Submission #396490

#	Time	Username	Problem	Language	Result	Execution time	Memory
396490		rama_pang	"The Lyuboyn" code (IZhO19_lyuboyn)	C++17	100 / 100	311 ms	6412 KiB

lyuboyn

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

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);

  int N, K, T; string S;
  cin >> N >> K >> T >> S;

  // Adjacent elements in cycle is xored by some value v, where popcount(v) == K.
  // For K = 1, the answer is encoded by "Gray Code". (Or, we could also create
  // the sequence recursively.).
  //
  // Generate all bitmasks with popcount == K. Then, if those bitmasks form a
  // Xor basis with size N, we can generate all 2^N possible bitmasks with those
  // bitmasks in the basis. Note that, since the basis has size N, it is sufficient
  // to solve the case for K = 1 on the basis - this would go through all 2^N
  // possible combinations of basis exactly once, and adjacent only differn in 1
  // ON/OFF basis.
  //
  // Time complexity: O(N 2^N).

  vector<pair<int, int>> basis; // xor basis (reduced value, original value)
  for (int mask = 0; mask < (1 << N); mask++) {
    if (__builtin_popcount(mask) == K) {
      pair<int, int> cur = {mask, mask};
      for (auto i : basis) {
        cur.first = min(cur.first, cur.first ^ i.first);
      }
      if (cur.first == 0) { // not independent
        continue;
      }
      basis.emplace_back(cur);
      for (int i = int(basis.size()) - 2; i >= 0; i--) { // basis is sorted in decreasing order
        if (basis[i].first < basis[i + 1].first) {
          swap(basis[i], basis[i + 1]);
        }
      }
    }
  }

  if (basis.size() != N) { // cannot generate all 2^N masks
    cout << -1 << '\n';
    return 0;
  }

  vector<int> gray(1 << N); // gray code
  for (int mask = 0; mask < (1 << N); mask++) {
    gray[mask] = mask ^ (mask >> 1);
  }

  cout << (1 << N) << '\n';
  for (int mask = 0; mask < (1 << N); mask++) {
    int Xor = 0;
    for (int i = 0; i < N; i++) {
      if ((gray[mask] >> i) & 1) {
        Xor ^= basis[i].second;
      }
    }
    for (int i = 0; i < N; i++) {
      cout << ((S[i] - '0') ^ ((Xor >> i) & 1));
    }
    cout << '\n';
  }
  return 0;
}

Compilation message (stderr)

lyuboyn.cpp: In function 'int main()':
lyuboyn.cpp:43:20: warning: comparison of integer expressions of different signedness: 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   43 |   if (basis.size() != N) { // cannot generate all 2^N masks
      |       ~~~~~~~~~~~~~^~~~

• Subtask 1: 0 / 0
• Subtask 2: 5 / 5
• Subtask 3: 3 / 3
• Subtask 4: 11 / 11
• Subtask 5: 15 / 15
• Subtask 6: 18 / 18
• Subtask 7: 31 / 31
• Subtask 8: 17 / 17