**Table of Contents**

No one ever believes me when I tell them how easy it is to develop
programs that write XML documents. In fact, writing a program to
output an XML document is unbelievably trivial. It’s something
an eight-year old typing BASIC in their first class
at computer camp can do. In Java, it’s even easier than that due to
Java’s strong Unicode support.
You don’t need to know any special APIs like DOM or SAX or JDOM.
All you have to know is how to `System.out.println()`.
If you want to store your XML document in a file, you can
use the
`FileOutputStream` class instead.
If you want to serve the document dynamically over a network, it
helps to know something about servlets;
but in the end it all reduces to writing bytes onto
an output stream.

In this chapter, I’m going to develop a program that writes Fibonacci numbers into an XML document. I chose this example because the Fibonacci numbers are a well-known series that’s very easy to generate algorithmically so the examples will be nicely self-contained. However, the principles of XML you learn here will be much more broadly applicable to other, more complex systems. The key idea is that data arrives from some source, is encoded in XML, and is then output. Where the input comes from, whether an algorithm, a file, a network socket, user input, or some other source, really doesn’t concern us here.

I’m going to show you how to use classes you’re already familiar with like
`OutputStreamWriter`, `String`,
and `HTTPServlet` to generate XML documents.
I am going to beat this idea into the ground until you are absolutely convinced that
there is nothing special about XML documents that requires any fancy tricks to
produce them. Once you’ve finished this chapter you’ll be thoroughly
immunized against the snake-oil peddlers who want to sell you
multi-hundred thousand dollar software to do what you can do
with your existing systems for free.

As far as we know, the Fibonacci series was first
discovered by Leonardo of Pisa around 1200 C.E.
Leonardo was trying to answer the question,
“*Quot paria coniculorum in
uno anno ex uno pario germinatur?*”, or,
in English, “How many pairs of rabbits are born in one year from one pair?”
To solve his problem,
Leonardo estimated that rabbits have a
one month gestation period, and can first mate at the age of one
month, so that each female rabbit has its first litter at two months.
He made the simplifying assumption that each litter consisted of exactly
one male and one female.

Leonardo begins with one pair of baby rabbits, a male and a female.
At the end of the first month,
these two have reached puberty and mate. There’s still one pair of rabbits.
At the end of the second month, the female gives birth to a new pair of rabbits.
There are now two pairs of rabbits, one pair of adults and one pair of babies.
The adult pair mates again, so that they will
produce one more pair at the end of the third month, at which point there are now
three pairs of rabbits. One of these pairs has just been born, but the other two
are old enough to mate, which, being rabbits, they do.
At the end of the third month, two of the three pairs have babies producing five pairs of rabbits.
Meanwhile all rabbits born in previous months mate, so that at the end of the fourth month
there will be three more pairs of rabbits. Leonardo realized that
the number of pairs at the end of each month was the sum of
the number of pairs the preceding month and the number of pairs the
month before that. The rabbits don’t simply double in population
each month because it takes two months before a rabbit can have
its first litter. Nonetheless, the numbers do grow only slightly
more slowly than exponentially; and
the process continues indefinitely, at least
until you run out of rabbit food or the rabbits take over the world,
whichever comes first.
The number of pairs each month—1, 1, 2, 3, 5, 8, 13, ...—
has come to be known as the Fibonacci series
after Leonardo’s Latin nickname, Fibonacci (short for
*filius Bonacci*,
son of Bonacci).

The rabbits aren’t so important, but the math is.
Each integer in the series is formed
by the sum of the two previous integers. The first two integers in the series
are 1 and 1.^{[1]} The Fibonacci series turns up in some very unexpected places
including decimal expansions of π, the golden ratio,
the Mandelbrot set, the number of petals on many flowers,
the number of spirals on pine cones and pineapples,
the number of chambers in a Nautilus shell, and many more.

It’s very easy to calculate the Fibonacci sequence
by computer. A simple `for` loop will do. For example,
this code fragment prints the first 40 Fibonacci numbers:

int low = 1; int high = 1; for (int i = 1; i <= 40; i++) { System.out.println(low); int temp = high; high = high+low; low = temp; }

However, the Fibonacci numbers do grow very large very quickly,
and exceed the bounds of an `int` shortly before the fiftieth
generation.
Consequently, it’s better to use the
`java.math.BigInteger`
class instead, as Example 3.1 demonstrates:

**Example 3.1. A program that calculates the Fibonacci numbers**

import java.math.BigInteger; public class FibonacciNumbers { public static void main(String[] args) { BigInteger low = BigInteger.ONE; BigInteger high = BigInteger.ONE; for (int i = 1; i <= 10; i++) { System.out.println(low); BigInteger temp = high; high = high.add(low); low = temp; } } }

When run, this program produces the first ten Fibonacci numbers:

C:\XMLJAVA>java FibonacciNumbers1 1 2 3 5 8 13 21 34 55

It would be straightforward to read the number of Fibonacci numbers to generate from the command line. However, since user interfaces aren’t the focus of this book, I don’t want to obscure the important parts with too much extraneous fluff.

^{[1] }
In some variations, the first two
integers are 0 and 1. Aside from the initial zero,
this produces the same series.

Copyright 2001, 2002 Elliotte Rusty Harold | elharo@metalab.unc.edu | Last Modified January 21, 2002 |

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