Loops inside loops

What you will be able to do

After this lesson you can

• put one loop inside another,
• say how many times the inner body runs,
• print a table or a grid, and
• follow a nested loop with a trace table.

A loop inside a loop

Think about a clock. The minute hand goes around completely for every one step of the hour hand. A nested loop works like that: the outer loop is the slow hand, and the inner loop is the fast hand.

• Round 1 of the outer loop: a = 1. The inner loop runs all of its rounds: b = 1, b = 2, b = 3.
• Round 2 of the outer loop: a = 2. The inner loop starts again from the beginning, and runs all of its rounds again.

The outer loop has 2 rounds, the inner loop has 3. So the body runs 2 times 3, which is 6 times. This is the rule: the number of times is the product of the rounds.

A table with two loops

Nested loops are perfect for tables and grids. The outer loop makes the rows, and the inner loop makes the columns.

If you forget that last print(), all the numbers stand in one long line. If you put it inside the inner loop, every number gets its own line. The indent decides.

The plain print() sits after the inner loop, so it runs once for each row and starts the next line.

A trace table for two loops

Write one row for each time the body runs, with a column for each loop variable.

The row changes slowly, and the col changes fast. The table continues in the same way, 12 rows in all.

Patterns

Patterns are a good way to practise nested loops. A pattern is made of rows, and each row is made of characters. Often the inner loop is not needed, because "*" * n makes a whole row at once. But when each character depends on both the row and the column, you need two loops.

How many stars are in row i of a triangle? i. And how many spaces come before the stars of a pyramid? The height minus i. Find these relations on paper before you write the code.

Common mistakes

• Using the same name for both loop variables. The inner loop overwrites the outer one. Use row and col, or i and j.
• The wrong indent of the print() that starts a new line.
• Forgetting that the inner loop starts again in every round of the outer one.
• Too many rounds. 1000 times 1000 is a million rounds. It can take a long time.
• *Writing a nested loop where one loop and `` is enough.**

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 Draw the triangle and print the shape.
2. Build. Open the problem A triangle of stars and the problem A rectangle of stars.
3. Stretch. Open the problem How many rounds? and say how many times the body runs for three nested loops.

Remember these

• The inner loop runs completely in every round of the outer loop.
• The number of times the inner body runs is the product of the rounds.
• end="" keeps the output on the same line. A plain print() after the inner loop starts a new line.
• Use two different names for the two loop variables.

Check yourself

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

1. How many times does the body run for for a in range(5): for b in range(4):?

2. What does a plain print() do?

3. Where does the plain print() for a new line go?