70. 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?

Note: Given n will be a positive integer.

 

Example 1:

Input: 2
Output:  2
Explanation:  There are two ways to climb to the top.

1. 1 step + 1 step
2. 2 steps

 

Example 2:

Input: 3
Output:  3
Explanation:  There are three ways to climb to the top.

1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

每次可以爬1级或2级台阶，爬n级有多少种走法
f(n) = f(n-1) + f(n-2)

C++(3ms):

class Solution {
public:
    int climbStairs(int n) {
        if (n == 1)
            return 1 ;
        int f1 = 1 ;
        int f2 = 1 ;
        int f3 ;
        for(int i = 1 ; i < n ; i++){
            f3 = f1 + f2 ;
            f1 = f2 ;
            f2 = f3 ;
        }
        return f3 ;        
    }
};