Guess Number Higher or Lower II

一、题目

英文：Guess Number Higher or Lower II

中文：猜数字大小

二、内容要求

英文：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.

中文：我们在玩猜谜游戏。游戏如下：

我从1到n选择一个数字，你得猜我选了哪个号码。

每次你猜错了，我都会告诉你我选的号码是高还是低。

然而，当你猜一个特定的数字X，你猜错了，你付出$ x你赢了游戏，当你猜我选的号码。

三、示例

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.

四、解析

For each number x in range[i~j]
we do: result_when_pick_x = x + max{DP([i~x-1]),
DP([x+1, j])}
--> // the max means whenever you choose a number, the feedback is always
bad and therefore leads you to a worse branch.
then we get DP([i~j]) = min{xi,
... ,xj}
--> // this min makes sure that you are minimizing your cost.

可知，其动态规划方程：matrix[s][e]=m+Math.max(matrix[s][m-1],matrix[m+1][e]) 注意控制边界条件。

五、代码

java代码

public int getMoneyAmount(int n) {
int[][] table = new int[n+1][n+1];//创建一个二维数组
return DP(table, 1, n);//调用函数并直接返回结果，传参有三个
}

int DP(int[][] t, int s, int e){
if(s >= e) return 0;//不满足条件的索引区间
if(t[s][e] != 0) return t[s][e];
int res = Integer.MAX_VALUE;
for(int x=s; x<=e; x++){
int tmp = x + Math.max(DP(t, s, x-1), DP(t, x+1, e));//动态规划方程
res = Math.min(res, tmp);//取其中最小的
}
t[s][e] = res;
return res;
}