Choosing the loop, and loops that go wrong

What you will be able to do

After this lesson you can

• choose between a for loop and a while loop,
• write the same job in both forms,
• find the reason for an endless loop, and
• find and fix an off-by-one fault.

for or while?

You now know two loops. How do you choose?

• Use for when you know the number of rounds, or when you go through the items of something: the numbers of a range(), the letters of a text.
• Use while when the number of rounds depends on a condition that is checked as you go: saving until there is enough, asking until the answer is right.

Many jobs can be done with either. Here is the same job, adding the numbers 1 to 5, in both forms.

Fault 1: the endless loop

An endless loop is a loop whose condition never becomes False. The computer goes on and on. This is the loop, written as text because we do not want to run it.

count = 1
while count <= 3:
    print(count)

Nothing changes count, so count <= 3 is always True. On a computer, you stop such a program with Ctrl + C. On this site, the run stops after a time limit, with a message.

How to find the cause. Ask three questions.

1. What is the condition? count <= 3.
2. Which variable does it use? count.
3. Which line in the body changes that variable, and in which direction? None. This is the fault.

Other causes: the line changes the variable in the wrong direction (count = count - 1), changes a different variable, or sits inside an if that is never True, or after a continue that skips it.

Fault 2: off by one

The loop runs, but one round too many or too few. The usual reason is < against <=.

Here is how to avoid it. Before you write the condition, write what the last round should be. If the last round has n = 5, the condition must be True for 5 and False for 6. That is n <= 5, or n < 6.

This is the off-by-one fault: the loop runs one round too many or one too few. Test the last round by hand.

How to find a fault in a loop

1. A trace table. Write a row for each round with the variable values. The mistake shows itself.
2. Print inside the loop. Add print("n is", n) as the first line of the body. You see each round on the screen.
3. A small case first. Test with 2 or 3 rounds. If the small case is wrong, you can follow it by hand.
4. Check the edges. What happens with 0 rounds? With 1 round?

Common mistakes

• Using while when for is simpler. More lines to go wrong.
• Starting the counter in the wrong place, for example inside the loop.
• Testing the wrong variable in the condition.
• Trusting a loop that you have run only once.

Practice

Start with two quick questions. Each New numbers gives you a fresh one, so you can practise as long as you like.

Then the labs and the problems:

1. Warm-up. Open the lab Fix the endless loop. The starter has a loop that would never end, and the checker has a safety limit.
2. Build. Open the problem Find the endless loop and the problem Doubling.
3. Stretch. Open the problem The Collatz puzzle and try it with several start values.

Remember these

• for for a known number of rounds or the items of something. while for a condition.
• A while loop needs a start, a test and a change. Check all three.
• An endless loop: the body never moves the condition towards False.
• Off by one: write the last round first, then the condition.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Which loop would you use to show the letters of a word, and why?

2. What are the three things that a while loop needs?

3. A loop while n < 5: starts with n = 1 and adds 1. Which numbers does it show?