leetcode - 70. Climbing Stairs

Description

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

Solution

Use dp[i] to denote the number of ways to reach step i, then the transform equation will be:
$$dp[i]=dp[i-1]+dp[i-2]$$
So the initial values are: $dp[1]=1,dp[2]=2$, it’s actually the fibonacci sequence.

Time complexity: $o(n)$
Space complexity: $o(1)$ by using variables instead of using list

Code

class Solution:
    def climbStairs(self, n: int) -> int:
        dp_1, dp_2 = 1, 2
        for i in range(2, n):
            dp_1, dp_2 = dp_2, dp_1 + dp_2
        return dp_2 if n > 1 else dp_1