70 - Climbing Stairs

[alfmunny]

2020/03/21

leetcode

Problem

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

Notes

The distinct ways to take n stair cases:

  1. take one step at last, the distinct ways to take n-1 stair cases -> f(n-1) ways
  2. take two steps at last, the distinct ways to take n-2 stair cases -> f(n-2) ways

So f(n) = f(n-1) + f(n-2)

Solution

class Solution():
    def climbStairs(self, n):
        if n < 2:
            return n

        dp = [0] * n

        dp[0] = 1
        dp[1] = 2

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

        return dp[-1]