375. Guess Number Higher or Lower II --------M

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.

 

Constraints:

• 1 <= n <= 200

 A:

就是检验各种情况，然后找出所有的来。

class Solution {
public:
    int getMoneyAmount(int n) {
        vector<vector<int>> V(n+1,vector<int>(n+1,-1));
        return helper(1,n,V);
    }
private:
    int helper(int start, int end, vector<vector<int>> &V){
        if(start >= end)
            return 0;
        
        if(V[start][end] >=0)
            return V[start][end];
            
        int res = INT_MAX;
        for(int i =start; i<=end;i++){
            int tmp = i + max(helper(start, i-1, V) , helper(i+1, end, V));
            res = min(res, tmp);
        }
        V[start][end] = res;
        return res;
    }
};

当然，这个题目，vector<vector<int>> V 也可以不用递归， 用DP来填上。 

Error:

一开始，我res = min(res, tmp) . 我写成max 了。  糊涂啊~~~~~