1. A simple example of program design
Fibonacci Numbers
A simple example of program design
17-Nov-18

2. 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

3. 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:
Let’s write a program to compute these

4. Starting the Fibonacci sequence
We need to supply the first two integers
int first = 1; int second = 1;
We need to print these out:
System.out.print(first + " "); System.out.print(second + " ");
We need to compute and print the next number:
int next = first + second; System.out.print(next + " ");

5. Taking the next step We need to compute and print the next number:
int next = first + second; System.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

6. Preparing for another step
This computation gave us our third number:
int next = first + second; System.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
Let’s move values around so that first + second does the job we need

7. Preparing to make many steps
We need to make these moves:
first second next
first second next
We can do it like this:
first = second; second = next;
We can put these statements in a loop and do them as many times as we please

8. The program so far
int first = 1; int second = 1; System.out.print(first + " "); System.out.print(second + " "); while ( ? ? ? ) { // when do we stop? int next = first + second; System.out.print(next + " "); first = second; second = next; }

9. Deciding when to stop
Suppose we stop when we get to a number that’s 1000 or bigger
So we continue as long as the number is less than 1000:
while (next < 1000) { ... }
Question: is the final number printed greater than 1000 or less than 1000?
while (next < 1000) { int next = first + second; System.out.print(next + " "); first = second; second = next; }

10. One other minor detail
We have been printing the numbers all on one line
We’ll get to 1000 quickly enough, so we won’t 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( );

11. The program so far
int first = 1; int second = 1; System.out.print(first + " "); System.out.print(second + " "); while (next < 1000) { int next = first + second; System.out.print(next + " "); first = second; second = next; } System.out.println( );
// oops--a bug

12. Fixing the bug
The first time we see the variable next, it’s in the test of the while loop:
while (next < 1000) {
next hasn’t been given a value yet
next hasn’t even been declared!
Solution: declare next up with the other variables, and give it some reasonable initial value

13. The (fixed) program so far
int first = 1; int second = 1; int next = 2; System.out.print(first + " "); System.out.print(second + " "); while (next < 1000) { next = first + second; // "int" was removed System.out.print(next + " "); first = second; second = next; } System.out.println( );

14. 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 doesn’t explain it

15. The “box” our program goes in
public class Fibonacci {
public static void main(String args[ ]) {
(code goes here) } }

16. 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 < 1000) { next = first + second; System.out.print(next + " "); first = second; second = next; } System.out.println( ); } }
Our code

17. 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