6.5: Nested Loops

The next step is to write loops that enumerate different values of a, b, and c. Create a new file called find_triples.m where we’ll develop the rest of the program.

We’ll start with a loop for a:

for a=1:3
    a
end

It might seem silly to start with such a simple program, but this is an essential element of incremental development: start simple and test as you go.

The output is as expected.

1
2
3

Now we’ll add a second loop for b. It might be tempting to write something like this:

for a=1:3
    disp(a)
end
for b=1:4
    disp(b)
end

But that loops through the values of a and then loops through the values of b, and that’s not what we want.

Instead, we want to consider every possible pair of values, like this:

for a=1:3
    for b=1:4
        disp([a,b])
    end
end

Now one loop is inside the other. The inner loop gets executed three times, once for each value of a, so here’s what the output looks like (I’ve adjusted the spacing to make the structure clear):

>> find_triples
     1     1
     1     2
     1     3
     1     4
     2     1
     2     2
     2     3
     2     4
     3     1
     3     2
     3     3
     3     4

The left column shows the values of a and the right column shows the values of b.

The next step is to search for values of c that might make a Pythagorean triple. The largest possible value for c is a + b, because otherwise we couldn’t form a triangle (see https://greenteapress.com/matlab/triangle).

for a=1:3
    for b=1:4
        for c=1:a+b
            disp([a,b,c])
        end
    end
end

After each small change, run the program again and check the output.