LeetCode 70 Climbing Stairs（记忆化搜索）

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.

题目大意：有N阶楼梯，每次可以选择上一阶或两阶，问从第一阶上到第N阶有多少种方法。

解题思路：令step[n]为上到第N阶楼梯的方法数，那么有以下状态转移方程：

    n == 1时，step[n] = 1

    n == 2时，step[n] = 2

    n > 2时，step[n] = step[n - 1] + step[n - 2]

代码如下：

#define maxn 105int step[maxn];int climbStairs(int n) {    if(step[n]) return step[n];    if(n == 1 || n == 2) step[n] = n;    else step[n] = climbStairs(n - 1) + climbStairs(n - 2);    return step[n];}