# microsoft reporting services qr code The factorial ( ) Function in Software Drawer QR Code 2d barcode in Software The factorial ( ) Function

EXAMPLE
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4.8 The factorial ( ) Function
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The factorial of a positive integer y2 is the number n! obtained by multiplying n by all the positive integers less than n: n! = (n)(n - 1) . (3)(2)(l) For example, 5! = (5)(4)(3)(2)(l) = 120. Here is an implementation of the factorial function:
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int {
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factorial(int
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if (n < 0) return 0; int f = 1; while (n > 1) f *= n--; return f;
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This function has two local variables: n and f. The parameter n is local because it is declared in the function s parameter list. The variable f is local because it is declared within the body of the function. Here is a test driver for the factorial function:
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int factorial(int); main0 { for (int i = -1; i < 6; i++) tout cc tl ' CC factorial(i); tout CC endl; '0' 1, f.26 .24 120 :;
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FUNCTIONS
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This program could be compiled separately, or it could be placed in the same file with the function and compiled together.
EXAMPLE 4.9 The Permutation Function
A permutation is an arrangement of elements taken from a finite set. The permutation function P(n,k) gives the number of different permutations of any k items taken from a set of YI items. One way to compute this function is by the formula
n! P(n, k ) = ~ (n-k)!
For example,
P(5,2) =
5! A-=-= 120=2()
(5-2)! 3! 6
So there are 20 different permutations of 2 items taken from a set of 5. The code below implements this formula for the permutation function:
// Returns P(n;k), the number of permutations of k from n: int perm(int n, int k) -t if (n < 0 II k < 0 II k > n) return 0; return factorial(n)/factorial(n-k); >
Notice that the condition (n < 0 11k < 0 I I k > n) is used to handle the cases where either parameter is out of range. In these cases the function returns an impossible value, 0, to indicate that its input was erroneous. That value would then be recognized by the calling program as an error flag. Here is a test driver for the perm ( ) function:
int perm(int,int);
main0 1 for (int i = -1; i < 8; i++) { for (int j = -1; j <= i+l; j++) tout << " il << perm(i,j); tout << endl; > >
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FUNCTIONS
4.7 void FUNCTIONS A function need not return a value. In other programming languages, such a function is called a procedure or a subroutine. In C++, such a function is identified simply by placing the keyword void where the function s return type would be. A type specifies a set of values. For example, the type short specifies the set of integers from -32,768 to 32,767. The void type specifies the empty set. Consequently, no variable can be declared with void type. A void function is simply one that returns no value.
EXAMPLE 4.10 A printDate () Function
This function prints the date in literal form, given its month, day, and year in numeric form:
void main0 int month, day, year; tin >> month >> day >> year; printDate(month,day,year); } while (month > 0); printDate(int, int, int);
void printDate(int
m, int d, int y)
if (m < 1 II m > 12 II d < 1 II d > 31 II y < 0) { tout C-C 'Error: parameter out of range.\n"; return; switch (m) { case 1: case 2: case 3: case 4: case 5: . case 6: case 7: case 8: case 9: case 10: case 11: case 12: tout << d <<
tout <<
tout <<
tout -C-C tout CC
tout <<
tout C-C tout << tout << tout <<
tout c-c
tout <<
tout -c-c
"January "; "February '; "March "; "April "; " May " ; "June "; "July "; "August "; "September "; "October '; "November "; "December ';
break; break; break; break; break; break; break; break; break; break; break; break;
C-C y << endl;
The printDa t e ( ) function returns no value. Its only purpose is to print the date. So its return type is void. The function uses a swi tch statement to print the month as a literal, and it prints the day and year as integers.