The interface of a black box is its connection with the rest of the world, such as the name and parameters of a subroutine or the dial for setting the temperature on a thermostat. The implementation refers to internal workings of the black box. To use the black box, you need to understand its interface, but you don't need to know anything about the implementation.

The contract of a subroutine says what must be done to call the subroutine correctly and what it will do when it is called. It is, in short, everything a programmer needs to know about the subroutine in order to use it correctly. (It does not include the "insides," or implementation, of the subroutine.)

The syntactic component of a subroutine's contract includes the name of the subroutine, the number of parameters, and the type of each parameter. This is the information needed to write a subroutine call statement that can be successfully compiled. The semantic component of the contract specifies the meaning of the subroutine, that is, the task that the subroutine performs. It might also specify limitations on what parameter values the subroutine can process correctly. The semantic component is not part of the program. It is generally expressed in comments.

Top-down refers to starting from the overall problem to be solved, and breaking it up into smaller problems that can be solved separately. When designing a program to solve the problem, you can simply make up a subroutine to solve each of the smaller problems. Then you can separately design and test each subroutine.

Parameters are used for communication between a subroutine and the part of the program that calls the subroutine. If a subroutine is thought of as a black box, then parameters are part of the interface to that black box. Formal parameters are found in the subroutine definition. Actual parameters are found in subroutine call statements. When the subroutine is called, the values of the actual parameters are assigned to the formal parameters before the body of the subroutine is executed.

A constant has a meaningful name, which makes the program easier to read. It's easier to understand what a name like INTEREST_RATE is for than it is to figure out how a literal number like 0.07 is being used.

A second reason for using named constants is that it's easy to modify the value of the constant if that becomes necessary. If a literal value is used throughout the program, the programmer has to track down each occurrence of the value and change it. When a constant is used correctly, it is only necessary to change the value assigned to the constant at one point in the program.

A third reason is that using the final modifier protects the value of a variable from being changed. This is especially important for member variables that are accessible from outside the class where they are declared.

An API is an Applications Programming Interface. It is the interface to a "toolbox" of subroutines that someone has written. It tells you what routines are available, how to call them, and what they do, but it does not tell you how the subroutines are implemented. An example is the standard Java API which describes the interfaces of all the subroutines in all the classes that are available in such packages as java.lang and java.awt.

The subroutine could be written as follows:

static void stars(int numberOfStars) {
     // output a line containing the specified number of stars
   for (int i = 0; i < numberOfStars; i++) {
       System.out.print('*');
   }
   System.out.println();  // output carriage return after the *'s
}

The main() routine can use a for loop that calls the stars() subroutine ten times, once to produce each line of output. (An occasional beginner's mistake in this problem is to rewrite the body of the subroutine inside the main() routine, instead of just calling it by name.) Here is the main routine -- which would, of course, have to be put together with the subroutine in a class in order to be used.

public static void main(String[] args) {
    int line;  // Line number, and also the number of stars on that line.
    for ( line = 1;  line <= 10;  line++ ) {
        stars( line );
    }
}

The returned value will be of type int. The function simply uses a for loop to look at each character in the string. When the character in the string matches the parameter value, it is counted.

static int countChars( String str, char searchChar ) {
      // Count the number of times searchChar occurs in
      // str and return the result.
    int i;     // A position in the string, str.
    char ch;   // A character in the string.
    int count; // Number of times searchChar has been found in str.
    count = 0;
    for ( i = 0;  i < str.length();  i++ ) {
        ch = str.charAt(i);  // Get the i-th character in str.
        if ( ch == searchChar )
           count++;
    }
    return count;
}

I'll call the subroutine smallest and the three parameters x, y, and z. The value returned by the subroutine has to be either x or y or z. The answer will be x if x is less than or equal to both y and z. The correct syntax for checking this is "if (x <= y && x <= z)". Similarly for y. The only other remaining possibility is z, so there is no necessity for making any further test before returning z. (In fact, doing so would be an error in Java, since with no "else" clause in the if statement, the compiler cannot determine that the function definitely returns a value in all possible cases.)

static int smallest(int x, int y, int z) {
   if (x <= y && x <= z) {
      return x;
   }
   else if (y <= x && y <= z) {
      return y;
   }
   else
      return z;
}

Note: Since a return statement causes the computer to terminate the execution of a subroutine anyway, this could also be written as follows, without the elses:

static int smallest(int x, int y, int z) {
   if (x <= y && x <= z) {
      return x;
   }
   if (y <= x && y <= z) {
      return y;
   }
   return z;
}

Note that the array must be passed as a parameter of type double[], and that the value returned by the function will be a double. For the value of N to make sense, it should be in the range 1 up to the length of the array. My answer throws an IllegalArgumentException if N is not in this range:

static double average( double[] numbers, int N ) {
    if ( N < 1 ) {
        throw new IllegalArgumentException("Can't find an average of " +
                       N + " numbers.");
    }
    if ( N > numbers.length ) {
        throw new IllegalArgumentsExcpetion( N + 
                      " is more than the length of the array." );
    }
    int sum = 0;  // the sum of the N numbers
    for ( int i = 0; i < N; N++ ) {
        sum = sum + numbers[i];  // add the i-th number to the sum
    }
    return sum/N;  // Return the average as the value of the function.
}

This function makes a copy of its parameter, except that it leaves out all the elements of list that are equal to zero. It builds a new array that contains all the non-zero elements of list, and it returns that array as the value of the function. (Note that this is an example of using an array type as the return type of a function.)

The function creates a new array to be the return value. But to do that, it must know how long to make the array. The first five lines of the function definition count the number of non-zero elements in list. This is how many spaces we need in the new array, so count is used as the length when the new array is created. The remainder of the function goes through the original list and copies elements into newList. An element is copied only if it is non-zero. We have to keep track of how many spaces in newList have been filled so far. That's what j is for. This is the "partially filled array" pattern from Subsection 3.8.4.