Question

I’m having a little troubling understanding the code below. I’ve worked out the vales for each of the variables for each loop and I understand how the values for each variable change after each loop but I’m confused about how int a = b; represents the sum of the two previous values. I was stuck on this problem for a long time and solved the problem only through trial and error.

I really don’t understand how int a = b; represents the sum of the two previous values. I was convinced that since int c = a + b; sums both variable a and variable b that was the variable i wanted to print in my program. Can you explain how int a represents the sum of the two previous values and why int c does not.

public class Fibonacci extends ConsoleProgram{
   public void run(){
   int i = 0; 
   int a = 0;
   int b = 1; 

   while ( i <= 12) {

     println(a);
     i++;
     int c = a + b; 
     a = b; 
     b = c; 
      }
    }
  }

Answer 1

I like to think of it as a staircase:

    0
0 + 1 = 1
    1 + 1 = 2
        1 + 2 = 3
            2 + 3 = 5
                3 + 5 = 8
                    5 + 8 = 13

An arbitrary step would look like:

a + b = c
    b + c = d

After the one step, c acts like b and b acts like a. But what about a and d? Since your solution is iterative, you just say that a becomes d and repeat the process again in a loop:

a + b = c
|   b + c = a
|___________|

Or in code:

int a = 0;
int b = 1;
int c = 0;

while (true) {
    c = a + b;  // `a + b = c` isn't valid, so you have to flip it around.
    a = b;      // `b` "becomes" `a`
    b = c;      // `c` "becomes" `b`
    c = a;      //  You don't need this step because `c` is just a temp variable
}