CSC110 Lecture 3: Comprehensions and Introduction to Functions

Exercise 1: Practice with comprehension expressions

Here is a summary of the three types of comprehensions, for your reference:

1. Suppose we assign the variable numbers = [1, 2, 3].

   1. Fill in the table below.

      Expression	Value
      numbers[0]
      numbers[1]
      numbers[2]
      numbers[0] ** 3
      numbers[1] ** 3
      numbers[2] ** 3

   2. Write a comprehension that evaluates to the list of every integer in numbers cubed (i.e., raised to the power of 3).

      
      >>>
      
      
      [1, 8, 27]   # Evaluating your expression should produce this

   3. Write a comprehension that evaluates to a dictionary mapping every integer in numbers to three times that integer.

      
      >>>
      
      
      {1: 3, 2: 6, 3: 9}   # Evaluating your expression should produce this

      Hint: the identity dictionary comprehension has the following form:

      >>> {x : x for x in numbers}

   4. Write a comprehension that evaluates to the given output dictionary shown.

      
      >>>
      
      
      
      {3: 1, 6: 2, 9: 3}   # Evaluating your expression should produce this

   5. Write a comprehension that is a translation of the set builder expression \(\{\frac{x}{x + 1} \mid x \in \texttt{numbers} \}\).

Exercise 2: Comprehensions and range

1. Write down the integers that are contained in each of the following Python range expressions.

   1. range(0, 5)

   2. range(5, 10, 2)

2. For each of the following descriptions, write a comprehension that evaluates to the described collection.

   1. The set of integers between 30 and 50, inclusive.

   2. The list of integers between -30 and 30, inclusive (in ascending order).

   3. The set of the squares of the natural numbers less than 2000.

   4. A mapping from a number to its square, for the natural numbers less than 2000.

3. You are given a variable s that refers to a (very very long) string:

   >>> s = 'nonsensenonsensenonsensenonsensenonsensenonsensenonsense'

   Write a list comprehension expression that evaluates to a list containing the first 20 characters in the string, in the order they appear.

   Hint: s[19] is the last character in s that should be included in the list.

Exercise 3: Practice with built-in functions

Suppose we have assigned the following variables in the Python console:

>>> n = -5
>>> numbers_list = [1, 10, n]
>>> numbers_set = {100, n, 200}

1. Complete the following table showing the value of each variable.

   Variable	Value
   n
   numbers_list
   numbers_set

2. Write down what each of the following expressions evaluate to. Do this by hand first! (Then check your work in the Python console.)

   You may find it helpful to consult Appendix A.1 Python Built-In Function Reference.

   >>> abs(n)
   
   
   
   >>> sorted(numbers_list)
   
   
   
   >>> sorted(numbers_set) + sorted(numbers_list)
   
   
   
   >>> len(numbers_set)
   
   
   
   >>> len(numbers_list) == n
   
   
   
   >>> sum(numbers_set) - n
   
   

3. The variable numbers refers to a list that contains a mix of positive and negative integers (e.g., [-1, 2, 3]). Write a comprehension that evaluates to the set of the absolute values of every integer in numbers.

   (Hint: the structure is the same as earlier problems on this worksheet. Use the abs function.)

Additional exercises

1. Comprehension practice. For each of the following mappings, write a Python dictionary expression that evaluates to the mapping.

   1. A mapping from a number to its square, for the first 50 natural numbers.

   2. A mapping from input to output of the function \(f(x) = \frac{x}{x-1}\), for integer inputs greater than 1 and less than 2000.

   3. A mapping from a number to a list that contains the same number of items, where every item is the string 'Hello', for the first 50 natural numbers. (e.g., 3 maps to the list ['Hello', 'Hello', 'Hello'].)

   4. A mapping from an integer to the set of integers between 0 and that integer inclusive, for integers 1 to 20, inclusive.

2. Comprehensions with multiple variables. Suppose you have the lists: nums1 = [1, 2, 3] and nums2 = [4, 5, 6].

   1. Using both nums1 and nums2, write a comprehension that evaluates to: [[1, 4], [1, 5], [1, 6], [2, 4], [2, 5], [2, 6], [3, 4], [3, 5], [3, 6]].

   2. Using both nums1 and nums2, write a comprehension that evaluates to: [[4, 1], [5, 1], [6, 1], [4, 2], [5, 2], [6, 2], [4, 3], [5, 3], [6, 3]].

   3. Using both nums1 and nums2, write a comprehension that evaluates to: {5, 6, 7, 8, 9}.

3. Function practice. Using the same variables defined in Exercise 3, determine the value of each of the following Python expressions.

   >>> type(n)
   
   
   
   >>> type(abs(n))
   
   
   
   >>> type(numbers_list == n)
   
   
   
   >>> type(numbers_list) == type(n)
   
   
   
   >>> max(numbers_list + [5])
   
   
   
   >>> max(numbers_list) + 5
   
   
   
   >>> max(sorted(numbers_list)) == max(numbers_list)
   
   
   

4. Interpreting errors. Your friend is practicing in the Python console again, and is trying to add two numbers. They type in the following, and get an error:

   >>> sum(3, 4)
   Traceback (most recent call last):
     ... [some output omitted] ...
     File "<stdin>", line 1, in <module>
   TypeError: 'int' object is not iterable

   Once again, explain this error to your friend, and how they can correctly add two numbers in Python. (Hint: treat “iterable” as another word for “collection”.)