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5.6 LOCAL VARIABLES AND FUNCTIONS A local variable is simply a variable that is declared inside a block. It is accessible only from within that block. Since the body of a function itself is a block, variables declared within a function are local to that function; they exist only while the function is executing. A function s formal parameters (arguments) are also regarded as being local to the function. The next two examples show functions with local variables. EXAMPLE 5.9 The Factorial Function
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The factorial numbers were introduced in Example 4.9 on page 65. The factorial of a positive integer n is the number n! obtained by multiplying n by all the positive integers less than n: n! = (n)(n 1) (3)(2)(1) For example, 5! = (5)(4)(3)(2)(1) = 120. Here is an implementation of the factorial function: long fact(int n) { // returns n! = n*(n-1)*(n-2)*...*(2)(1) if (n < 0) return 0; int f = 1; while (n > 1) f *= n--; return f; } 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: long fact(int); // returns n! = n*(n-1)*(n-2)*...*(2)(1)
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int main() { // tests the factorial() function: for (int i=-1; i < 6; i++) cout << " " << fact(i); cout << endl; } 0 1 1 2 6 24 120 This program could be compiled separately, or it could be placed in the same file with the function and compiled together.
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EXAMPLE 5.10 The Permutation Function
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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 n items. One way to compute this function is by the formula
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n! P ( n, k ) = ----------------( n k )!
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5! 5! 120 P ( 5, 2 ) = ------------------ = ---- = -------- = 20 3! 6 ( 5 2 )!
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So there are 20 different permutations of 2 items taken from a set of 5. For example, here are the 20 different permutations of length 2 taken from the set {A, B, C, D, E}: AB, AC , AD, AE, BC, BD , BE, CD, CE, DE, BA, CA, DA, EA, CB, DB, EB, DC, EC , ED. The code below implements this formula for the permutation function: long perm(int n, int k) { // returns P(n,k), the number of permutations of k from n: if (n < 0 || k < 0 || k > n) return 0; return fact(n)/fact(n-k); } Notice that the condition (n < 0 || k < 0 || 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: long perm(int,int); // returns P(n,k), the number of permutations of k from n;
int main() { // tests the perm() function: for (int i = -1; i < 8; i++) { for (int j=-1; j <= i+1; j++) cout << " " << perm(i,j); cout << endl; } } 0 0 0 1 0 0 1 1 0 0 1 2 2 0 0 1 3 6 6 0 0 1 4 12 24 24 0 0 1 5 20 60 120 120 0 0 1 6 30 120 360 720 720 0 0 1 7 42 210 840 2520 5040 5040 0 Note that the test driver checks the exceptional cases where i < 0, j < 0, and j > i. Such values are called boundary values because they lie on the boundary of the output set (where perm() returns 0).
5.7 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 5.11 A Function that Prints Dates
void printDate(int,int,int); // // prints the given date in literal form;