Leetcode 651. 4 Keys Keyboard

Imagine you have a special keyboard with the following keys:

Key 1: (A): Print one 'A' on screen.

Key 2: (Ctrl-A): Select the whole screen.

Key 3: (Ctrl-C): Copy selection to buffer.

Key 4: (Ctrl-V): Print buffer on screen appending it after what has already been printed.

Now, you can only press the keyboard for N times (with the above four keys), find out the maximum numbers of 'A' you can print on screen.

Example 1:

Input: N = 3
Output: 3
Explanation: 
We can at most get 3 A's on screen by pressing following key sequence:
A, A, A

Example 2:

Input: N = 7
Output: 9
Explanation: 
We can at most get 9 A's on screen by pressing following key sequence:
A, A, A, Ctrl A, Ctrl C, Ctrl V, Ctrl V

Note:

1. 1 <= N <= 50
2. Answers will be in the range of 32-bit signed integer.

Code (Java):

class Solution {
    public int maxA(int N) {
        int[] dp = new int[N + 1];
        dp[1] = 1;
        
        for (int i = 2; i <= N; i++) {
            for (int j = 1; j < i - 2; j++) {
                dp[i] = Math.max(dp[i], dp[j] * (i - j - 1));
            }
            
            dp[i] = Math.max(dp[i], dp[i - 1] + 1);
        }
        
        return dp[N];
    }
}