509. Fibonacci Number、509. 斐波那契数
(剑指offer - 10. 斐波那契数列)
The Fibonacci numbers, commonly denoted F(n) form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1.
斐波那契数,通常用 F(n) 表示,形成的序列称为斐波那契数列。该数列由 0 和 1 开始,后面的每一项数字都是前面两项数字的和。
That is,
F(0) = 0, F(1) = 1
F(N) = F(N - 1) + F(N - 2), for N > 1.
Given N, calculate F(N).
Example 1:
Input: 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.
Example 2:
Input: 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.
Example 3:
Input: 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.
Note:
0 ≤ N ≤ 30.
解答:
方法一:递归,时间复杂度为n的指数级,效率很低。不推荐。
方法二:循环,从下往上计算,将数列中间项保存起来。时间复杂度 O(n)。
class Solution:
def fib(self, N: int) -> int:
temp_arr = [0, 1]
if N >= 2:
for i in range(2, N + 1):
temp_arr[i % 2] = temp_arr[0] + temp_arr[1]
return temp_arr[N % 2]