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?

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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 oops--a bug next first second
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)

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The End