Java Reference
In-Depth Information
for using this code, we change the program segment to set a boolean variable
depending on whether
i
is prime and then use this task before the test and change
the test accordingly:
// Set x to the number of primes in 2..99
int
x= 0;
// {
invariant:
x =
the number of primes in
2..i-1 }
for
(
int
i= 2; i != 100; i= i + 1) {
Set fresh variable
b
to
"i
is prime
";
if
(b) { x= x + 1; }
See lesson
page 7.6 to
obtain the final
program
}
Implementing the assignment to b
We now implement the statement
b = "i
is prime
"
, using the code from
Fig. 7.4, with slight adjustments. With this preparation, we can now move this
code into the program. The result appears in Fig. 7.6. This completes the devel-
opment of the program to compute the number of primes in
2..99
.
How to read Fig. 7.6
When reading the program segment of Fig. 7.6 for the first time, try to un-
derstand the outer loop. In doing so, view its repetend as a sequence of two state-
ments:
Activity
7.6-2
Set fresh variable
b
to
"i
is prime
";
if
(b) { x= x + 1; }
//
Set
x
to the number of primes in
2..99
int
x= 0;
// {
invariant:
x=
the number of primes in
2..i-1 }
for
(
int
i= 2; i != 100; i= i + 1) {
//
Set fresh variable
b
to
"i
is prime
";
boolean
b= i > 1;
int
k= 2;
// {
invariant:
b==i>1and
no integer in
2..k-1
divides
i }
while
(b && k != i) {
if
(i % k == 0) { b=
false
; }
k= k + 1;
}
if
(b) { x= x + 1; }
}
Figure 7.6:
Computing the number of primes in
2..99
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