2 Keys Keyboard

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'.
 

Note:

The n will be in the range [1, 1000].

题意：开始只有一个A，只能Ctrl+A 或 Ctrl+C，要显示n个A最少操作几次
解法一：dp[n] 表示n个A的最少操作。

class Solution{
public:
    int minSteps(int n) {
        vector dp(n + 1, 0);
        for(int i = 2; i <= n; ++i){
            dp[i] = i;//i个A最多要i次操作
            for(int j = i / 2; j > 1; --j){
                if(i % j == 0){
                    dp[i] = dp[j] + i / j;//由j个A操作i/j次，1次复制，n-1次粘贴
                    break;
                }
            }
        }
        return dp[n];
    }
};

解法二：道理相同

public:
    int minSteps(int n) {
        int ans = 0;
        for(int i = 2; i <= n; ++i){
            while(n % i == 0){
                ans += i;
                n /= i;
            }
        }
        return ans;
    }
};