70. Climbing Stairs

题目

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

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解法

# leetcode submit region begin(Prohibit modification and deletion)
class Solution:
    def climbStairs(self, n: int) -> int:
        dp = [0] * n

        dp[0] = 1
        if n > 1: dp[1] = 2

        for i in range(2, n):
            dp[i] = dp[i - 1] + dp[i - 2]

        return dp[n-1]
# leetcode submit region end(Prohibit modification and deletion)

复杂度分析

• 时间复杂度 O(N)
• 空间复杂度 O(N)