- Climbing Stairs Easy
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Share 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?
Example 1:
Input: 2 Output: 2 Explanation: There are two ways to climb to the top.
- 1 step + 1 step
- 2 steps Example 2:
Input: 3 Output: 3 Explanation: There are three ways to climb to the top.
- 1 step + 1 step + 1 step
- 1 step + 2 steps
- 2 steps + 1 step
思路：动态规划
1.问题拆解，找到问题之间的具体联系 到达n阶楼梯需要的步数f(n)，跟f(n-1),f(n-2)有关，f(n-1)又跟f(n-2),f(n-3)有关
2.状态定义 f(n)就是f(n-1)加一级阶梯的所有可能 + f(n-2)加两级阶梯的所有可能
3.递推方程推导 f(n) = f(n-1)+f(n-2)
4.实现 f(0)=0 f(1)=1 f(2)=2 后面的递归就行
代码：python3
class Solution:
def climbStairs(self, n):
if n is 1:
return 1
if n is 2:
return 2
dp=[0]*(n+1)
dp[0]=0
dp[1]=1
dp[2]=2
for i in range(3,n+1):
dp[i]=dp[i-1]+dp[i-2]
return dp[n]
if __name__ == '__main__':
print(Solution().climbStairs(10))
