LeetCode 2 Keys Keyboard-优快云博客

本文链接：https://blog.youkuaiyun.com/py184473894/article/details/103734807

Initially on a notepad only one character 'A' is present. You can perform two operations on this notepad for each step:

Copy All: You can copy all the characters present on the notepad (partial copy is not allowed).
Paste: You can paste the characters which are copied last time.

Given a number n. You have to get exactly n 'A' on the notepad by performing the minimum number of steps permitted. Output the minimum number of steps to get n 'A'.

Example 1:

Input: 3
Output: 3
Explanation:
Intitally, we have one character 'A'.
In step 1, we use Copy All operation.
In step 2, we use Paste operation to get 'AA'.
In step 3, we use Paste operation to get 'AAA'.

思路：

如果n能被2整除的话，那么就可以通过n//2的长度+2步（copy,paste）得到

如果n不能被2整除的话，那么就要找n的因子，对n的两个因子进行递归得到结果

如果n没有因子的话，说明n是素数，只能通过1进行n步得到（copy，n-1步paste）

因此就可以递归得到最终的结果

class Solution:
    def minSteps(self, n: int) -> int:
        if n==1:
            return 0
        if n%2==0:
            return 2+self.minSteps(n//2)
        for i in range(2,int(math.sqrt(n))+1):
            if n%i==0:
                t=n//i
                return self.minSteps(t)+self.minSteps(i)
        return n