Question

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

Solution

To climb n steps, one can climb first n-1 steps and climb the last 1 step, or climb the first n-2 step and climb the last 2 steps. Thus, the answer for n is the sum of those for n-1 and n-2.

class Solution:
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n == 1:
            return 1
        if n == 2:
            return 2

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

        return dp[-1]