Nested loops

Introduction

A loop's body can contain another loop. For every single round of the outer loop, the inner loop runs all of its rounds.

Many things in the world are two-dimensional: seats in a cinema, days in a calendar, pixels on a screen. A loop inside a loop is the natural way to visit every combination of row and column.

How it works

Every combination

colors = ["red", "blue"]
sizes = ["S", "M"]
for c in colors:
    for s in sizes:
        print(c, s)

Two choices for colour times two for size gives four combinations. In general, an outer loop of n rounds around an inner loop of m rounds runs the inner body n × m times.

break in a nested loop

for i in range(1, 4):
    for j in range(1, 4):
        if j > i:
            break
        print(i, j)

break leaves only the loop it is in. When j > i, the inner loop stops, but the outer loop carries on with the next i. That is why each row prints one more pair than the last.

Syntax

for row in range(3):
    for col in range(4):
        print(row, col)

Example

for row in range(1, 4):
    for col in range(1, 4):
        print(row * col, end=" ")
    print()

Watch row and col in the variables panel. row stays at 1 while col goes 1, 2, 3; then row becomes 2 and col starts again from 1. end=" " keeps the numbers on one line, and the empty print() ends each row.

Line by line

1. The outer for sets row to 1.
2. The inner for sets col to 1, 2 and 3 in turn.
3. print(row * col, end=" ") prints one value and stays on the same line.
4. After the inner loop ends, print() finishes the row.
5. The outer loop moves to the next row, and the inner loop starts again from 1.

Expected result

1 2 3 
2 4 6 
3 6 9 

In the real world

Spreadsheets, timetables and image filters all work row by row and column by column. Nested loops are also where programs often become slow, because the work is multiplied.

Common mistakes

• Reusing the same variable name for both loops: the inner loop overwrites the outer one's value.
• Putting the row-ending print() inside the inner loop, which prints a new line after every value.
• Expecting break to stop both loops. Use a flag variable, or put the loops in a function and return.

Best practices

• Name the variables after what they mean, such as row and col.
• Check where the row-ending print() sits.
• Move an inner loop into a function if the code gets hard to follow.

Summary

A nested loop runs the inner loop completely for each round of the outer loop, so the work multiplies. end keeps output on one line, and break leaves only the loop it is in.

Practice

Print a right triangle of numbers for n = 4: line i shows the numbers 1 to i, separated by spaces.

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