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.

public int getMoneyAmount(int n) {
        int[][] dp = new int[n + 1][n + 1];
       
       for (int i = 2; i <= n; ++i) {
            for (int j = i - 1; j > 0; --j) {
                int global_min = Integer.MAX_VALUE;
                for (int k = j + 1; k < i; ++k) {
                    int local_max = k + Math.max(dp[j][k - 1], dp[k + 1][i]);
                    global_min = Math.min(global_min, local_max);
                }
                dp[j][i] = j + 1 == i ? j : global_min;
            }
        }
        return dp[1][n];
    }