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Section 3.4
The for Statement

WE TURN IN THIS SECTION to another type of loop, the for statement. Any for loop is equivalent to some while loop, so the language doesn't get any additional power by having for statements. But for a certain type of problem, a for loop can be easier to construct and easier to read than the corresponding while loop. It's quite possible that in real programs, for loops actually outnumber while loops.

The for statement makes a common type of while loop easier to write. Many while loops have the general form:

            while ( continuation-condition ) {

For example, consider this example, copied from an example in Section 2:

            years = 0;  // initialize the variable years
            while ( years < 5 ) {   // condition for continuing loop
                interest = principal * rate;    //
                principal += interest;          // do three statements
                System.out.println(principal);  //
                years++;   // update the value of the variable, years

This loop can be written as the following equivalent for statement:

            for ( years = 0;  years < 5;  years++ ) {
               interest = principal * rate;
               principal += interest;

The initialization, continuation condition, and updating have all been combined in the first line of the for loop. This keeps everything involved in the "control" of the loop in one place, which helps makes the loop easier to read and understand. The for loop is executed in exactly the same way as the original code: The initialization part is executed once, before the loop begins. The continuation condition is executed before each execution of the loop, and the loop ends when this condition is false. The update part is executed at the end of each execution of the loop, just before jumping back to check the condition.

The formal syntax of the for statement is as follows:

            for ( initialization; continuation-condition; update )

or, using a block statement:

            for ( initialization; continuation-condition; update ) {

The continuation-condition must be a boolean-valued expression. The initialization can be any expression, as can the update. Any of the three can be empty. If the continuation condition is empty, it is treated as if it were "true," so the loop will be repeated forever or until it ends for some other reason, such as a break statement. (Some people like to begin an infinite loop with "for (;;)" instead of "while (true)".)

Usually, the initialization part of a for statement assigns a value to some variable, and the update changes the value of that variable with an assignment statement or with an increment or decrement operation. The value of the variable is tested in the continuation condition, and the loop ends when this condition evaluates to false. A variable used in this way is called a loop control variable. In the for statement given above, the loop control variable is years.

Certainly, the most common type of for loop is the counting loop, where a loop control variable takes on all integer values between some minimum and some maximum value. A counting loop has the form

            for ( variable = min;  variable <= max; variable++ ) {

where min and max are integer-valued expressions (usually constants). The variable takes on the values min, min+1, min+2, ...,max. The value of the loop control variable is often used in the body of the loop. The for loop at the beginning of this section is a counting loop in which the loop control variable, years, takes on the values 1, 2, 3, 4, 5. Here is an even simpler example, in which the numbers 1, 2, ..., 10 are displayed on standard output:

             for ( N = 1 ;  N <= 10 ;  N++ )
                System.out.println( N );

For various reasons, Java programmers like to start counting at 0 instead of 1, and they tend to use a "<" in the condition, rather than a "<=". The following variation of the above loop prints out the ten numbers 0, 1, 2, ..., 9:

             for ( N = 0 ;  N < 10 ;  N++ )
                System.out.println( N );

Using < instead of <= in the test, or vice versa, is a common source of off-by-one errors in programs. You should always stop and think, do I want the final value to be processed or not?

It's easy to count down from 10 to 1 instead of counting up. Just start with 10, decrement the loop control variable instead of incrementing it, and continue as long as the variable is greater than or equal to one.

             for ( N = 10 ;  N >= 1 ;  N-- )
                System.out.println( N );

Now, in fact, the official syntax of a for statemenent actually allows both the initialization part and the update part to consist of several expressions, separated by commas. So we can even count up from 1 to 10 and count down from 10 to 1 at the same time!

          for ( i=1, j=10;  i <= 10;  i++, j-- ) {
             TextIO.put(i,5);   // Output i in a 5-character wide column.
             TextIO.putln(j,5); // Output j in a 5-character column
                                //     and end the line.

As a final example, let's say that we want to use a for loop that prints out just the even numbers between 2 and 20, that is: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. There are several ways to do this. Just to show how even a very simple problem can be solved in many ways, here are four different solutions (three of which would get full credit):

          (1)   // There are 10 numbers to print.
                // Use a for loop to count 1, 2,
                // ..., 10.  The numbers we want
                // to print are 2*1, 2*2, ... 2*10.
                for (N = 1; N <= 10; N++) {
                   System.out.println( 2*N );
          (2)   // Use a for loop that counts
                // 2, 4, ..., 20 directly by
                // adding 2 to N each time through
                // the loop.
                for (N = 2; N <= 20; N = N + 2) {
                   System.out.println( N );
          (3)   // Count off all the numbers
                // 2, 3, 4, ..., 19, 20, but
                // only print out the numbers
                // that are even.
                for (N = 2; N <= 20; N++) {
                   if ( N % 2 == 0 ) // is N even?
                      System.out.println( N );
          (4)   // Irritate the professor with
                // a solution that follows the
                // letter of this silly assignment
                // while making fun of it.
                for (N = 1; N <= 1; N++) {
                   System.out.print("2 4 6 8 10 12 ");
                   System.out.println("14 16 18 20");

