375. Guess Number Higher or Lower II

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.

class Solution {
public int getMoneyAmount(int n) {
int[][] dp = new int[n+1][n+1];
for (int i = 1; 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(local_max, global_min);
}
dp[j][i] = j+1==i?j:global_min;
}
}
return dp[1]
;
}
}