70 Climbing Stairs - Easy

Problem:

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

Problem Analysis:

• use dynamic programming, memorization. Specifically, the solution can be constructed by the previous 2 values in the memorization array, so we don't have to store the whole memorization table.

Solutions:

class Solution(object):
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        # memorization by just rmbing the prev 2 values

        one_step, two_step = 1, 1

        for i in range(n-1):
            temp = one_step + two_step
            one_step = two_step
            two_step = temp
        
        return two_step

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