斐波那契数列（fabnacci）java实现

斐波那契数列定义：From Wikipedia, the free encyclopedia

http://en.wikipedia.org/wiki/Fibonacci_number

In mathematics, the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence:^[2]^[3]

1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\;

or (often, in modern usage):

0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\;

(sequence A000045 in OEIS).

By definition, the first two numbers in the Fibonacci sequence are 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two.

In mathematical terms, the sequence F_n of Fibonacci numbers is defined by the recurrence relation

F_n = F_{n-1} + F_{n-2},\!\,

with seed values^[2]^[3]

F_1 = 1,\; F_2 = 1

or^[4]

F_0 = 0,\; F_1 = 1.

本例以后一种为例：

最简单的一种：两层递归

     public static long fibonacci(int n){if(n==0) return 0;else if(n==1) return 1;else return fibonacci(n-1)+fibonacci(n-2);}

问题是：随着n的数值逐渐增多，时间和空间耗费太大，读者可以自行实验。在我的机器上n=50时就不能忍受了。

考虑优化：一层递归

    public static void main(String[] args) {long tmp=0;// TODO Auto-generated method stubint n=10;Long start=System.currentTimeMillis();for(int i=0;i<n;i++){System.out.print(fibonacci(i)+" ");}System.out.println("-------------------------");System.out.println("耗时："+(System.currentTimeMillis()-start));}    public static long fibonacci(int n) {long result = 0;if (n == 0) {result = 0;} else if (n == 1) {result = 1;tmp=result;} else {result = tmp+fibonacci(n - 2);tmp=result;}return result;}

递归时间减少了到不到50%

最好的方式，不使用递归的方式来做。

    public static long fibonacci(int n){long before=0,behind=0;long result=0;for(int i=0;i<n;i++){if(i==0){result=0;before=0;behind=0;}else if(i==1){result=1;before=0;behind=result;}else{result=before+behind;before=behind;behind=result;}}return result;}