C# Fibonacci Sequence

For loop

Fibonacci numbers are a fascinating sequence. This sequence models and predicts financial markets and natural phenomena. We can compute Fibonacci numbers with recursion. This can be slow. It is also possible to use iteration.

Example

Note

First, this is an iterative method. Conceptually, an iterative Fibonacci method stores the result of the previous Fibonacci number before computing the next one. This reduces the time required.

Note:To compute a Fibonacci number at a certain position N, we have to loop through all previous numbers starting at position 0.

For
Program that computes Fibonacci iteratively: C#

using System;

class Program
{
    public static int Fibonacci(int n)
    {
	int a = 0;
	int b = 1;
	// In N steps compute Fibonacci sequence iteratively.
	for (int i = 0; i < n; i++)
	{
	    int temp = a;
	    a = b;
	    b = temp + b;
	}
	return a;
    }

    static void Main()
    {
	for (int i = 0; i < 15; i++)
	{
	    Console.WriteLine(Fibonacci(i));
	}
    }
}

Output

1
1
2
3
5
8
13
21
34
55
89
144
233
377

If you just want to list Fibonacci numbers, you could change Fibonacci() to simply use Console.WriteLine(a). This would make the method print out each number as it is computed, which would reduce the total amount of computation required.

But:The time spent printing to the Console would dominate the program's real-world runtime.

Console.WriteLine

Overflow

Programming tip

One problem with this implementation is that the int types will overflow past the 47th Fibonacci number. To solve this problem, you can change Fibonacci() to return double. Also change a, b, and temp to be of type double.

IntDouble

Summary

The C# programming language

Fibonacci numbers don't just reveal some interesting aspects of the world. They also teach us about computer programming. By storing the previous value in a loop iteration, we avoid a tremendous amount of computational work.

And:In the rare cases where Fibonacci numbers are critical, an iterative solution dramatically improves software.


C#: Method: Algorithm