Problem 2 : Even Fibonacci numbers

Problem:

  1. Each new term in the Fibonacci sequence is generated by adding the previous two terms.By starting with1and2, the first 10 terms will be:
  3. 1,2,3,5,8,13,21,34,55,89,...
  5. 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。
 



posted on 2016-11-16 20:26  foundkey  阅读(318)  评论(0)  编辑  收藏  举报

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