动态规划-650. 2 Keys Keyboard

题目

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'.

题意解读：给定一个数字n,你必须在notepad上得到精确的n个A，你可以采取复制所有和粘贴两个操作。notepad上初始只有1个A.求最少需要多少个操作

//定义dp[i] 表示得到i个A所需要的最少操作数
class Solution {
public int minSteps(int n) {
int[] dp = new int[n+1];
//n<2返回0
if(n < 2) return 0;
dp[2] = 2;//copy one and paste
for (int i = 3; i <= n; i++){
for(int j = i-1 ; j>=2; j--){//j代表依次复制的个数，这里要倒着走，因为优先考虑一次复制多的
if(i%j == 0){
dp[i] = dp[j] + 1 + (i-j)/j;//copy one  and paste (j-i)/j
break;//一定要跳出，否则最优值会被覆盖
}
else
dp[i] = i;
}
}
return dp
;
}
}