70. Climbing Stairs(爬楼梯+斐波那契+动态规划+递归+优化)

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.

Example 1:

Input: 2 Output: 2 Explanation: There are two ways to climb to the
top.

1. 1 step + 1 step
2. 2 steps

Example 2:

Input: 3 Output: 3 Explanation: There are three ways to climb to the
top.

1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

   HashMap memo = new HashMap();

    public int climbStairs(int n) {
       if(n<=0) return 0;
        if(n==1) return 1;
        if(n==2) return 2;
        if(memo.containsKey(n)) {//为了方便f(n-2)使用f(n-1)的过程结果，如果不用的话会超时。
            return memo.get(n);
        }
        int result = climbStairs(n-1) + climbStairs(n-2);
        memo.put(n,result);
        return result;
    }