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 <= N <= 50
- Answers will be in the range of 32-bit signed integer.
C++:
class Solution {
public:
int maxA(int N) {
int res = N;
for (int i = 1; i < N - 2; ++i) {
res = max(res, maxA(i) * (N - 1 - i));
}
return res;
}
};
C++:
class Solution {
public:
int maxA(int N) {
vector<int> dp(N + 1, 0);
for (int i = 0; i <= N; ++i) {
dp[i] = i;
for (int j = 1; j < i - 2; ++j) {
dp[i] = max(dp[i], dp[j] * (i - j - 1));
}
}
return dp[N];
}
};
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