Perhaps it is worth stressing one more time that a for statement, like any statement, never occurs on its own in a real program. A statement must be inside the main routine of a program or inside some other subroutine. And that subroutine must be defined inside a class. I should also remind you that every variable must be declared before it can be used, and that includes the loop control variable in a for statement. In all the examples that you have seen so far in this section, the loop control variables should be declared to be of type int. It is not required that a loop control variable be an integer. Here, for example, is a for loop in which the variable, ch, is of type char:

          // Print out the alphabet on one line of output.
          char ch;  // The loop control variable;
                    //       one of the letters to be printed.
          for ( char ch = 'A';  ch <= 'Z';  ch++ )

Let's look at a less trivial problem that can be solved with a for loop. If N and D are positive integers, we say that D is a divisor of N if the remainder when D is divided into N is zero. (Equivalently, we could say that N is an even multiple of D.) In terms of Java programming, D is a divisor of N if N % D is zero.

Let's write a program that inputs a positive integer, N, from the user and computes how many different divisors N has. The numbers that could possibly be divisors of N are 1, 2, ...,N. To compute the number of divisors of N, we can just test each possible divisor of N and count the ones that actually do divide N evenly. In pseudocode, the algorithm takes the form

           Get a positive integer, N, from the user
           Let divisorCount = 0
           for each number, testDivisor, in the range from 1 to N:
               if testDivisor is a divisor of N:
                   Count it by adding 1 to divisorCount
           Output the count

This algorithm displays a common programming pattern that is used when some, but not all, of a sequence of items are to be processed. The general pattern is

            for each item in the sequence:
               if the item passes the test:
                   process it

The for loop in our divisor-counting algorithm can be translated into Java code as

            for (testDivisor = 1; testDivisor <= N; testDivisor++) {
               if ( N % testDivisor == 0 )

On a modern computer, this loop can be executed very quickly. It is not impossible to run it even for the largest legal int value, 2147483647. (If you wanted to run it for even larger values, you could use variables of type long rather than int.) However, it does take a noticeable amount of time for very large numbers. So when I implemented this algorithm, I decided to output a period every time the computer has tested one million possible divisors. In the improved version of the program, there are two types of counting going on. We have to count the number of divisors and we also have to count the number of possible divisors that have been tested. So the program needs two counters. When the second counter reaches 1000000, we output a '.' and reset the counter to zero so that we can start counting the next group of one million. Reverting to pseudocode, the algorithm now looks like

           Get a positive integer, N, from the user
           Let divisorCount = 0  // Number of divisors found.
           Let numberTested = 0  // Number of possible divisors tested
                                 //       since the last period was output.
           for each number, testDivisor, in the range from 1 to N:
               if testDivisor is a divisor of N:
                   Count it by adding 1 to divisorCount
               Add 1 to numberTested
               if numberTested is 1000000:
                   print out a '.'
                   Let numberTested = 0
           Output the count

Finally, we can translate the algorithm into a complete Java program. Here it is, followed by an applet that simulates it:

     public class CountDivisors {
        /*  This program reads a positive integer from the user.
            It counts how many divisors that number has, and
            then it prints the result.
        public static void main(String[] args) {
           int N;  // A positive integer entered by the user.
                   // Divisors of this number will be counted.
           int testDivisor;  // A number between 1 and N that is a
                             // possible divisor of N.
           int divisorCount;  // Number of divisors of N that have been found.
           int numberTested;  // Used to count how many possible divisors
                              // of N have been tested.  When the number
                              // reaches 1000000, a period is output and
                              // the value of numberTested is reset to zero.
           /* Get a positive integer from the user. */
           while (true) {
              TextIO.put("Enter a positive integer: ");
              N = TextIO.getlnInt();
              if (N > 0)
              TextIO.putln("That number is not positive.  Please try again.");
           /* Count the divisors, printing a "." after every 1000000 tests. */
           divisorCount = 0;
           numberTested = 0;
           for (testDivisor = 1; testDivisor <= N; testDivisor++) {
              if ( N % testDivisor == 0 )
              if (numberTested == 1000000) {
                 numberTested = 0;
           /* Display the result. */
           TextIO.putln("The number of divisors of " + N
                               + " is " + divisorCount);
        } // end main()
     } // end class CountDivisors

(Applet "CountDivisorsConsole" would be displayed here
if Java were available.)

Nested Loops

Control structures in Java are statements that contain statements. In particular, control structures can contain control structures. You've already seen several examples of if statements inside loops, but any combination of one control structure inside another is possible. We say that one structure is nested inside another. You can even have multiple levels of nesting, such as a while loop inside an if statement inside another while loop. The syntax of Java does not set a limit on the number of levels of nesting. As a practical matter, though, it's difficult to understand a program that has more than a few levels of nesting.

