Learn Pascal in a Three Days (2nd Ed.)
(Publisher: Wordware Publishing, Inc.)
Author(s):
ISBN: 1556225679
Publication Date: 07/01/97

Example: The Factorial

The factorial of a positive integer “N” is defined as:

    N! = N * (N-1) * (N-2)... * 3 * 2 * 1

Thus the factorial of 4 is 4 * 3 * 2 * 1, and the factorial of 3 is 3 * 2 * 1. You can then express the following relationships for the factorial:

    4! = 4 * 3!
    3! = 3 * 2!
    2! = 2 * 1!
    1! = 1

In general, you can write the following Pascal statement to calculate the factorial using a counter:

    Factorial := Factorial * Kounter;

The variable “Kounter” can be incremented from 1 to “N” or decremented from “N” to 1. The following program uses this logic in a loop with a decremented step.

{ ------------------------------ figure 4-5 ------------------------------ }
PROGRAM FactorialProg1(INPUT,OUTPUT);
VAR
 Factorial   :REAL;
 Kounter, Number :INTEGER;
BEGIN
 WRITE('Give me a number, and I will tell you the factorial: ');
 READLN(Number);
 Factorial := 1;
 FOR kounter := Number DOWNTO 1 DO
  Factorial := Factorial * Kounter;
 WRITELN('The factorial of ', Number,' is ', Factorial:0:0);
 WRITELN;
 WRITELN('Press ENTER to continue..');
 READLN
END.

Notice that the variable “Factorial” must be initialized to the value 1 before starting the iterative process. A sample run of the program gives the following:

Give me a number, and I will tell you the factorial: 8
The factorial of 8 is 40320

Press ENTER to continue..

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TIP:  Although the factorial of a number is always an integer, using the type REAL (or the Turbo Pascal type LONGINT) for the variable “Factorial” gives you a large storage size with which to receive the quickly increasing results of factorial calculations. If you use the INTEGER type, the program will start giving you funny results after “7”!

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4-4 Nested Loops

Like any other statement, the FOR loop statement can be used inside another loop. In this case it is said that the inner loop is nested inside the outer loop. You can nest as many loops as you wish inside one another, according to your application. The next program displays on your screen the following array of numbers.

1 2 3 4 5
1 2 3 4 5
1 2 3 4 5

The array consists of three rows and five columns. You can control the number of rows and columns by using the counters of two nested loops. As you can see, for each round of the outer loop counter (Row), the inner loop counter (Column) loops five times. The values that appear in the output are the values of the counter “Column.” Notice that a blank line is displayed after a complete row is done, using the outer loop counter.

{ ------------------------------ figure 4-6 ------------------------------ }
PROGRAM NestedLoops(OUTPUT);
VAR
 Row, Column :INTEGER;
BEGIN
 FOR Row := 1 TO 3 DO               { Start of the outer loop }
  BEGIN
   FOR Column := 1 to 5 DO { Start of the inner loop }
    WRITE(Column, ' ');    { End of the inner loop }
   WRITELN           { This statement belongs to the outer loop }
  END                         { The end of the outer loop }
END.

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TIP:  Notice the two END keywords in the previous program. The first one comes without a semicolon because it is the last statement in the main block (the program main body). Also, the keyword WRITELN, which comes before this END, was not terminated by a semicolon. This is because it is the last statement in the loop block. All of these are options, but you may use the semicolons if you wish. If you add another statement at the end of the program (to suspend the screen, for instance), the situation will change.

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