programming-for-dummies

228
Repeating a Subprogram with Recursion
To calculate a factorial, you could use a BASIC program like this:
FUNCTION Factorial (N as INTEGER) as REAL
IF N > 1 THEN
Factorial = N * Factorial (N– 1)
ELSE
Factorial = 1
END FUNCTION
This function uses recursion to run another copy of itself, as shown in
Figure 6-8.
Figure 6-8:
Recursion
makes
multiple
copies of
the same
subprogram.
Factorial (4) = 4 * Factorial (3)
Factorial (3) = 3 * Factorial (2)
To calculate the factorial of N!, you
need to calculate the factorial of (N – 1).
Factorial (2) = 2 * Factorial (1)
Factorial (1) = 1
Factorial (2) = 2 * 1 = 2
Factorial (3) = 3 * 2 = 6
Factorial (4) = 4 * 6 = 24
Eventually a recursive subprogram must calculate a
single value, which then gets used in previous recursive
subprograms until they calculate a single value.
Ultimately, every subprogram that calls itself needs to end. (Otherwise, it can
get trapped in an endless loop, which hangs or freezes your computer.) When
a subprogram finally ends, it returns a value to the preceding subprogram,
which returns its value to the preceding subprogram, and so on until a value
is finally calculated by the first copy of the subprogram that initially ran.
The advantage of recursion is that it’s much simpler to write. If you didn’t
use recursion, this is how you could calculate factorials using an ordinary
FOR-NEXT loop:
FUNCTION Factorial (N as INTEGER) as REAL
DIM Total as REAL
DIM M as INTEGER
Total = 1
FOR M = N DOWNTO 1
Total = Total * M
Factorial = Total
END FUNCTION
Compared to the much smaller and simpler recursive subprogram, this subprogram
is harder to understand although it calculates the exact same
results.