Climbing Stairs

Q : 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?

A: 动态规划的题。

记f(n)是爬n steps stair的不同方式。

爬到n层，那么有两种选择：

1. 先爬n-1层，再往上1step

2. 先爬n-2层，再往上2 steps。

那么f(n) = f(n-2) + f(n-1)  (Fibonacci数)  注意不要用递归，用DP，o(n)

    int climbStairs(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if(n<=0)
            return 0;
            
        if(n==1)
            return 1;
            
        if(n==2)
            return 2;
            
        int a = 1,b = 2,result;
        
        for(int i=3;i<=n;i++)
        {
            result = a+b;
            a = b;
            b = result;   
        }
        
        return result;
        
    }