<< problem 1 - Multiples of 3 and 5 | Largest prime factor - problem 3 >> |

# Problem 2: Even Fibonacci numbers

(see projecteuler.net/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, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million,

find the sum of the even-valued terms.

# Algorithm

As explained in the problem statement, you can compute all Fibonacci numbers in an iterative way:

F_i=F_{i-2}+F_{i-1}

My variables `a`

and `b`

stand for F_{i-2} and F_{i-1} whereas `next`

is F_i

After each iteration, `next=a+b`

and then `a`

becomes `b`

and `b`

becomes `next`

.

A number is even if there is no remainder when divided by 2.

In most programming languages it's written as `variable % 2 == 0`

Internally, your compiler might translate this to the more efficient `(variable & 1) == 0`

## Note

`unsigned long long`

is required to pass all Hackerrank tests.

# My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too.

#include <iostream>
int main()
{
unsigned int tests;
std::cin >> tests;
while (tests--)
{
unsigned long long last;
std::cin >> last;
unsigned long long sum = 0;
// first Fibonacci numbers
unsigned long long a = 1;
unsigned long long b = 2;
// until we reach the limit
while (b <= last)
{
// even ?
if (b % 2 == 0)
sum += b;
// next Fibonacci number
auto next = a + b;
a = b;
b = next;
}
std::cout << sum << std::endl;
}
return 0;
}

This solution contains 5 empty lines, 4 comments and 1 preprocessor command.

# Interactive test

You can submit your own input to my program and it will be instantly processed at my server:

This is equivalent to`echo "1 1000" | ./2`

Output:

*Note:* the original problem's input `4000000`

cannot be entered

because just copying results is a soft skill reserved for idiots.

*(this interactive test is still under development, computations will be aborted after one second)*

# Benchmark

The correct solution to the original Project Euler problem was found in **less than 0.01** seconds on a Intel® Core™ i7-2600K CPU @ 3.40GHz.

(compiled for x86_64 / Linux, GCC flags: `-O3 -march=native -fno-exceptions -fno-rtti -std=c++11 -DORIGINAL`

)

See here for a comparison of all solutions.

**Note:** interactive tests run on a weaker (=slower) computer. Some interactive tests are compiled without `-DORIGINAL`

.

# Changelog

February 23, 2017 submitted solution

March 24, 2017 added comments

# Hackerrank

see https://www.hackerrank.com/contests/projecteuler/challenges/euler002

My code solved **5** out of **5** test cases (score: **100%**)

# Difficulty

Project Euler ranks this problem at **5%** (out of 100%).

Hackerrank describes this problem as **easy**.

*Note:*

Hackerrank has strict execution time limits (typically 2 seconds for C++ code) and often a much wider input range than the original problem.

In my opinion, Hackerrank's modified problems are usually a lot harder to solve. As a rule thumb: brute-force is never an option.

# Links

projecteuler.net/thread=2 - **the** best forum on the subject (*note:* you have to submit the correct solution first)

Code in various languages:

Python: www.mathblog.dk/project-euler-problem-2/ (written by Kristian Edlund)

Haskell: github.com/nayuki/Project-Euler-solutions/blob/master/haskell/p002.hs (written by Nayuki)

Java: github.com/nayuki/Project-Euler-solutions/blob/master/java/p002.java (written by Nayuki)

Mathematica: github.com/nayuki/Project-Euler-solutions/blob/master/mathematica/p002.mathematica (written by Nayuki)

C: github.com/eagletmt/project-euler-c/blob/master/1-9/problem2.c (written by eagletmt)

Go: github.com/frrad/project-euler/blob/master/golang/Problem002.go (written by Frederick Robinson)

Javascript: github.com/dsernst/ProjectEuler/blob/master/2 Even Fibonacci numbers.js (written by David Ernst)

Scala: github.com/samskivert/euler-scala/blob/master/Euler002.scala (written by Michael Bayne)

# Heatmap

green problems solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too.

yellow problems score less than 100% at Hackerrank (but still solve the original problem).

gray problems are already solved but I haven't published my solution yet.

blue problems are already solved and there wasn't a Hackerrank version of it (at the time I solved it) or I didn't care about it because it differed too much.

*Please click on a problem's number to open my solution to that problem:*

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<< problem 1 - Multiples of 3 and 5 | Largest prime factor - problem 3 >> |