Project Euler 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.

首两项为a与b的Fibonacci序列为

　　a, b, a+b, a+2b, 2a+3b

若b为偶数，则下一偶数项为2a+3b，尝试在循环中将a与b分别前进到a+2b与2a+3b

　　a' = a + 2b

　　b' = 2a + 3b = 2a' - b

Python代码：

max = 4000000
sum = 0

a = 1
b = 2

while(b <= max):
    sum += b
    a += b * 2
    b = a * 2 - b
    
print sum

时间复杂度O(log(n))（Fibonacci数列通项公式为指数型）

空间复杂度O(1)