e 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.

 1 public class Solution {
 2     public int getMoneyAmount(int n) {
 3         int[][] dp = new int[n+2][n+2];
 4         for (int len=1; len<=n-1; len++) {
 5             for (int from=1, to=from+len; to<=n; from++, to++) {
 6                 dp[from][to] = Integer.MAX_VALUE;
 7                 for (int k=from; k<=to; k++) {
 8                     dp[from][to] = Math.min(dp[from][to], k+Math.max(dp[from][k-1], dp[k+1][to]));
 9                 }
10             }
11         }
12         return dp[1][n];
13     }
14 }