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.

• 这道题目比较有意思，刚开始猜错了题目的意思。

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