Foundations of Python Programming: Functions First

When children first encounter word problems in their math classes, they find it difficult to translate those words into arithmetic expressions involving addition, subtraction, multiplication, and division. Teachers offer heuristics. If the problem says “how many…altogether”, that’s an addition problem. If it says “how many are left”, that’s going to be a subtraction problem.

Learning to use the accumulator pattern can be similarly confusing. The first step is to recognizing something in the problem statement that suggests an accumulation pattern. Here are a few. You might want to try adding some more of your own.

For example, if the problem is to compute the total distance traveled in a series of small trips, you would want to accumulate a sum. If the problem is to make a list of the cubes of all the numbers from 1-25, you want a list accumulation, starting with an empty list and appending one more cube each time. If the problem is to make a comma separated list of all the people invited to a party, you should think of concatenating them; you could start with an empty string and concatenate one more person on each iteration through a list of name.

Before writing any code, we recommend that you first answer the following questions:

We recommend writing your answers to these questions in a comment. As you encounter bugs and have to look things up, it will help remind you of what you were trying to implement. Sometimes, just writing the comment can help you to realize a potential problem and avoid it before you ever write any code.

The final piece of advice regarding accumulation strategies is to be intentional when choosing variable names for the accumulator and iterator variables. A good name can help remind you of what the value is assigned to the variable as well as what you should have by the end of your code. While it might be tempting at first to use a short variable name, such as a or x, if you run into any bugs or look at your code later, you may have trouble understanding what you intended to do and what your code is actually doing.

For the accumulator variable, one thing that can help is to make the variable name end with “so_far”. The prefix can be something that helps remind you of what you’re supposed to end up with. For example: count_so_far, total_so_far, or cubes_so_far.

Note that the iterator variable should be a singular noun. It should describe what one item in the original sequence, not what one item in the final result will be. For example, when accumulating the cubes of the numbers from 1-25, don’t write for cube in range(25):. Instead, write for num in range(25):. If you name the iterator variable cube you run the risk of getting confused that it has already been cubed, when that’s an operation that you still have to write in your code.