[LeetCode] Climbing stairs 爬楼梯问题

声明：原题目转载自LeetCode，解答部分为原创

Problem ：

    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.

Solution：

   
思路：爬楼梯问题，每次可以爬1步楼梯或者2步楼梯，询问爬n步楼梯共有多少种方法? 很明显的动态规划问题，状态转换方程为

   
num_of_way(n) = num_of_way(n - 1) + num_of_way(n - 2)

   
代码如下：

class Solution {
public:
int climbStairs(int n) {
vector<int> steps(n,0);
steps[0] = 1;
steps[1] = 2;
for(int i = 2; i < n ; i ++)
{
steps[i] = steps[i - 1] + steps[i - 2];
}
return steps[n - 1];
}
};