Program Logic and Indefinite Loops - Building Java Programs: A Back to Basics Approach - page 346

values might have been reversed, in which case y will be larger than x . So, that asser-
tion is sometimes true and sometimes false at point F.
What about the assertion x == y ? We know it doesn't have to be true because we
have seen cases in which x is greater than y or y is greater than x . Is it possible for it
to be true? Are there any values of x and y that would lead to this outcome? Consider
the case in which x is 218 and y is 21 . Then we would divide x by 10 to get 21 ,
which would equal y . So, this assertion also is sometimes true and sometimes false.
There was no change to z between points D and E and point F, so we simply carry
our answer down from the previous columns. So we would fill in the table as follows
for point F:

x > y x == y z == 0

sometimes sometimes never

Point F

Point G appears after the while loop:

while (x != y) {
...

}
// Point G

We can escape the while loop only if x becomes equal to y . So, at point G we know
that the assertion x == y is always true. That means that the assertion x > y can never
be true. The assertion z == 0 is a little tricky. At point F it was never true, so you
might imagine that at point G it can never be true. But we weren't necessarily at point F
just before we reached point G. We might never have entered the while loop at all, in
which case we would have been at point A just before point G. At point A the variable z
was equal to 0 . Therefore, the right answer for this assertion is that it is sometimes true,
sometimes false at point G. The final row of our table thus looks like this:

x > y x == y z == 0

Point G never always sometimes

When we combine this information, we can fill in our table as follows:

x > y x == y z == 0

Point A sometimes sometimes always

Point B sometimes never sometimes

Point C sometimes never never

Point D always never never

Point E never never never

Point F sometimes sometimes never

Point G never always sometimes