#70 Climbing Stairs——Top 100 Liked Questions
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
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第一次:递归,通过找规律发现,f(1)=1,f(2)=2,f(n)=f(n-1)+f(n-2)
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def climbStairs(n):
"""
:type n: int
:rtype: int
"""
if not n:
return 0
if n == 1:
return 1
if n == 2:
return 2
if n > 2:
res = climbStairs(n - 2) + climbStairs(n - 1)
return res
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超时,但结果是对的
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第二次:动态规划,res中保存当前路径个数,res[i]对应res[i - 1] + res[i - 2]
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class Solution(object):
def climbStairs(self, n):
"""
:type n: int
:rtype: int
"""
res = [1, 2]
if n == 1:
return res[0]
if n == 1:
return res[1]
for i in range(2, n):
res.append(res[i - 1] + res[i - 2])
return res[-1]
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Runtime: 16 ms, faster than 97.24% of Python online submissions for Climbing Stairs.
Memory Usage: 11.8 MB, less than 44.01% of Python online submissions for Climbing Stairs.
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