Problem

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.

Answer

4613732

---

python

def compute():
	ans = 0
	x = 1  # Represents the current Fibonacci number being processed
	y = 2  # Represents the next Fibonacci number in the sequence
	while x <= 4000000:
		if x % 2 == 0:
			ans += x
		x, y = y, x + y
	return str(ans)

if __name__ == "__main__":
	print(compute())

---

JavaScript

let s = 0
let f = [1, 1]
while (f[0] < 4e6) {
    if (f[0] % 2 === 0) s+= f[0]
    f = [f[1], f[0]+f[1]]
}
console.log(s)

---

Ruby

#!/usr/bin/env ruby
sum a, b = 0, 1, 2
while b < 4000000
  sum += b if b.even?
  a, b = b, a+b
end
puts sum

---

Go

package main

import "fmt"

func main() {
    sum := 0
    for a, b := 1, 2; b <= 4e6; a, b = b, a+b {
        if b%2 == 0 {
            sum += b
        }
    }
    fmt.Println(sum)
}

---

Haskell

fibs :: [Integer]
fibs = 0:1:zipWith (+) fibs (tail fibs)

main :: IO()
main = print $sum $ filter even $ takeWhile (<4000000) fibs

---

Clojure

#!/usr/bin/env clojure
(def fibs (lazy-cat [0 1] (map + (rest fibs) fibs)))
(println (reduce + (filter even? (take-while #(< % 4000000) fibs))))

---

Mathematica

s = 0;
For[i = 0, (f = Fibonacci[i]) <= 4000000, i++,
  If[EvenQ[f],
    s += f]]
s

---

Java

public final class p002 implements EulerSolution {
	
	public static void main(String[] args) {
		System.out.println(new p002().run());
	}
	
	
	/* 
	 * Computers are fast, so we can implement this solution directly without any clever math.
	 * Because the Fibonacci sequence grows exponentially by a factor of 1.618, the sum is
	 * bounded above by a small multiple of 4 million. Thus the answer fits in a Java int type.
	 */
	public String run() {
		int sum = 0;
		int x = 1;  // Represents the current Fibonacci number being processed
		int y = 2;  // Represents the next Fibonacci number in the sequence
		while (x <= 4000000) {
			if (x % 2 == 0)
				sum += x;
			int z = x + y;
			x = y;
			y = z;
		}
		return Integer.toString(sum);
	}
	
}