Submission #1219385

#	Time	Username	Problem	Language	Result	Execution time	Memory
1219385		j_vdd16	COVID tests (CEOI24_covid)	C++20	97.70 / 100	1153 ms	636 KiB

Main

#include <cassert>
#include <cstdio>
#include <string>
#include <vector>
#include <math.h>
#include <iostream>
#include <random>

using namespace std;

/// You may use:

// The number of students
int N;

// The probability any given student is positive
double P;

vector<pair<double, int>> f, g;

int solve(std::vector<bool>& result, int l, int r, bool containsPositive);

bool bruteforce = false;
int queryCount = 0;
vector<bool> answers;
void testAll(int num) {
    bruteforce = true;

    std::random_device rd;
    std::mt19937 gen(rd());
    std::bernoulli_distribution d(P);

    answers.assign(N, false);

    queryCount = 0;
    for (int i = 0; i < num; i++) {
        for (int j = 0; j < N; j++) {
            answers[j] = d(gen);
        }
        
        std::vector<bool> answer(N);
        solve(answer, 0, N, false);

        if (i % (num / 100) == 0) {
            cout << g[N].first << " ";
            cout << double(queryCount) / double(i + 1) << endl;
        }
    }


    bruteforce = false;
}

// This function performs a test on a subset of samples.
// Its argument is a vector of Booleans of length N,
// where the i-th element is true if the i-th sample should be added to the mix.
// It returns true if (and only if) at least one of the samples in the mix is positive.
bool test_students(const std::vector<bool>& mask) {
    assert(mask.size() == (size_t)N);

    if (bruteforce) {
        queryCount++;
        for (int i = 0; i < N; i++)
            if (mask[i] && answers[i])
                return true;

        return false;
    }

    std::string mask_str(N, ' ');
    for (int i = 0; i < N; i++)
        mask_str[i] = mask[i] ? '1' : '0';

    printf("Q %s\n", mask_str.c_str());
    fflush(stdout);

    char answer;
    scanf(" %c", &answer);
    return answer == 'P';
}

/*
f(n) = argmin(
    (f(k) + g(n - k)) * (k / n + (n - k) / n * (1 - (1 - P)^k)) + 

)
*/

void init() {
    f.assign(N + 1, {100000.0, -1});
    g.assign(N + 1, {100000.0, -1});

    f[0] = {0, 0};
    f[1] = {0, 0};
    g[0] = {0, 0};
    g[1] = {1, 1};
    vector<double> pw(N + 1);
    for (int i = 0; i <= N; i++)
        pw[i] = pow(1.0 - P, i);

    for (int n = 2; n <= N; n++) {
        for (int k = 1; k < n; k++) {
            double p = (1.0 - pw[k]) / (1 - pw[n]);//double(k) / double(n) + double(n - k) / double(n) * (1.0 - pw[k]);
            double exp = 1.0 +
                p * (f[k].first + g[n - k].first) +
                (1 - p) * (f[n - k].first);

            if (exp < f[n].first) {
                f[n] = {exp, k};
            }
        }
        for (int k = 1; k <= n; k++) {
            double p = 1.0 - pw[k];
            double exp = 1.0 +
                p * (f[k].first + g[n - k].first) +
                (1 - p) * (g[n - k].first);

            if (exp < g[n].first) {
                g[n] = {exp, k};
            }
        }
    }
}

/*
1100010010

0001
*/


int solve(std::vector<bool>& result, int l, int r, bool containsPositive) {
    int n = r - l;
    if (n == 0)
        return -1;

    if (containsPositive && n == 1) {
        result[l] = true;
        return l;
    }

    int k = containsPositive ? f[n].second : g[n].second;

    vector<bool> mask(N);
    for (int i = l; i < l + k; i++)
        mask[i] = true;
    
    bool res = test_students(mask);
    if (containsPositive) {
        if (res)
            return solve(result, l, l + k, true);
        else
            return solve(result, l + k, r, true);
    }
    else {
        if (res) {
            int firstPositive = solve(result, l, l + k, true);
            return solve(result, firstPositive + 1, r, false);
        }
        else {
            return solve(result, l + k, r, false);
        }
    }
}

std::vector<bool> find_positive() {
    init();
    //testAll(1000);

    std::vector<bool> answer(N);
    //return answer;

    if (P == 0.0)
        return answer;
    if (P == 1.0) {
        for (int i = 0; i < N; i++)
            answer[i] = true;
        
        return answer;
    }

    //cerr << g[N].first << endl;

    solve(answer, 0, N, false);

    return answer;
}

int main() {
    int T;
    scanf("%d %lf %d", &N, &P, &T);

    // You may perform any extra initialization here.

    for (int i = 0; i < T; i++) {
        std::vector<bool> answer = find_positive();
        assert(answer.size() == (size_t)N);

        std::string answer_str(N, ' ');
        for (int j = 0; j < N; j++)
            answer_str[j] = answer[j] ? '1' : '0';

        printf("A %s\n", answer_str.c_str());
        fflush(stdout);

        char verdict;
        scanf(" %c", &verdict);
        if (verdict == 'W')
            exit(0);
    }

    return 0;
}

Compilation message (stderr)

Main.cpp: In function 'bool test_students(const std::vector<bool>&)':
Main.cpp:78:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   78 |     scanf(" %c", &answer);
      |     ~~~~~^~~~~~~~~~~~~~~~
Main.cpp: In function 'int main()':
Main.cpp:191:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  191 |     scanf("%d %lf %d", &N, &P, &T);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
Main.cpp:207:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  207 |         scanf(" %c", &verdict);
      |         ~~~~~^~~~~~~~~~~~~~~~~

• Subtask 0: 0 / 0
• Subtask 1: 10 / 10
• Subtask 2: 87.7 / 90