LeetCode 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.

分析

自底向上的动态规划

const int inf=9999999;
class Solution {
public:
    int getMoneyAmount(int n) {
        vector<vector<int>> dp(n+1,vector<int>(n+1,0));
        for(int i=2;i<=n;i++)
            for(int j=i-1;j>=1;j--){
                int globalmin=inf;
                for(int k=j+1;k<i;k++){
                    int localmax=k+max(dp[j][k-1],dp[k+1][i]);
                    globalmin=min(localmax,globalmin);
                }
                dp[j][i]=j+1==i?j:globalmin;
            }
        return dp[1][n];
    }
};