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.

class Solution {
public:
    int getMoneyAmount(int n) {
        if(n==1) return 0;
        if(n==2) return 1;
        vector<vector<int>> dp(n+1,vector<int>(n+1));
        
        int res = INT_MAX;
        for(int j = 1;j<=n;j++)
            for(int i = j-1;i>0;i--)
            {
                int res = INT_MAX;
                for(int k = i+1;k<j;k++)
                {
                    int local = k + max(dp[i][k-1],dp[k+1][j]);
                    res = min(res,local);
                }
                dp[i][j] = i+1==j?i:res;
            }
        return dp[1][n];
        //return dfs(1,n,dp);
    }
    int dfs(int start,int end,vector<vector<int>> dp)
    {    
        if(start>=end) return 0;
        if(dp[start][end]!=0) return dp[start][end];
        int res = INT_MAX;
        for(int i = start;i<=end;i++)
        {
            int local = i+max(dfs(start,i-1,dp),dfs(i+1,end,dp));
            res = min(res,local);
        }
        dp[start][end] = res;
        return res;    
    }
};