Problem Solving with Algorithms and Data Structures using Java: The Interactive Edition

The earlier example of procedural abstraction called upon a Java method called sqrt from the Math module to compute the square root. In general, we can hide the details of any computation by defining a method. A method definition requires a name, a group of parameters, and a body. It may also explicitly return a value. For example, the method defined below returns the square of the value you pass into it.

jshell> public static double square(double n) {
   ...>     return n * n;
   ...> }
|  created method square(double)

jshell> square(2.5);
$2 ==> 6.25

Let’s look at the first line of the method one token at a time:

The details of how the method works are hidden “inside the box”; it returns the result of multiplying result of n * n.

We can invoke or call the method function giving its name and passing an actual parameter value, in this case, 2.5 to fill in the parameter. Note that the call to square returns a double that can in turn be passed to another method invocation.

We could implement our own square root function by using a well-known technique called Newton’s method or the Newton–Raphson method, named after Isaac Newton and Joseph Raphson. The Newton–Raphson method for approximating square roots performs an iterative computation that converges on the correct value. The equation \(newguess = \frac {1}{2} * (oldguess + \frac {n}{oldguess})\) takes a value \(n\) and repeatedly guesses the square root by making each \(newguess\) the \(oldguess\) in the subsequent iteration. The initial guess used here is \(\frac {n}{2}\text{.}\) Listing 1.14.1 shows a program with a method definition that accepts a value \(n\) and returns the square root of \(n\) after making 20 guesses. Again, the details of the Newton–Raphson method are hidden inside the method definition and the user does not have to know anything about the implementation to use the method for its intended purpose. Listing 1.14.1 also shows the use of the // characters as a comment marker. Any characters that follow the // on a line are ignored.