375. Guess Number Higher or Lower II

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本文介绍了一种猜数字游戏的最优策略实现。通过动态规划的方法，我们构建了一个算法来确定玩家为确保胜利所需的最大花费。文章详细展示了如何通过迭代计算找到每个范围内的最佳猜测数。

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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.

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];
    }
}