[CF1363D] Guess The Maximums

[CF1363D] Guess The Maximums

Description

给定序列 \(a\) 的长度 \(n\) 和 \(k\) 个互不相交的子集 \(S_i\)，每次查询可以输出一些下标 \(q_1,q_2,...,q_c\) 并得到序列中这些位置的数的最大值。对每个子集 \(S_i\)，求出序列 a 中不在该子集下标范围内的最大值。

Solution

通过不超过 11 次询问找出序列中最大值的下标 m，含有 m 的子集显然只有一个 \(S_x\)，则对任意 \(S_i, i \neq x\) 其答案显然为 m，对于 \(S_x\)，我们手动求一次不在该子集内的最大值即可。

#include <bits/stdc++.h>
using namespace std;

#define int long long

int make_query(int l, int r)
{
    cout << "? " << r - l + 1 << " ";
    for (int i = l; i <= r; i++)
        cout << i << " ";
    cout << endl;
    int ans = 0;
    cin >> ans;
    return ans;
}

signed main()
{
    int t;
    cin >> t;

    while (t--)
    {
        int n, k;
        cin >> n >> k;

        vector<int> qid(n + 2);
        for (int i = 1; i <= k; i++)
        {
            int size;
            cin >> size;
            for (int j = 1; j <= size; j++)
            {
                int t;
                cin >> t;
                qid[t] = i;
            }
        }

        int l = 1, r = n;
        int max_value = make_query(1, n);

        while (l < r)
        {
            int mid = (l + r) / 2;
            if (make_query(l, mid) == max_value)
                r = mid;
            else
                l = mid + 1;
        }

        int m = l;

        vector<int> vec;
        for (int i = 1; i <= n; i++)
            if ((qid[i] != qid[m]) || !qid[m])
                vec.push_back(i);

        cout << "? " << vec.size() << " ";
        for (auto i : vec)
            cout << i << " ";
        cout << endl;
        int ans;
        cin >> ans;

        cout << "! ";
        for (int i = 1; i <= k; i++)
            if (i == qid[m])
                cout << ans << " ";
            else
                cout << max_value << " ";
        cout << endl;

        string cor;
        cin >> cor;
    }
}