70. Climbing Stairs

70. Climbing Stairs

1. 题目

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

2. 思路

跳台阶，一次只跳1级或者2级，到最后一级有几种跳法。经典的dp题目。dp[i] 表示到达i阶的时候总共有多少跳法。则：

dp[i] = dp[i-1] + dp[i-2]

dp[0] = 0

dp[1] = 1

dp[2] = 2

3. 实现

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