Let’s Think Python: COMSC020 PreTeXt Interactive Edition

If we want to print our table of squares and cubes of the numbers 1 to 5, we can also do it with a for loop:

for n in [1, 2, 3, 4, 5]:
  print(n, n * n, n * n * n)

It turns out that generating lists with a specific number of integers is a very common thing to do, especially when you want to write simple for loop controlled iteration. Even though you can use any four items, or any four integers for that matter, the conventional thing to do is to use a list of integers starting with 0.

In fact, these lists are so popular that Python gives us a special built-in range function that can deliver a sequence of values to the for loop. When called with one argument, the sequence provided by range always starts with 0. If you ask for range(4), then you will get 4 values starting with 0. In other words, 0, 1, 2, and finally 3. Notice that 4 is not included since we started with 0. Likewise, range(10) provides 10 values, 0 through 9.

Here’s how we can do our table from 1 to 5 using range. We have to add one to transform the numbers 0 to 4 into 1 to 5. To save some typing, we will use the exponentiation operator **:

The number in the parentheses can also be a variable, so we can let the user choose the end number for the table:

The range¹ function is actually a very powerful function when it comes to creating sequences of integers. It can take one, two, or three arguments. We have seen the simplest case of one argument such as range(4) which creates [0, 1, 2, 3]. But what if we really want to have the sequence [1, 2, 3, 4]? We can do this by using a two argument version of range where the first argument is the starting point and the second argument is the ending point. The evaluation of range(1, 5) produces the desired sequence [1, 2, 3, 4].

The two-argument version of range(start, stop) gives you the sequence starting with the start value up to but not including the stop value. That’s why we have to put in 5 for our stop value to get the sequence [1, 2,3, 4].

Here are two examples for you to run. Try them and then add another line below to create a sequence starting at 10 and going up to 20 (including 20).

Codelens will help us to further understand the way range works. In this case, the variable i will take on values produced by the range function.

Finally, suppose we want to have a sequence of even numbers. How would we do that? We add another argument, a step, that tells range what to count by. For even numbers we want to start at 0 and count by 2’s. So, if we wanted the first ten even numbers we would use range(0, 19, 2).

The most general form of the range is range(start, stop, step). This will produce a sequence starting at the start value, adding the step to get the next number in the sequence, up to but not including the stop value. You can also create a sequence of numbers that starts big and gets smaller by using a negative value for the step parameter.

Try it in codelens. Do you see why the first two statements produce the same result?