[LeetCode] Problem 375 - Guess Number Higher or Lower II

Posted on | In ,

We are playing the Guess Game. The game is as follows:

I pick a number from 1 to n. You have to guess which number I picked.

Every time you guess wrong, I’ll tell you whether the number I picked is higher or lower.

However, when you guess a particular number x, and you guess wrong, you pay $x. You win the game when you guess the number I picked.

Example

n = 10, I pick 8.

First round: You guess 5, I tell you that it’s higher. You pay $5.
Second round: You guess 7, I tell you that it’s higher. You pay $7.
Third round: You guess 9, I tell you that it’s lower. You pay $9.

Game over. 8 is the number I picked.

You end up paying $5 + $7 + $9 = $21.

Given a particular n ≥ 1, find out how much money you need to have to guarantee a win.

Code

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
// dp[i][j] = min{k + max{dp[i][k-1], dp[k+1][j]}}, i <= k <= j
public int getMoneyAmount(int n) {
    int[][] dp = new int[n+2][n+2];

    for (int len = 2; len <= n; len++) {
        for (int i = 1; i <= n - len + 1; i++) {
            int j = i + len - 1;
            int min = Integer.MAX_VALUE;

            for (int k = i; k <= j; k++) {
                int max = k + Math.max(dp[i][k-1], dp[k+1][j]);
                min = Math.min(min, max);
            }

            dp[i][j] = min;
        }
    }

    return dp[1][n];
}