 3 + 1) or 1 + hailstone(n // 2). The 1 + represents the length increasing by one.
2. Set a base case (left as an exercise to the student)

Higher Order Functions

Q3: Parent Trap

What would Python print? Walk students through an environment diagram if they're stuck!

>>> def p(f):
...     y = 1
...     def r(y):
...         f(y)
...         return p(lambda x: print(y + x))
...     return r
...
>>> y = 8
>>> f = p(lambda x: print(y + x))
>>> f = f(3)
______
11
>>> f(7)
______
10
<Function>

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