C++ Primer Plus

C++ adds a feature to C loops that requires some artful adjustments to the for loop syntax. This was the original syntax:

for (expression; expression; expression)

     statement

In particular, the control section of a for structure consisted of three expressions, as defined earlier in this chapter, separated by semicolons. C++ loops allow you do to things like the following, however:

for (int i = 0; i < 5; i++)

That is, you can declare a variable in the initialization area of a for loop. This can be convenient, but it doesn’t fit the original syntax because a declaration is not an expression. This once outlaw behavior was originally accommodated by defining a new kind of expression, the declaration-statement expression, which was a declaration stripped of the semicolon, and which could appear only in a for statement. That adjustment has been dropped, however. Instead, the syntax for the for statement has been modified to the following:

for (for-init-statement condition; expression)

     statement

At first glance, this looks odd because there is just one semicolon instead of two. But that’s okay because for-init-statement is identified as a statement, and a statement has its own semicolon. As for for-init-statement, it’s identified as either an expression-statement or a declaration. This syntax rule replaces an expression followed by a semicolon with a statement, which has its own semicolon. What this boils down to is that C++ programmers want to be able to declare and initialize a variable in a for loop initialization, and they’ll do whatever is necessary to C++ syntax and to the English language to make it possible.

There’s a practical aspect to declaring a variable in for-init-statement that you should know about. Such a variable exists only within the for statement. That is, after the program leaves the loop, the variable is eliminated:

for (int i = 0; i < 5; i++)

    cout << "C++ knows loops.\n";

cout << i << endl;  // oops! i no longer defined

Another thing you should know is that some older C++ implementations follow an earlier rule and treat the preceding loop as if i were declared before the loop, thus making it available after the loop terminates.

Back to the for Loop

Let’s be a bit more ambitious with loops. Listing 5.4 uses a loop to calculate and store the first 16 factorials. Factorials, which are handy for computing odds, are calculated the following way. Zero factorial, written as 0!, is defined to be 1. Then, 1! is 1 * 0!, or 1. Next, 2! is 2 * 1!, or 2. Then, 3! is 3 * 2!, or 6, and so on, with the factorial of each integer being the product of that integer with the preceding factorial. (One of the late pianist-comedian Victor Borge’s best-known monologues featured phonetic punctuation, in which the exclamation mark is pronounced something like phffft pptz, with a moist accent. However, in this case, “!” is pronounced “factorial.”) The program uses one loop to calculate the values of successive factorials, storing them in an array. Then it uses a second loop to display the results. Also the program introduces the use of external declarations for values.

Listing 5.4. formore.cpp

// formore.cpp -- more looping with for

#include

const int ArSize = 16;      // example of external declaration

int main()

{

    long long factorials[ArSize];

    factorials[1] = factorials[0] = 1LL;

    for (int i = 2; i < ArSize; i++)

        factorials[i] = i * factorials[i-1];

    for (int i = 0; i < ArSize; i++)

        std::cout << i << "! = " << factorials[i] << std::endl;

    return 0;

}

Here is the output from the program in Listing 5.4:

0! = 1

1! = 1

2! = 2

3! = 6

4! = 24

5! = 120

6! = 720

7! = 5040

8! = 40320

9! = 362880

10! = 3628800

11! = 39916800

12! = 479001600

13! = 6227020800

14! = 87178291200

15! = 1307674368000

Factorials get big fast!

Note

This listing uses the long long type. If your system doesn’t have that type available, you can use double. However, the integer format gives a nicer visual representation of how the numbers grow larger.

Program Notes

The program in Listing 5.4 creates an array to hold the factorial values. Element 0 is 0!, element 1 is 1!, and so on. Because the first two factorials equal 1, the program sets the first two elements of the factorials array to 1.0. (Remember, the first element of an array has an index value of 0.) After that, the program uses a loop to set each factorial to the product of the index with the previous factorial. The loop illustrates that you can use the loop counter as a variable in the body of the loop.