#include "ancient2.h"
#include <bits/stdc++.h>
using namespace std;
const int MAX_BITS = 1000;
const int BOUND = 51;
#define bs bitset<MAX_BITS>
vector<pair<bs,array<int,3>>> MIS(const vector<pair<bs,array<int,3>>>& vectors) {
vector<bs> basis; // Store the basis vectors here
vector<pair<bs,array<int,3>>> mis;
for (const auto& vec : vectors) {
bs v = vec.first; // Copy the vector
// Try to eliminate the current vector with the basis vectors
for (const auto& b : basis) {
if (v.none()) break; // If the vector is already zero, skip
if (v.test(b._Find_first())) { // If leading bit matches
v ^= b; // Subtract the basis vector (add in GF(2))
}
}
// If the vector is not zero after elimination, it's linearly independent
if (v.any()) {
basis.push_back(v);
mis.push_back(vec); // Add the original vector to the mis
}
}
return mis;
}
void gaussian_elimination(vector<bs> &A, bs &S, bs &b, int N) {
int row = 0;
for (int col = 0; col < N; ++col) {
// Find pivot row
int pivot = -1;
for (int i = row; i < N; ++i) {
if (A[i][col]) {
pivot = i;
break;
}
}
if (pivot == -1) continue; // No pivot found, move to the next column
// Swap pivot row with the current row
swap(A[row], A[pivot]);
// swap(b[row], b[pivot]);
int tmp = b[row];
b[row] = b[pivot];
b[pivot] = tmp;
// Eliminate below
for (int i = row + 1; i < N; ++i) {
if (A[i][col]) {
A[i] ^= A[row];
// b[i] ^= b[row];
if (b[row]) b[i] = !b[i];
}
}
++row;
}
// Backward substitution
S.reset();
for (int i = row - 1; i >= 0; --i) {
if (A[i].any()) {
int leading_one = A[i]._Find_first();
S[leading_one] = b[i];
for (int j = leading_one + 1; j < N; ++j) {
if (A[i][j]) {
// S[leading_one] ^= S[j];
if (S[j]) S[leading_one] = !S[leading_one];
}
}
}
}
}
string solve(int N, vector<pair<bs,int>> &info) {
// Create bitsets
vector<bs> A(N);
bs S, b;
// Populate the matrix A and vector b with parity information
for (int i=0; i<N; i++) {
A[i] = info[i].first;
b[i] = info[i].second;
}
// Perform Gaussian elimination
gaussian_elimination(A, S, b, N);
// Output the reconstructed binary string
string s = S.to_string();
reverse(s.begin(), s.end());
return s.substr(0, N);
}
string Solve(int N) {
vector<pair<bs,int>> info;
function<int(int,int)> solve1 = [&](int i, int j) -> int {
int m = 2 * j;
vector<int> a(m), b(m);
for (int r=0; r<j; r++) {
a[r] = (r + 1) % j;
b[r] = (r + 1) % j;
a[j + r] = j + ((r + 1) % j);
b[j + r] = j + ((r + 1) % j);
}
swap(b[i], b[i + j]);
return Query(m, a, b) / j;
};
vector<int> bits(N);
function<int(int)> solve2 = [&](int k) -> int {
int m = k + 3;
vector<int> a(m), b(m);
for (int r=0; r<k; r++) {
a[r] = r + 1;
b[r] = r + 1;
}
a[k] = k + 1;
b[k] = k + 2;
a[k + 1] = b[k + 1] = k + 1;
a[k + 2] = b[k + 2] = k + 2;
return Query(m, a, b) - k - 1;
};
function<int(int)> solve3 = [&](int i) -> int {
if (bits[i-1] == 0) {
int nzero = 0;
for (int j=0; j<i; j++) nzero += bits[j] == 0;
int m = nzero + 3;
vector<int> a(m), b(m);
for (int r=0; r<nzero; r++) {
a[r] = r + 1;
b[r] = r;
}
a[nzero] = nzero + 1;
b[nzero] = nzero + 2;
return Query(m, a, b) - nzero - 1;
} else {
int none = 0;
for (int j=0; j<i; j++) none += bits[j] == 1;
int m = none + 3;
vector<int> a(m), b(m);
for (int r=0; r<none; r++) {
a[r] = r + 1;
b[r] = r;
}
a[none] = none + 1;
b[none] = none + 2;
return Query(m, a, b) - none - 1;
}
};
vector<pair<bs,array<int,3>>> all;
for (int i=0; i<=min(99,N); i++) {
bs here;
here[i] = 1;
bits[i] = solve2(i);
all.push_back({here, {1, i, i}});
}
for (int i=100; i<=min(199,N); i++) {
bs here;
here[i] = 1;
bits[i] = solve3(i);
all.push_back({here, {1, i, i}});
}
for (int j=1; j<=BOUND; j++) {
for (int i=0; i<j; i++) {
bs here;
for (int k=i; k<N; k+=j) {
here[k] = 1;
}
all.push_back({here, {0, i, j}});
}
}
vector<pair<bs,array<int,3>>> mis = MIS(all);
for (auto &[HELP, bruh] : mis) {
if (bruh[0] == 0) {
info.push_back({HELP, solve1(bruh[1], bruh[2])});
} else if (bruh[0] == 1) {
info.push_back({HELP, bits[bruh[1]]});
} else {
assert(false);
}
}
assert(info.size() >= N);
// cout << info.size() << "\n";
return solve(N, info);
}
Compilation message
In file included from /usr/include/c++/10/cassert:44,
from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:33,
from ancient2.cpp:3:
ancient2.cpp: In function 'std::string Solve(int)':
ancient2.cpp:192:24: warning: comparison of integer expressions of different signedness: 'std::vector<std::pair<std::bitset<1000>, int> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
192 | assert(info.size() >= N);
| ~~~~~~~~~~~~^~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
29 ms |
1368 KB |
Wrong Answer [3] |
| 2 |
Halted |
0 ms |
0 KB |
- |
