LeetCode||70. Climbing Stairs
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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: 2Output: 2Explanation: There are two ways to climb to the top.1. 1 step + 1 step2. 2 steps
Example 2:
Input: 3Output: 3Explanation: There are three ways to climb to the top.1. 1 step + 1 step + 1 step2. 1 step + 2 steps3. 2 steps + 1 step爬楼梯问题。经典的动态规划问题。每次上一个台阶或者两个台阶,问一共有多少种方法到楼顶。这个实际上就是斐波那契数列的求解。可以逆向来分析问题,如果有n个台阶,那么走完n个台阶的方式有f(n)种。而走完n个台阶有两种方法,先走完n-2个台阶,然后跨2个台阶;先走完n-1个台阶,然后跨1个台阶。所以f(n) = f(n-1) + f(n-2)。
class Solution(object): def climbStairs(self, n): """ :type n: int :rtype: int """ dp = [1 for i in range(n+1)] for i in range(2,n+1): dp[i] = dp[i-1] + dp[i-2] return dp[n]
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