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This example illustrates several new ideas. The main idea is the use of the boolean functions isdigit(), islower() , isupper(), isspace(), iscntrl() , and ispunct(). For example, the call isspace(c) tests the character c to determine whether it is a white space character. (There are six white space characters: the horizontal tab character \t, the newline character \n, the vertical tab character \v, the form feed character \f, the carriage return character \r, and the space character.) If c is any of these characters, then the function returns a nonzero integer for true; otherwise it returns 0 for false. Placing the call as the condition in the if statement causes the corresponding output statement to execute if and only if c is one of these characters. Each character is tested within the printCharCategory() function. Although the program could have been written without this separate function, its use modularizes the program, making it more structured. We are conforming here to the general programming principle that recommends that every task be relegated to a separate function.
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Functions such as isdigit() and ispunct() which are defined in the C header files (such as <cctype>) were originally defined for the C programming language. Since that language does not have a standard boolean type, those boolean functions return an integer instead of true or false. But since those C++ boolean values are stored as integers (see Section 2.2), the conversion from integer value to bool value is automatic. EXAMPLE 5.13 A Function that Tests Primality
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Here is a boolean function that determines whether an integer is a prime number: bool isPrime(int n) { // returns true if n is prime, false otherwise: float sqrtn = sqrt(n); if (n < 2) return false; // 0 and 1 are not primes if (n < 4) return true; // 2 and 3 are the first primes if (n%2 == 0) return false; // 2 is the only even prime for (int d=3; d <= sqrtn; d += 2) if (n%d == 0) return false; // n has a nontrivial divisor return true; // n has no nontrivial divisors } This function works by looking for a divisor d of the given number n. It tests divisibility by the value of the condition (n%d == 0). This will be true precisely when d is a divisor of n. In that case, n cannot be a prime number, so the function immediately returns false. If the for loop finishes without finding any divisors of n, then the function returns true. We can stop searching for divisors once we get past the square root of n because if n is a product d*a, then one of these factors must be less than or equal to the square root of n. We define the sqrtn outside the loop so that it only has to be evaluated once. It is also more efficient to check for even numbers (n%2 == 2) first. This way, once we get to the for loop, we need only check for odd divisors. This is done by incrementing the divider d by 2 on each iteration. Here is a test driver and a test run for the isPrime() function: #include <cmath> // defines the sqrt() function #include <iostream> // defines the cout object using namespace std;
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bool isPrime(int); // returns true if n is prime, false otherwise;
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int main() { for (int n=0; n < 80; n++) if (isPrime(n)) cout << n << " "; cout << endl; } 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 Notice that, like the c-type functions in the previous example, a verb phrase is used for the name of this function. The name isPrime makes the function s use more readable for humans: the code if (isPrime(n)) . . . is almost the same as the ordinary English phrase if n is prime... It should be noted that this function is not optimal. In searching for divisors, we need only check prime numbers, because every composite (non-prime) number is a unique product of primes. To modify this function so that it checks only prime divisors requires that the primes be stored as they are found. That requires using an array. (See Problem 6.22 on page 144.)
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