LeetCode 070 Climbing Stairs

LeetCode

You are climbing a staircase. It takes n steps to reach the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Example 1:

Input: n = 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:

Input: n = 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

Constraints:

* 1 <= n <= 45

题目大意：

爬楼梯的方法数。一次可以爬一级或二级

解题思路：

DP的经典题
递归式

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

解题步骤：

N/A

注意事项：

递归式含两个前状态，所以用两个变量。Python的优势是可以同时赋值，所以不需要用临时变量

Python代码：

# dp[n] = dp[n - 1] + dp[n - 2]
def climbStairs(self, n: int) -> int:
	prev, cur = 1, 1
	for i in range(2, n + 1): # 4
		cur, prev = cur + prev, cur # 5, 3
	return cur

算法分析：

时间复杂度为O(n)，空间复杂度O(1)