LeetCode 650. 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].

分析

如果n是质数的话，就要一个一个粘贴上去，次数就是n.
如果不是质数的话，由先由一个A获得n的最大公因子m为模版，在copy all,在paste n/m-1 次。

class Solution {
public:
    int isprime(int n){
        int i;
        if(n==1) return 1;
        for(i=2;i<=sqrt(n);i++)
            if(n%i==0) return i;
        return -1;
    }
    int minSteps(int n) {
        int dp[11001]={0};
        if(isprime(n)==-1)
           return n;
        for(int i=2;i<=n;i++)
            if(isprime(i)==-1)
               dp[i]=i;
            else
               dp[i]=dp[i/isprime(i)]+isprime(i);
        return dp[n];
    }
};

一种更棒的写法

class Solution {
public:
    int minSteps(int n) {
        if (n == 1) return 0;
        for (int i = 2; i < n; i++)
            if (n % i == 0) return i + minSteps(n / i);
        return n;
    }
};