375. Guess Number Higher or Lower II

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本文介绍了一种猜数字游戏中的最优策略算法，该算法通过动态规划的方法计算出玩家为确保胜利所需准备的最低金额。文章提供了完整的Java实现代码。

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