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.

    int getMoneyAmount(int n) {        vector<vector<int> >cost(n+2,vector<int>(n+2,0));//下标0和n+1纯粹是为了计算方便而引入的，于是下面guess-1和guess+1无需判断是否越界         for(int diff=1;diff<=n;diff++){            for(int left=1;left+diff<=n;left++){                int right=left+diff;                int minCostInThisRange=INT_MAX;                for(int guess=left;guess<=right;guess++){                    minCostInThisRange=min(minCostInThisRange,guess+max(cost[left][guess-1],cost[guess+1][right]));                }                cost[left][right]=minCostInThisRange;            }        }        return cost[1][n];    }