Problem
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
Notes
The distinct ways to take n stair cases:
- take one step at last, the distinct ways to take n-1 stair cases -> f(n-1) ways
- take two steps at last, the distinct ways to take n-2 stair cases -> f(n-2) ways
So f(n) = f(n-1) + f(n-2)
Solution
class Solution():
def climbStairs(self, n):
if n < 2:
return n
dp = [0] * n
dp[0] = 1
dp[1] = 2
for i in range(2, n):
dp[i] = dp[i-1] + dp[i-2]
return dp[-1]