Nested for Loops

1Why put a loop inside a loop?

One loop prints the table of 7. What prints the tables of 2, 3 and 4? You need to repeat the whole table — and the table is itself a repetition. A repetition of a repetition is a nested loop.

Anything with rows and columns is the same shape: a seating plan, a calendar month, a pattern of stars, marks for every student in every subject. The outer loop takes the rows; the inner loop takes what is in one row.

2How it is written

for i in range(1, 4):          <- outer header
    for j in range(1, 5):      <- inner header: indented, so it IS the outer body
        print(i, j)            <- inner body: indented twice
    print('row done')          <- outer body again, after the inner loop ends
print('all done')              <- at the margin: outside both loops

The indentation is doing all the work, exactly as it has since the if statement — only now there are two levels of it. Four spaces means “inside the outer loop”. Eight means “inside the inner loop”. Back at the margin means outside both.

And each loop needs its own loop variable. The outer one is traditionally i and the inner one j. Using i for both would mean the inner loop overwriting the outer loop's value on every round — which is not an error, and does not do what anybody wants.

3Watch both counters

Step through it and watch j go all the way from 1 to 4 before i moves at all — and then start again from 1.

4Three tables from one program

The outer loop picks the table; the inner loop prints the rows of it. The print() calls between them are worth studying — where a statement sits decides how often it happens:

# the tables of 2, 3 and 4 — a loop inside a loop
for n in range(2, 5):
    print('Table of', n)

    for i in range(1, 4):
        print(n, 'x', i, '=', n * i)

    print()

Table of 2
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6

Table of 3
3 x 1 = 3
3 x 2 = 6
3 x 3 = 9

Table of 4
4 x 1 = 4
4 x 2 = 8
4 x 3 = 12

print('Table of', n) is in the outer body, so it runs three times — once per table. The multiplication line is in the inner body, so it runs nine times. And the empty print() at the end of the outer body puts a blank line after each table, which is why the output has three blocks rather than one wall of numbers.

5Counting the rounds

Exam questions ask this constantly, and the counting is simple once you stop adding:

# how many times does the inner body run?
count = 0

for i in range(1, 4):
    for j in range(1, 5):
        count = count + 1

print('The outer body ran 3 times')
print('The inner body ran', count, 'times')

The outer body ran 3 times
The inner body ran 12 times

Three values in the outer range, four in the inner: 3 × 4 = 12. Multiply, do not add — because the inner loop starts over from its first value on each round of the outer, rather than carrying on from where it stopped.

6When the inner loop depends on the outer one

The inner range does not have to be a fixed set of numbers. It can be built out of the outer loop variable — and then each row is a different length. That is how patterns are made:

# a triangle of stars, built one row at a time
for row in range(1, 5):
    line = ''

    for star in range(1, row + 1):
        line = line + '*'

    print(line)

*
**
***
****

On the first round row is 1, so the inner range is range(1, 2) — one star. On the fourth it is range(1, 5) — four. The inner loop is not counting to a fixed number; it is counting to whatever the outer round is.

Note also where line lives. It is created inside the outer body but outside the inner one: emptied at the start of each row, added to by every star in that row, and printed once the row is complete. Above the outer loop it would collect every star in the triangle into one line; inside the inner loop it would be emptied after each star and only ever print one.

7Try it

Run it, then change range(1, 5) to range(1, 8). Then try moving the print(line) in by four spaces and see the triangle grow a step at a time.

# a triangle of stars, built one row at a time
for row in range(1, 5):
    line = ''

    for star in range(1, row + 1):
        line = line + '*'

    print(line)

8Recap