leetcode70 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.
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
"""
"""
共有三种解法
解法一：递归，判题器超时
解法二：斐波拉契数列
解法三：维护一个数组，循环相加
解法二和三的时间复杂度都为O(n)，但解法二的空间复杂度更低。
"""
"""
解法一：
Time Limit Exceeded
Last executed input 38
"""
class Solution1:
    def climbStairs(self, n):
        if n == 1:
            return 1
        if n == 2:
            return 2
        return self.climbStairs(n-1) + self.climbStairs(n-2)
"""
解法二
"""
class Solution2:
    def climbStairs(self, n):
        if n == 1:
            return 1
        if n == 2:
            return 2
        first = 1
        second = 2
        res = 0
        for i in range(3, n+1):
            res = first + second
            first = second
            second = res
        return res
"""
解法三
"""
class Solution3:
    def climbStairs(self, n):
        res = [0]*(n+1)
        if n == 1:
            return 1
        if n == 2:
            return 2
        res[1] = 1
        res[2] = 2
        for i in range(3, n+1):
            res[i] = res[i-1] + res[i-2]
        return res[n]