Climbing Stairs
Created: August 28, 2019 by [lek-tin]
Last updated: August 28, 2019
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:
def climbStairs(self, n):
"""
:type n: int
:rtype: int
"""
# The result is observes Fibonacci sequence
s1, s2 = 1, 2
if n == 1:
return s1
elif n == 2:
return s2
else:
while n > 2:
s1, s2 = s2, s1+s2
n -= 1
return s2
or
class Solution:
def climbStairs(self, n: int) -> int:
if n == 1:
return 1
if n == 2:
return 2
dp = [1] * n
dp[0] = 1
dp[1] = 2
for i in range(2, n):
dp[i] = dp[i-1] + dp[i-2]
return dp[n-1]