LeetCode : 650. 2 Keys Keyboard 复制粘贴字符串

试题
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’.
代码：
我们假设我们的操作如下[CPP][CPPPP]，取最后一组[CPPPP]来看，这个相当于我们做了5份粘贴操作（其实是1份copy，4份paste），且每份包含字符数量相等。那么份数的可能性有哪些？2-n，其中2表示copy一次paste一次，n表示copy一次，paste了n-1次。而且这里边还存在一个约束条件，那就是总份数*每份字符数=n。

class Solution {
    public int minSteps(int n) {
        if(n==1) return 0;
        int out = n;
        for(int i=2; i<n; i++){
            if(n%i==0)
                out = Math.min(out,i+minSteps(n/i));
        }
        return out;
    }
}