Problem 2 : Even Fibonacci numbers

Problem:

Each new term in the Fibonacci sequence is generated by adding the previous two terms.By starting with1and2, 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 donot exceed four million, find the sum of the even-valued terms.

第二题与斐波那契数列相关，求所有不大于4000000的偶数斐波那契数之和。

逐一求斐波那契数，判断后决定是否累加，代码很简单：

1 #ProjectEuler promble 2: Even Fibonacci numbers
2 RANGE = 4000000
3 prev = 1
4 cur = 1
5 sum = 0
6 while cur <= 4000000:
7     if cur % 2 == 0:
8         sum += cur
9     temp = cur
10     cur += prev
11     prev = temp
12 print(sum)

结束这个问题前，再看看斐波那契数列
1 1 2 3 5 8 13 21 34 ……
a b c a b c a b c ……

可见，斐波那契数列偶数项的分布是有规律的，这样可以省略判断是否为偶数的步骤:

1 #ProjectEuler promble 2: Even Fibonacci numbers
2 RANGE = 4000000
3 odd1 = 1
4 odd2 = 1
5 even = odd1 + odd2
6 sum = 0
7 while even <= 4000000:
8     sum += even
9     odd1 = odd2 + even
10     odd2 = even + odd1
11     even = odd1 + odd2
12
13 print(sum)

本题结束。