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
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]