19. Nested loops

A loop repeats a block. What if that block holds another loop? That's a nested loop: the inner one runs fully on every turn of the outer one. They build grids, tables, anything with rows and columns.

A loop inside a loop

Put one for inside another. The inner loop finishes before the outer one moves:

for outer in range(1, 4):
    for inner in range(1, 3):
        print(outer, inner)

Output:

1 1
1 2
2 1
2 2
3 1
3 2

Follow the order. While outer is 1, the inner loop runs (1, 2). Then outer becomes 2 and it runs again. That's 3 × 2 = 6 runs.

Building a row at a time

One value per line rarely suits a grid. The usual trick: the outer loop handles rows; the inner loop builds one string, printed when the row is done:

for row in range(1, 4):
    line = ""
    for col in range(1, 4):
        line = line + str(row * col) + "\t"
    print(line)

Output (a 3×3 multiplication grid):

1   2   3
2   4   6
3   6   9

Notice line = "" sits inside the outer loop but outside the inner one. It resets each row, fills up in the inner loop, then prints.

A triangle with a changing inner range

The inner range can depend on the outer variable. Run it 1 to row and you get a triangle:

for row in range(1, 5):
    line = ""
    for star in range(1, row + 1):
        line = line + "*"
    print(line)

Output:

*
**
***
****

Row 1 runs range(1, 2) — once; row 4 runs range(1, 5) — four times. The shape falls out of the maths.

How many times does the body run?

Multiply the counts. An outer loop of 10 around an inner loop of 10 runs the body 10 × 10 = 100 times. It grows fast: three loops of 100 each is a million runs. Powerful, so watch the numbers.

Homework

Homework files are in exercises/19/homework/.

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Stuck or finished? Open the homework solutions page.