I found this really cool exercise that maybe all of us, in one time of our lives, we saw the Fibonacci sequence in mathematics and this will be a small explanation of how it works in code with a couple lines.

Well, basically the sequence consist that every number after the first two is the sum of the two preceding ones.

 
n = 0   1   2   3   4   5   6   7    8    9    10   11   12   13   14...
xn= 0   1   1   2   3   5   8   13   21   34   55   89   144  233  377...

So the xn are the sequence and we start with 0, so 0 + 1 = 1, then 1 + 1 = 2, then 2 + 1 = 3, then 3 + 2 = 5, etc.. etc.. etc… And how this works in code, well this is the souce code:

 
class Program
{
    static void Main(string[] args)
    {
        int a = 1;
        int b = 0;
        for (var i = 0; i <= 14; i++)
        {
            int temp = a;
            a = b;
            b = temp + b;

            Console.WriteLine(i + " - " + a);
        }
    }
}

As you can see it looks really simple and easy, but how it works?, well the key is on these 3 lines:

int temp = a;
a = b;
b = temp + b; 

so if we can replace each value on each loop we can see how the sequence starts to begin, so let’s start to replace values with the first loop at the beginning we have “a” and “b” with a default value, in these case 1 and 0, so if we replace on the first loop

int temp = 1;
a = 0;
b = 1 + 0; // (1) 

our result of the sequence should be “a”, now if we replace the numbers of the second loop, we should have this

int temp = 0 // because "a" takes the value of 0 in the last loop;
a = 1; // because b takes the last value of the last loop that now is 1
b = 0 + 1; // (1)  

the third loop

int temp = 1 // because "a" takes the value of 1 in the last loop;
a = 1; // because b takes the last value of the last loop that now is 1
b = 1 + 1; // (2)  

the fourth loop

int temp = 1 // last value loop
a = 2;
b = 1 + 2; // (3)  

fifth loop

int temp = 2 // last value loop
a = 3;
b = 2 + 3; // (5)  

sixth loop

int temp = 3 // last value loop
a = 5;
b = 3 + 5; // (8)  

etc.. etc.. etc..

output

 
0 - 0
1 - 1
2 - 1
3 - 2
4 - 3
5 - 5
6 - 8
7 - 13
8 - 21
9 - 34
10 - 55
11 - 89
12 - 144
13 - 233
14 - 377

So maybe it’s a simple thing but I really like to see how some simple things work