Project euler #2

 /*https://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.

Analysis:

    2                    8                               34                       144

  1 2 (1+2) (1+2*2) (1*2 + 2*3) (1*3+2*5) (1*5+2*8) (1*8+2*13) (13, 21) (21 34) (34,55)

    x                    x                              x                          x

So,

each even number is represented as P=1*a + 2*b

next even number is P_next=1*p + 2*(2a+3b)

It's trivial to write program with above fomular

*/

#include <iostream>

int main()

{

    unsigned int a=0, b=1, i = 2, sum = 0;

    unsigned int nextA, nextB;

    

    while (i <= 4000000)

    {

        sum += i;

        nextB = 2*a + 3*b;

        nextA = i;

        i = 1*nextA + 2*nextB;

        a = nextA;

        b = nextB;

    }

    std::cout << "sum: " << sum << std::endl;

    return sum; 

}