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

# Problem 2: Even Fibonacci numbers

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:

Number of test cases (1-5):

Input data (separated by spaces or newlines):

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

# Hackerrank

My code solves 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.

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)
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 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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The 163 solved problems had an average difficulty of 22.2% at Project Euler and I scored 11,907 points (out of 13200) at Hackerrank's Project Euler+.
My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.
 << problem 1 - Multiples of 3 and 5 Largest prime factor - problem 3 >>
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