Loops that build answers

What you will be able to do

After this lesson you can

• add numbers in a loop to get a total,
• count how many items pass a test,
• multiply in a loop, as for a factorial,
• use a trace table to follow a loop, and
• find the mistake when the starting line is in the wrong place.

Starting with a total

A loop can add up numbers. The idea has three steps.

1. Before the loop, make a variable with the right starting value: total = 0.
2. In the loop, change it in every round: total = total + i.
3. After the loop, show it. It holds the answer.

A trace table

If you are not sure what a loop does, write a trace table, with one row for each round. Put the loop variable and the answer so far in the columns.

The trace is one of the best ways to understand a program, to check it, and to find its mistakes.

The usual mistake: the starting line in the wrong place

What happens if the line total = 0 is inside the loop?

total = 0 comes before the loop, so it runs once. Inside the loop it would set the total back to 0 in every round.

Counting

To count how many items pass a test, start a counter at 0, and add 1 when the test is True.

Multiplying: the factorial

The factorial of 5 is 5 times 4 times 3 times 2 times 1. A loop can multiply in the same way as it added. But the starting value is 1, not 0. A starting 0 would make every product 0.

Building text

A loop can also build a picture out of text. In Python, "*" * 3 gives ***. Put it in a loop, and you can draw a triangle.

Going through a text to count

The same idea works on a text. Look at this program, which counts the vowels.

Three starting values to remember

Common mistakes

• The starting line inside the loop. The variable starts again in every round.
• Starting a product at 0. Every answer is 0.
• Showing the answer inside the loop when you need it only at the end. The program shows a line for each round.
• The wrong indent of the if or of count + 1.
• Forgetting the new value: total + i alone changes nothing. You need total = total + i.

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 The sum of the first 100 and write the loop that adds the numbers.
2. Build. Open the problem The sum of 1 to 100 and the problem 5 factorial.
3. Stretch. Open the problem Count the vowels. Then change it so that it counts the letters that are not vowels.

Remember these

• Make the starting variable before the loop. Change it inside. Show it after.
• A total starts at 0, a count starts at 0, and a product starts at 1.
• A trace table, with a row for each round, finds the mistakes.

Check yourself

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

1. Where does total = 0 go: before the loop or inside it?

2. What does result = 1 followed by for i in range(1, 5): result = result * i give?

3. How do you count the numbers that are divisible by 7?