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
Solution:
class Solution(object):
def climbStairs(self, n):
"""
:type n: int
:rtype: int
"""
def choose(n, x):
nl = 1
for i in range(1, n+1, 1):
nl *= i
xl = 1
for i in range(1, x+1, 1):
xl *= i
n_xl = 1
for i in range(1, n-x+1, 1):
n_xl *= i
return nl/xl/n_xl
num = 0
for i in range(n/2+1):
num += choose(n-i, i)
return num
