Java Reference
In-Depth Information
EXAMPLE:
(continued)
Translating this formula into Java says that the value returned by
power(x, n)
should be the same as the value of the expression
power(x, n - 1)*x
The definition of the method
power
given in Display 11.3 does return this value for
power(x, n)
, provided
n > 0
.
The case where
n
is equal to
0
is the stopping case. If
n
is
0
, then
power(x, n)
simply returns
1
(because x
0
is
1
).
Let's see what happens when the method
power
is called with some sample values.
First, consider the simple expression:
power(2, 0)
When the method is called, the value of
x
is set equal to
2
, the value of
n
is set equal
to
0
, and the code in the body of the method definition is executed. Because the
value of
n
is a legal value, the
if-else
statement is executed. Because this value of
n
is not greater than
0
, the
return
statement after the
else
is used, so the method call
returns
1
. Thus, the following would set the value of
result3
equal to
1
:
int
result3 = power(2, 0);
Now let's look at an example that involves a recursive call. Consider the expression
power(2, 1)
When the method is called, the value of
x
is set equal to
2
, the value of
n
is set equal
to
1
, and the code in the body of the method definition is executed. Because this
value of
n
is greater than
0
, the following
return
statement is used to determine the
value returned:
return
( power(x, n - 1)*x );
which in this case is equivalent to
return
( power(2, 0)*2 );
At this point, the computation of
power(2, 1)
is suspended, a copy of this suspended
computation is placed on the stack, and the computer then starts a new method call to
compute the value of
power(2, 0)
. As you have already seen, the value of
power(2, 0)
is
1
. After determining the value of
power(2, 0)
, the computer replaces the expression
(continued)
