[Leetcode]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) {        vector<vector<int>> pay(n + 1, vector<int>(n));        for (int i = n - 1; i >= 0; --i) {            for (int j = i + 1; j < n; ++j) {                pay[i][j] = numeric_limits<int>::max();                for (int k = i; k <= j; ++k) {                    pay[i][j] = min(pay[i][j], k + 1 + max(pay[i][k - 1], pay[k + 1][j]));                }            }        }        return pay[0][n - 1];    }};