A step-by-step illustration of Find n-th Fibonacci function to help you walk through a series of operations. Illustration is accompanied by actual code with bold line indicating the current operation. https://github.com/yoshiwatanabe/Algorithms/blob/master/Finding/Fibonacci.cs

1. Find n-th Fibonacci
iteratively
Illustrated walk through

2. public static long FindNthFibonacciIterative(int n)
{
if (n == 0) return 0;
if (n == 1) return 1;
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
}

3. Let’s just get over with two special cases
when n == 0
[0]
[1]
[2]
[3]
[4]
[5]
[6]
0
1
?
?
?
?
?
if (n == 0) return 0;
if (n == 1) return 1;
Always return 0
when n == 1
[0]
[1]
[2]
[3]
[4]
[5]
[6]
0
1
?
?
?
?
?
if (n == 0) return 0;
if (n == 1) return 1;
Always return 1

4. [0]
[1]
[2]
[3]
[4]
[5]
[6]
0
1
?
?
?
?
?
fibNMinusTwo
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
fibN

5. when n == 6
0
fibNMinusTwo
1
?
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

6. 0
fibNMinusTwo
1
0
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

7. n == 6
i=2
0
fibNMinusTwo
1
0
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

8. n == 6
i=2
0
fibNMinusTwo
1
0
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN
2 <= 6 is true

9. n == 6
i=2
0
+
fibNMinusTwo
1
1
?
?
fibNMinusOne
?
?
fibN
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
2nd Fibonacchi is 1

10. n == 6
i=2
1
fibNMinusTwo
1
1
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

11. n == 6
i=2
1
fibNMinusTwo
1
1
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

12. n == 6
i=3
1
fibNMinusTwo
1
1
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

13. n == 6
i=3
1
fibNMinusTwo
1
1
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN
3 <= 6 is true

14. 3ed fib.
n == 6
i=3
1
+
fibNMinusTwo
1
2
?
?
fibNMinusOne
?
?
fibN
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
3nd Fibonacchi is 2

15. n == 6
i=3
1
fibNMinusTwo
1
2
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

16. n == 6
i=3
1
fibNMinusTwo
2
2
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

17. n == 6
i=4
1
fibNMinusTwo
2
2
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

18. n == 6
i=4
1
fibNMinusTwo
2
2
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN
4 <= 6 is true

19. n == 6
i=4
1
+
fibNMinusTwo
2
3
?
?
fibNMinusOne
?
?
fibN
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
4-th Fibonacchi is 3

20. n == 6
i=4
2
fibNMinusTwo
2
3
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

21. n == 6
i=4
2
fibNMinusTwo
3
3
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

22. n == 6
i=5
2
fibNMinusTwo
3
3
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

23. n == 6
i=5
2
fibNMinusTwo
3
3
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN
5 <= 6 is true

24. n == 6
i=5
2
+
fibNMinusTwo
3
5
?
?
fibNMinusOne
?
?
fibN
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
5-th Fibonacchi is 5

25. n == 6
i=5
3
fibNMinusTwo
3
5
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

26. n == 6
i=5
3
fibNMinusTwo
5
5
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

27. n == 6
i=6
3
fibNMinusTwo
5
5
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

28. n == 6
i=6
3
fibNMinusTwo
5
5
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN
6 <= 6 is true

29. n == 6
i=6
3
+
fibNMinusTwo
5
8
?
?
fibNMinusOne
?
?
fibN
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
6-th Fibonacchi is 8

30. n == 6
i=6
5
fibNMinusTwo
5
8
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

31. n == 6
i=6
5
fibNMinusTwo
8
8
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

32. n == 6
i=7
5
fibNMinusTwo
8
8
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN

33. n == 6
i=7
5
fibNMinusTwo
8
8
?
?
fibNMinusOne
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
?
?
fibN
7 <= 6 is false

34. n == 6
i=7
5
fibNMinusTwo
8
8
?
?
fibNMinusOne
?
?
fibN
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;
Exit the for loop

35. n == 6
i=7
5
fibNMinusTwo
8
8
?
?
fibNMinusOne
?
?
fibN
Return fibN = 8
long fibNMinusTwo = 0;
long fibNMinusOne = 1;
long fibN = 0;
6-th Fibonacchi is 8
for (int i = 2; i <= n; ++i)
{
fibN = fibNMinusOne + fibNMinusTwo;
fibNMinusTwo = fibNMinusOne;
fibNMinusOne = fibN;
}
return fibN;