# | Time | Username | Problem | Language | Result | Execution time | Memory |
---|---|---|---|---|---|---|---|
1218354 | j_vdd16 | COVID tests (CEOI24_covid) | C++20 | 771 ms | 404 KiB |
#include <cassert>
#include <cstdio>
#include <string>
#include <vector>
/// You may use:
// The number of students
int N;
// The probability any given student is positive
double P;
// 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(std::vector<bool> mask) {
assert(mask.size() == (size_t)N);
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, p) = 1 + min(
(1 - (1 - p)^k) * f(n - k, p) +
(1 - p)^k * f(n, 1/k + (1 - 1/k)*p)
)
*/
/*
1100010010
*/
using namespace std;
void solve(std::vector<bool>& result, int l, int r) {
bool foundPositive = false;
int i = l;
while (i < r) {
double p;
if (foundPositive)
p = P;
else {
p = 1.0 / double(r - i) + (1.0 - (1.0 / double(r - i))) * P;
}
if (abs(p - 1.0) < 0.0000001) {
for (int j = i; j < r; j++)
result[j] = true;
return;
}
double probAllNegative = 1.0;
int count = 0;
while (probAllNegative > 0.5) {
probAllNegative *= 1.0 - p;
count++;
}
if (0.5 - probAllNegative > probAllNegative / (1.0 - p) - 0.5 && count > 1)
count--;
count = min(count, r - i);
std::vector<bool> mask(N);
for (int j = i; j < i + count; j++) {
mask[j] = true;
}
bool res = test_students(mask);
if (res && count == 1) {
foundPositive = true;
result[i] = true;
}
else if (res) {
foundPositive = true;
solve(result, i, i + count);
}
i += count;
}
}
/// You should implement:
// This function will be called once for each test instance.
// It should use test_students to determine which samples are positive.
// It must return a vector of Booleans of length N,
// where the i-th element is true if and only if the i-th sample is positive.
std::vector<bool> find_positive() {
std::vector<bool> answer(N);
if (P == 0.0)
return answer;
if (P == 1.0) {
for (int i = 0; i < N; i++)
answer[i] = true;
return answer;
}
std::vector<int> students(N);
for (int i = 0; i < N; i++)
students[i] = i;
std::vector<bool> mask(N, true);
if (!test_students(mask))
return answer;
solve(answer, 0, N);
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;
}
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