Iterative Factorial Implementation

To illustrate the differences between iteration and recursion, let’s examine an iterative solution to the factorial problem (Fig. 6.30). A repetition statement is used (lines 23–24 of Fig. 6.30) rather than the selection statement of the recursive solution (lines 20–23 of Fig. 6.27). Both solutions use a termination test. In the recursive solution, line 20 (Fig. 6.27) tests for the base case. In the iterative solution, line 23 (Fig. 6.30) tests the loop-continuation condition—if the test fails, the loop terminates. Finally, instead of producing simpler versions of the original problem, the iterative solution uses a counter that is modified until the loop-continuation condition becomes false.

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 1   // Fig. 6.30: fig06_30.cpp
 2   // Iterative function factorial.
 3   #include <iostream>
 4   #include <iomanip>
 5   using namespace std;
 6
 7   unsigned long factorial( unsigned int ); // function prototype
 8
 9   int main()
10   {
11      // calculate the factorials of 0 through 10
12      for ( unsigned int counter = 0; counter <= 10; ++counter )
13         cout << setw( 2 ) << counter << "! = " << factorial( counter )
14            << endl;
15   } // end main
16
17   // iterative function factorial
18   unsigned long factorial( unsigned int number )
19   {
20      unsigned long result = 1;
21
22      // iterative factorial calculation          
23      for ( unsigned int i = number; i >= 1; --i )
24         result *= i;                             
25
26      return result;
27   } // end function factorial

 0! = 1
 1! = 1
 2! = 2
 3! = 6
 4! = 24
 5! = 120
 6! = 720
 7! = 5040
 8! = 40320
 9! = 362880
10! = 3628800

Fig. 6.30. Iterative function factorial.

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