LeetCode070 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

 

<思路>一：这道题乍一看可以用递归的方式,不过数字过大的时候会Time Limit Exceeded

class Solution(object):
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n<3:
            return n
        else:
            return self.climbStairs(n-1)+self.climbStairs(n-2)

 

<思路>二：然后看网上别人的做法，发现爬楼梯法符合斐波那契数列,再想想。

class Solution(object):
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        a = b = 1

        for i in xrange(n):
            a,b = b,a+b

        return a