070--Climbing Stairs.md

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

class Solution(object):
    def __init__(self):
        self.cache = {0: 1, 1: 1}
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n not in self.cache: 
            self.cache[n] = (self.climbStairs(n - 2)) + (self.climbStairs(n - 1))
        return self.cache[n]