Environment Diagrams

Q1: Nested Calls Diagrams

Draw the environment diagram that results from executing the code below. You may not need to use all of the frames and blanks provided to you.

def f(x):
    return x

def g(x, y):
    if x(y):
        return not y
    return y

x = 3
x = g(f, x)
f = g(f, 0)

HOFs

Q2: Currying

Write a function curry that will curry any two argument function.

First, try implementing curry with def statements. Then attempt to implement curry in a single line using lambda expressions.

Recursion

Q3: Subsequences

A subsequence of a sequence S is a subset of elements from S, in the same order they appear in S. Consider the list [1, 2, 3]. Here are a few of its subsequences [], [1, 3], [2], and [1, 2, 3].

Write a function that takes in a list and returns all possible subsequences of that list. The subsequences should be returned as a list of lists, where each nested list is a subsequence of the original input.

In order to accomplish this, you might first want to write a function insert_into_all that takes an item and a list of lists, adds the item to the beginning of each nested list, and returns the resulting list.

OOP

Q4: Bear

Implement the SleepyBear and WinkingBear classes so that calling their print method matches the doctests. Use as little code as possible and try not to repeat any logic from Eye or Bear. Each blank can be filled with just two short lines.

Linked Lists

Q5: Linear Sublists

Definition: A sublist of linked list s is a linked list of some of the elements of s in order. For example, <3 6 2 5 1 7> has sublists <3 2 1> and <6 2 7> but not <5 6 7>. A linear sublist of a linked list of numbers s is a sublist in which the difference between adjacent numbers is always the same. For example <2 4 6 8> is a linear sublist of <1 2 3 4 6 9 1 8 5> because the difference between each pair of adjacent elements is 2.

Implement linear which takes a linked list of numbers s (either a Link instance or Link.empty). It returns the longest linear sublist of s. If two linear sublists are tied for the longest, return either one.

Trees

Q6: Long Paths

Implement long_paths, which returns a list of all paths in a tree with length at least n. A path in a tree is a list of node labels that starts with the root and ends at a leaf. Each subsequent element must be from a label of a branch of the previous value's node. The length of a path is the number of edges in the path (i.e. one less than the number of nodes in the path). Paths are ordered in the output list from left to right in the tree. See the doctests for some examples.

Iterators & Generators

Q7: Something Different

Implement differences, a generator function that takes t, a non-empty iterator over numbers. It yields the differences between each pair of adjacent values from t. If t iterates over a positive finite number of values n, then differences should yield n-1 times.

for x in t:
    yield x - previous_x

SQL

Q8: A Secret Message

A substitution cipher replaces each word with another word in a table in order to encrypt a message. To decode an encrypted message, replace each word x with its corresponding y in a code table.

Write a select statement to decode the original message It's The End using the code table.

What happens now? Write another select statement to decode this encrypted message using the same code table.