Using a Recursive factorial Function to Calculate Factorials

Figure 6.27 uses recursion to calculate and print the factorials of the integers 0–10. (The choice of the data type unsigned long is explained momentarily.) The recursive function factorial (lines 18–24) first determines whether the terminating condition number <= 1 (line 20) is true. If number is less than or equal to 1, the factorial function returns 1 (line 21), no further recursion is necessary and the function terminates. If number is greater than 1, line 23 expresses the problem as the product of number and a recursive call to factorial evaluating the factorial of number - 1, which is a slightly simpler problem than the original calculation factorial (number).

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 1   // Fig. 6.27: fig06_27.cpp
 2   // Recursive function factorial.
 3   #include <iostream>
 4   #include <iomanip>
 5   using namespace std;
 6
 7   unsigned long factorial( unsigned long ); // 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   // recursive definition of function factorial   
18   unsigned long factorial( unsigned long number ) 
19   {                                               
20      if ( number <= 1 ) // test for base case     
21         return 1; // base cases: 0! = 1 and 1! = 1
22      else // recursion step                       
23         return number * factorial( number - 1 );  
24   } // 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. 6.27. Recursive function factorial.

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