Project Euler: Problem 2

Problem: Find the sum of all the even numbers in the Fibonacci sequence whose values do not exceed 4 million.

Q: What is the minimum section of the sequence that we need to keep in memory at any one time?
A: 3 elements – current element and previous two elements (which are used to calculate the current element).

Q: What is the starting point?
A: 1, 1, 2 (the first three elements).

Q: What is the rule to update the elements?
A: Remove element 0, push elements 1 and 2 back one space, recalculate the new element 2 as the sum of elements 0 and 1.

Memory requirements: 3 integers to hold the current element and the previous elements, and 1 integer for the sum of all even elements.

```<?php

declare(strict_types=1);
error_reporting(E_ALL);

define('MAX_SEQUENCE', 4000000);

// Fibonnaci sequence actually starts 1, 2 but pretending it is 1, 1, 2 allows
// us to use the same logic for every step instead of treating the first one
// as a special case
\$sequence = [1, 1, 2];
\$sum = 0;

while (\$sequence[2] <= MAX_SEQUENCE)
{
if (\$sequence[2] % 2 === 0)
{
\$sum += \$sequence[2];
}

// Move all elements back one space, then recalculate current element
\$sequence[0] = \$sequence[1];
\$sequence[1] = \$sequence[2];
\$sequence[2] = \$sequence[0] + \$sequence[1];
}

print("\$sum\n");```