You can put a loop inside another loop.

That is a simple statement, but it is one of the hardest concepts for students to wrap their minds around.

Let’s first look at an example of a double-nested loop, i.e., a loop which contains one other loop. Usually programmers talk about an “outer loop” and an “inner loop.” The inner loop is part of the code block for the outer loop.

for i in range( 3 ):
    print( "Entering the outer loop for i =", i )
    for j in range( 3 ):
        print( "    Entering the inner loop for j =", j )
        print( "    (i,j) = ({},{})".format( i, j ) )
        print( "    Leaving the inner loop for j =", j )
    print( "Leaving the outer loop for i =", i )

Study this code and its output until you fully understand it!

The code first gives i the value 0, and then lets j take on the values 0, 1, and 2. It then gives i the value 1, and then lets j take on the values 0, 1, and 2. Finally, it gives i the value 2, and then lets j take on the values 0, 1, and 2. So this code runs through all possible pairs of (i,j) with i and j being 0, 1, or 2.

Notice how variables for the outer loop are also accessible by the inner loop. i exists in both the outer and the inner loop.

Suppose that you want to print all pairs (i,j) where i and j can take on the values 0 to 3, but j must be higher than i. Code that does that is:

for i in range( 4 ):
    for j in range( i+1, 4 ):
        print( "({},{})".format( i, j ) )

See how I cleverly use i to set the range for j?

Write code that prints all pairs (i,j) where i and j can take on the values 0 to 3, but they cannot be equal.

You can, of course, also nest while loops, or mix nesting for loops with while loops.

You should be aware that when you use a break or continue in an inner loop, it will only break out of the inner loop or continue with the inner loop, respectively. There is no command that you can give in an inner loop that breaks out of both the inner and outer loop immediately.¹¹

Once you understand double-nested loops, it should come as no surpise that you can also triple-nest loops, quadruple-nest loops, or go even deeper. However, in practice I have seldom seen a nesting deeper than triple-nested.

for i in range( 3 ):
    for j in range( 3 ):
        for k in range( 3 ):
            print( "({},{},{})".format( i, j, k ) )