0. 题目

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?
Note: Given n will be a positive integer.

Example 1:
Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
方式1. 1 step + 1 step
方式2. 2 steps

Example 2:
Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
方式1. 1 step + 1 step + 1 step
方式2. 1 step + 2 steps
方式3. 2 steps + 1 step

1. c++版本

int climbStairs(int n) {
    if ( n==1 || n==2)
        return n;
    return climbStairs(n-1) + climbStairs(n-2);
}

直接递归，会出现栈溢出

    int climbStairs(int n) {
        if (n == 1 || n == 2)
            return n;
        double f1 = 1, f2 = 2, tmp;
        while (n > 2) {
            tmp = f1;
            f1 = f2;
            f2 = tmp + f1;
            n--;
        }
        return f2;
    }

2.python版本

    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n == 1 or n == 2:
            return n
        f1, f2 = 1, 2
        while n > 2:
            tmp = f1
            f1 = f2
            f2 = f1 + tmp
            n = n - 1
        return f2