lc 70 Climbing Stairs

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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.

DP Accepted

这是一道特别经典又简单的动态规划题目，先考虑简单的情况，上第一层的方式只有1种，而上第二层的方式有两种。再考虑复杂的情况，上第n层的前一层要么是n-1层，要么是n-2层。其实，该问题很类似斐波那契数列，还是很容易解答的。

class Solution {

public:

    int climbStairs(int n) {

        vector<int> stairs(n+1, 0);

        stairs[1] = 1;

        stairs[2] = 2;

        for (int i = 3; i < n+1; i++)   stairs[i] = stairs[i-1]+stairs[i-2];

        return stairs[n];

    }

};