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

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LeetCode：链接

典型的动态规划问题。

 n = 1 时 ways = 1； 
n = 2 时 ways = 2； 
n = 3 时 ways = 3； 
… 
n = k 时 ways = ways[k-1] + ways[k-2]。

class Solution(object):
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n < 3:
            return n
        dp = [0] * n
        dp[0], dp[1] = 1, 2
        for i in range(2, n):
            dp[i] = dp[i-1] + dp[i-2]
        return dp[-1]