Visual Basic.NET How to Program (PDF)

Chapter 6 Procedures 219
The factorial of an integer number greater than or equal to 0 can be calculated iteratively
(nonrecursively) using a For repetition structure, as follows:
Dim counter, factorial As Integer = 1
For counter = number To 1 Step -1
factorial *= counter
Next
We arrive at a recursive definition of the factorial procedure with the following relationship:
n! = n · ( n - 1 )!
For example, 5! is clearly equal to 5 · 4!, as is shown by the following:
5! = 5 · 4 · 3 · 2 · 1
5! = 5 · ( 4 · 3 · 2 · 1 )
5! = 5 · ( 4! )
A recursive evaluation of 5! would proceed as in Fig. 6.18. Figure 6.18a shows how
the succession of recursive calls proceeds until 1! is evaluated to be 1, which terminates the
recursion. Figure 6.18b depicts the values that are returned from each recursive call to its
caller until the final value is calculated and returned.
The program of Fig. 6.19 recursively calculates and prints factorials. (The choice of
the data type Long will be explained soon). The recursive method Factorial (lines 33–
41) first tests (line 35) to determine whether its terminating condition is true (i.e., number
is less than or equal to 1). If number is less than or equal to 1, Factorial returns 1, no
further recursion is necessary, and the method returns. If number is greater than 1, line 38
expresses the problem as the product of number and a recursive call to Factorial, evaluating
the factorial of number - 1. Note that Factorial(number - 1) is a slightly
simpler problem than the original calculation, Factorial(number).
5!
5 * 4!
4 * 3!
3 * 2!
2 * 1!
Fig. Fig. Fig. 6.18 6.18 Recursive evaluation of 5!.
1
5!
5 * 4!
Final value = 120
4 * 3!
5! = 5 * 24 = 120 is returned
3 * 2!
4! = 4 * 6 = 24 is returned
2 * 1!
3! = 3 * 2 = 6 is returned
(a) Procession of recursive calls (b) Values returned from each recursive call
1
2! = 2 * 1 = 2 is returned
1 returned