Now that my previous WPF project is done, I can get back to some F#! Again, I am using Project Euler as my demo platform.

#### Project Euler: Problem 2

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

Find the sum of all the even-valued terms in the sequence which do not exceed four million.

#### Example

Given the first 10 terms, the sum of the even valued terms will be:

2 + 8 + 34 = 44

#### Solution

This problem is divided into two parts: creating the Fibonacci sequence and then summing up the even valued terms. The listing illustrates the solution.

1 #light

2 #r "FSharp.PowerPack.dll"

3

4 // create recursive function to

5 // generate Fibonacci sequence

6 let rec fibo = function

7 | 0 | 1 -> 1

8 | x -> fibo(x - 1) + fibo(x - 2)

9

10 // generate the first 33 Fibonacci numbers

11 // using lazy evaluation

12 let fibs = seq{ for i in 1 .. 33 -> fibo i }

13

14 // filter out even terms

15 // filter out terms less then 4 million

16 // add each term together

17 fibs |> Seq.filter (fun x -> x % 2 = 0)

18 |> Seq.filter (fun x -> x < 4000000)

19 |> Seq.fold (+) 0

20

21 // the result is: 4613732

Notes:

This was not the best approach to use, in that I sort of cheated to know how many terms I need to iterate to fall in the 4 million range. That is, I got these numbers by trial and error since **fibo 32 = 3524578** and **fibo 33 = 5702887**, I knew that by using **33**, I will be in the range needed. However, I will try to address this in a revised version. Since it's been a while since I did F#, I wanted to just knock this one out as quickly as possible. My apologies for the little trick.

## No comments:

Post a Comment