LeetCode Everyday -- 70

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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?

class Solution {public:    int climbStairs(int n) {        int a,b,c;        a = 1;        b = 2;        if(n == 1){            return a;        }        if(n == 2){            return b;        }        for(int i =2;i < n;i++){            c = a + b;            a = b;            b = c;        }        return c;    }};

解题思路：题目是一个动态规划的问题，因为每次只能走1或2步，所以到达最后一步之前有两种选择。设d(n)是到达第n级阶梯的解，则d(n) = d(n-1) + 1 + d(n-2) + 2,所以可以通过递归推出d(n),跟斐波那契数列很像，同样，如果n比较大，递归效率会很低，所以采用动态规划方法，将d(n-1)和d(n-2)记录下来，推出d(n).

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