Fibonacci Numbers

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Fibonacci Numbers

• A simple example of program design

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Purpose of this presentation

• The whole point of this presentation is to give
  you some idea of how to put together the
  components we have so far (declarations,
  assignments, if and while statements) into a
  working program
• The example we use is writing a program to
  compute and display a Fibonacci sequence

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Fibonacci sequences

• A Fibonacci sequence is an infinite list of
  integers
• The first two numbers are given
• Usually (but not necessarily) these are 1 and 1
• Each subsequent number is the sum of the two
  preceding numbers
• 1 1 2 3 5 8 13 21 34 55 89 144 ...
• Lets write a program to compute these

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Starting the Fibonacci sequence

• We need to supply the first two integers
• int first 1int second 1
• We need to print these out
• System.out.print(first " ")System.out.print(se
  cond " ")
• We need to compute and print the next number
• int next first secondSystem.out.print(next
  " ")

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Taking the next step

• We need to compute and print the next number
• int next first secondSystem.out.print(next
  " ")
• Now what?
• We don't want to make up a lot more names
• If we use a loop, we must reuse names

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Preparing for another step

• This computation gave us our third number
• int next first secondSystem.out.print(next
  " ")
• The sequence so far is first second next
• To get another number, we need second next
• Variable first is no longer useful for anything
• Lets move values around so that first second
  does the job we need

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Preparing to make many steps

• We need to make these moves

• We can do it like this
• first secondsecond next
• We can put these statements in a loop and do them
  as many times as we please

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The program so far
int first 1int second 1System.out.print(fi
rst " ")System.out.print(second " ")while
( ? ? ? ) // when do we stop? int next
first second System.out.print(next "
") first second second next
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Deciding when to stop

• Suppose we stop when we get to a number thats
  1000 or bigger
• So we continue as long as the number is less than
  1000
• while (next
• Question is the final number printed greater
  than 1000 or less than 1000?
• while (next second System.out.print(next " ")
  first second second next

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One other minor detail

• We have been printing the numbers all on one line
• Well get to 1000 quickly enough, so we wont
  have a terribly long line
• For neatness sake, we really ought to end the
  line (rather than hoping Java does it for us)
• System.out.println( )

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The program so far
int first 1int second 1System.out.print(fi
rst " ")System.out.print(second " ")while
(next second System.out.print(next " ")
first second second nextSystem.out.pr
intln( )
// oops--a bug
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Fixing the bug

• The first time we see the variable next, its in
  the test of the while loop
• while (next
• next hasnt been given a value yet
• next hasnt even been declared!
• Solution declare next up with the other
  variables, and give it some reasonable initial
  value

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The (fixed) program so far
int first 1int second 1int next
2System.out.print(first " ")System.out.print
(second " ")while (next first second // "int" was removed
System.out.print(next " ") first
second second nextSystem.out.println(
)
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Finishing up

• We have the commands we need, but we do not have
  a complete application
• We need to put the commands into a method
• We need to put the method into a class
• The next slide shows the extra stuff we need, but
  doesnt explain it

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The box our program goes in
public class Fibonacci public static void
main(String args) (code goes here)

If we were to use multiple methods, we would want
a more complex box to avoid issues with static
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The complete final program
public class Fibonacci public static void
main(String args) int first 1
int second 1 int next 2
System.out.print(first " ")
System.out.print(second " ") while
(next second System.out.print(next "
") first second
second next
System.out.println( )
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Where is it?

• When we run Eclipse, we declare some folder to be
  a workspace
• All our projects go into this (or some other)
  workspace
• To create a new program in Eclipse, we must
  first create a project to hold all our classes
• Eclipse will create a directory with the same
  name as the project
• You should not rename this directory
• When you create a class in Eclipse, such as
  Fibonacci, it will be put in a file with the same
  name but with the .java extensionfor example,
  Fibonacci.java
• You must not change the name of this file!
• Java uses the file names to find the classes it
  needs

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The End
Always code as if the guy who ends up
maintaining your code will be a violent
psychopath who knows where you live.

--Martin Golding