375. Guess Number Higher or Lower II

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.

Credits:
Special thanks to @agave and @StefanPochmann for adding this problem and creating all test cases.

my solution:

#include <vector>
#include <deque>
using namespace std;

class Solution {
public:
    int getMoneyAmount(int n) {
        vector<vector<int>> u(n + 2, vector<int>(n + 2));
        for (int b = 2; b <= n; ++b) {
            int k0 = b - 1;
            deque<pair<int, int>> v;
            for (int a = b - 1; a; --a) {
                while (u[a][k0 - 1] > u[k0 + 1][b]) {
                    if (!v.empty() && v.front().second == k0) v.pop_front();
                    --k0;
                }
                int vn = a + u[a + 1][b];
                while (!v.empty() && vn < v.back().first) v.pop_back();
                v.emplace_back(vn, a);
                int u1 = u[a][k0] + k0 + 1;
                int u2 = v.front().first;
                u[a][b] = u1 < u2 ? u1 : u2;
            }
        }
        return u[1][n];
    }
};