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; }