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CSC110 Week 2A: Introduction to Functions

Exercise 1: 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 last week’s worksheet. Use the abs function.)

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.

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 1, 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”.)