[LeetCode&Python] Problem 70. Climbing Stairs

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

Recursion with memory:
M(n)=M(n-1)+M(n-2)

class Solution(object):
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        a=[0]*n
        def findM(n):
            if n==1:
                a[0]=1
                return 1
            elif n==2:
                a[1]=2
                return 2
            else:
                if a[n-1-1]==0:
                    a[n-1-1]=findM(n-1)
                if a[n-2-1]==0:
                    a[n-2-1]=findM(n-2)
                a[n-1]=a[n-1-1]+a[n-2-1]
                return a[n-1]
        findM(n)
        return a[n-1]