Nested for loops arise naturally in many algorithms, and it is important to understand how they work. Let's look at a couple of examples. First, consider the problem of printing out a multiplication table like this one:

            1   2   3   4   5   6   7   8   9  10  11  12
            2   4   6   8  10  12  14  16  18  20  22  24
            3   6   9  12  15  18  21  24  27  30  33  36
            4   8  12  16  20  24  28  32  36  40  44  48
            5  10  15  20  25  30  35  40  45  50  55  60
            6  12  18  24  30  36  42  48  54  60  66  72
            7  14  21  28  35  42  49  56  63  70  77  84
            8  16  24  32  40  48  56  64  72  80  88  96
            9  18  27  36  45  54  63  72  81  90  99 108
           10  20  30  40  50  60  70  80  90 100 110 120
           11  22  33  44  55  66  77  88  99 110 121 132
           12  24  36  48  60  72  84  96 108 120 132 144

The data in the table are arranged into 12 rows and 12 columns. The process of printing them out can be expressed in a pseudocode algorithm as

           for each rowNumber = 1, 2, 3, ..., 12:
              Print the first twelve multiples of rowNumber on one line
              Output a carriage return

The first step in the for loop can itself be expressed as a for loop:

              for N = 1, 2, 3, ..., 12:
                 Print N * rowNumber

so a refined algorithm for printing the table has one for loop nested inside another:

           for each rowNumber = 1, 2, 3, ..., 12:
              for N = 1, 2, 3, ..., 12:
                 Print N * rowNumber
              Output a carriage return

Assuming that rowNumber and N have been declared to be variables of type int, this can be expressed in Java as

         for ( rowNumber = 1;  rowNumber <= 12;  rowNumber++ ) {
            for ( N = 1;  N <= 12;  N++ ) {
                        // print in 4-character columns
               TextIO.put( N * rowNumber,  4 );

This section has been weighed down with lots of examples of numerical processing. For our final example, let's do some text processing. Consider the problem of finding which of the 26 letters of the alphabet occur in a given string. For example, the letters that occur in "Hello World" are D, E, H, L, O, R, and W. More specifically, we will write a program that will list all the letters contained in a string and will also count the number of different letters. The string will be input by the user. Let's start with a pseudocode algorithm for the program.

           Ask the user to input a string
           Read the response into a variable, str
           Let count = 0  (for counting the number of different letters)
           for each letter of the alphabet:
              if the letter occurs in str:
                 Print the letter
                 Add 1 to count
           Output the count

Since we want to process the entire line of text that is entered by the user, we'll use TextIO.getln() to read it. The line of the algorithm that reads "for each letter of the alphabet" can be expressed as "for (letter='A'; letter<='Z'; letter++)". But the body of this for loop needs more thought. How do we check whether the given letter, letter, occurs in str? One idea is to look at each letter in the string in turn, and check whether that letter is equal to letter. We can get the i-th character of str with the function call str.charAt(i), where i ranges from 0 to str.length() - 1. One more difficulty: A letter such as 'A' can occur in str in either upper or lower case, 'A' or 'a'. We have to check for both of these. But we can avoid this difficulty by converting str to upper case before processing it. Then, we only have to check for the upper case letter. We can now flesh out the algorithm fully. Note the use of break in the nested for loop. It is required to avoid printing or counting a given letter more than once. The break statement breaks out of the inner for loop, but not the outer for loop. Upon executing the break, the computer continues the outer loop with the next value of letter.

             Ask the user to input a string
             Read the response into a variable, str
             Convert str to upper case
             Let count = 0
             for letter = 'A', 'B', ..., 'Z':
                 for i = 0, 1, ..., str.length()-1:
                     if letter == str.charAt(i):
                         Print letter
                         Add 1 to count
                         break  // jump out of the loop
             Output the count

Here is the complete program and an applet to simulate it:

        public class ListLetters {
           /* This program reads a line of text entered by the user.
              It prints a list of the letters that occur in the text,
              and it reports how many different letters were found.
           public static void main(String[] args) {
              String str;  // Line of text entered by the user.
              int count;   // Number of different letters found in str.
              char letter; // A letter of the alphabet.
              TextIO.putln("Please type in a line of text.");
              str = TextIO.getln();
              str = str.toUpperCase();
              count = 0;
              TextIO.putln("Your input contains the following letters:");
              TextIO.put("   ");
              for ( letter = 'A'; letter <= 'Z'; letter++ ) {
                  int i;  // Position of a character in str.
                  for ( i = 0; i < str.length(); i++ ) {
                      if ( letter == str.charAt(i) ) {
                          TextIO.put(' ');
              TextIO.putln("There were " + count + " different letters.");
           } // end main()
        } // end class ListLetters

(Applet "ListLettersConsole" would be displayed here
if Java were available.)

In fact, there is an easier way to determine whether a given letter occurs in a string, str. The built-in function str.indexOf(letter) will return -1 if letter does not occur in the string. It returns a number greater than or equal to zero if it does occur. So, we could check whether letter occurs in str simply by checking "if (str.indexOf(letter) >= 0)". If we used this technique in the above program, we wouldn't need a nested for loop. This gives you preview of how subroutines can be used to deal with complexity.

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