Fibonacci
最后更新于：2022-04-02 01:09:49
# Fibonacci
### Source
- lintcode: [(366) Fibonacci](http://www.lintcode.com/en/problem/fibonacci/)
~~~
Find the Nth number in Fibonacci sequence.
A Fibonacci sequence is defined as follow:
The first two numbers are 0 and 1.
The i th number is the sum of i-1 th number and i-2 th number.
The first ten numbers in Fibonacci sequence is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
Example
Given 1, return 0
Given 2, return 1
Given 10, return 34
Note
The Nth fibonacci number won't exceed the max value of
signed 32-bit integer in the test cases.
~~~
### 题解
斐波那契数列使用递归极其容易实现，其实使用非递归的方法也很容易，不断向前滚动即可。
### Java
~~~
class Solution {
/**
* @param n: an integer
* @return an integer f(n)
*/
public int fibonacci(int n) {
if (n < 0) return -1;
if (n == 1) return 0;
if (n == 2) return 1;
int fn = 0, fn1 = 1, fn2 = 0;
for (int i = 3; i <= n; i++) {
fn = fn1 + fn2;
fn2 = fn1;
fn1 = fn;
}
return fn;
}
}
~~~
### 源码分析
1. corner cases
1. 初始化 fn, fn1, fn2, 建立地推关系。
1. 注意 fn, fn2, fn1的递推顺序。
### 复杂度分析
遍历一次，时间复杂度为 O(n)O(n)O(n), 使用了两个额外变量，空间复杂度为 O(1)O(1)O(1).
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