70. Climbing Stairs

Easy

Problem:

You are climbing a staircase. To reach the top, you must ascend n steps. If you can climb either 1 step or 2 steps at a time, calculate the number of distinct ways you can reach the top.

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

https://leetcode.com/problems/climbing-stairs/

Solution:

Fibonacci numbers

The method of solving this problem with memoization is similar to that of calculating Fibonacci numbers, with only a slight difference in the initial values.

class Solution:
    dp = collections.defaultdict(int)

    def climbStairs(self, n: int) -> int:
        if n <= 2:
            return n
        
        if self.dp[n]:
            return self.dp[n]
        self.dp[n] = self.climbStairs(n - 1) + self.climbStairs(n - 2)
        return self.dp[n]

Reference: NeetCode

https://www.youtube.com/watch?v=Y0lT9Fck7qI

class Solution:
    def climbStairs(self, n: int) -> int:
        one, two = 1, 1
        for i in range(n -1):
            tmp = one
            one = one + two
            two = tmp
        return one