[leetcode] climbing Stairs

Climbing Stairs

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Fibonacci数列的题目，三种做法：

1. 递归

2. 循环

3. 利用Fibonacci数列通项公式

AC代码就不贴了，简单证明下通项公式：

递推公式为a[n+2]=a[n+1]+a[n],

其特征方程为x*x-x-1=0,它的两个根即为特征根.即(1＋√5）/2和（1－√5）/2,

为表达方便,设它们为A,B.则其通项公式为a[n]=p*A^n+q*b^n,

其中p,q为代定系数,通过a[0],a[1]的值可得p,q.