Problem p02651 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
// type alias
typedef long long LL;
typedef pair<int, int> II;
typedef tuple<int, int, int> III;
typedef vector<int> VI;
typedef vector<string> VS;
typedef unordered_map<int, int> MAPII;
typedef unordered_set<int> SETI;
template <class T> using VV = vector<vector<T>>;
// minmax
template <class T> inline T SMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
template <class T> inline T SMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
// repetition
#define FORE(i, a, b) for (int i = (a); i <= (b); ++i)
#define REPE(i, n) for (int i = 0; i <= (n); ++i)
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define FORR(x, arr) for (auto &x : arr)
#define SZ(a) int((a).size())
// collection
#define ALL(c) (c).begin(), (c).end()
// DP
#define MINUS(dp) memset(dp, -1, sizeof(dp))
#define ZERO(dp) memset(dp, 0, sizeof(dp))
// stdout
#define println(args...) fprintf(stdout, ##args), putchar('\\n');
// debug cerr
template <class Iter> void __kumaerrc(Iter begin, Iter end) {
  for (; begin != end; ++begin) {
    cerr << *begin << ',';
  }
  cerr << endl;
}
void __kumaerr(istream_iterator<string> it) {
  (void)it;
  cerr << endl;
}
template <typename T, typename... Args>
void __kumaerr(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << "=" << a << ", ", __kumaerr(++it, args...);
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &_os, const std::pair<S, T> &_p) {
  return _os << "{" << _p.first << ',' << _p.second << "}";
}
#define __KUMATRACE__ true
#ifdef __KUMATRACE__
#define dump(args...)                                                          \\
  {                                                                            \\
    string _s = #args;                                                         \\
    replace(_s.begin(), _s.end(), ',', ' ');                                   \\
    stringstream _ss(_s);                                                      \\
    istream_iterator<string> _it(_ss);                                         \\
    __kumaerr(_it, args);                                                      \\
  }
#define dumpc(ar)                                                              \\
  {                                                                            \\
    cerr << #ar << ": ";                                                       \\
    FORR(x, (ar)) { cerr << x << ','; }                                        \\
    cerr << endl;                                                              \\
  }
#define dumpC(beg, end)                                                        \\
  {                                                                            \\
    cerr << "~" << #end << ": ";                                               \\
    __kumaerrc(beg, end);                                                      \\
  }
#else
#define dump(args...)
#define dumpc(ar)
#define dumpC(beg, end)
#endif

// $ cp-batch XorBattle | diff XorBattle.out -
// $ g++ -std=c++14 -Wall -O2 -D_GLIBCXX_DEBUG -fsanitize=address XorBattle.cpp
// && ./a.out
template <class T> void gf2_GE(vector<T> &V) {
  // gaussian elimination in GF(2)
  int N = V.size();
  for (int i = 0; i < N; ++i) {
    sort(V.begin() + i, V.end(), greater<T>());
    if (V[i] == 0)
      break;
    T msb = 1;
    while ((msb << 1) <= V[i])
      msb <<= 1;
    for (int j = i + 1; j < N; ++j)
      if (V[j] & msb)
        V[j] ^= V[i];
  }
}
template <class T> int gf2_rank(vector<T> &V) {
  gf2_GE<T>(V);
  return (int)V.size() - count(V.begin(), V.end(), 0);
}
/*

 6/7/2020

 5:00-6:30 give up

 16:00-18:15, 21:50-

 https://twitter.com/hanseilimak/status/1269799620579692549

 https://twitter.com/satanic0258/status/1269638393975107587
 https://twitter.com/satanic0258/status/1269654741346217984
 https://twitter.com/chokudai/status/1269662729712750592
 https://twitter.com/ngtkana/status/1269638258486464513
 https://twitter.com/noshi91/status/1269660771086041088
 https://twitter.com/kyort0n/status/1269712783852986368

 */

const int MAX_N = 1e3 + 1;
LL A[MAX_N];
int N;
string S;

int solve() {
  vector<LL> V(1, 0);
  for (int i = N - 1; i >= 0; --i) {
    if (S[i] == '0') {
      V.push_back(A[i]);
      gf2_GE(V);
    } else {
      int rank = gf2_rank(V);
      V.push_back(A[i]);
      int rank2 = gf2_rank(V);
      if (rank2 > rank)
        return 1;
    }
  }
  return 0;
}

VI s;
int memo[MAX_N][1 << 5];

int f(int i, int cur) {
  int &res = memo[i][cur];
  if (res >= 0)
    return res;
  if (i == N) {
    return cur != 0;
  }

  bool res1 = f(i + 1, cur);
  bool res2 = f(i + 1, cur ^ A[i]);

  if (s[i] == 0) {
    res = (!res1 || !res2) ? false : true;
  } else {
    res = (res1 || res2);
  }
  return res;
}

mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
int genRandNum(int lb, int ub) {
  assert(lb < ub);
  // Helper to generate random integer in range [lb, ub)
  int x = rnd() % (int)(ub - lb);
  return x + lb;
}
vector<int> genRandSeq(int size, int lb, int ub) {
  if (size == 0)
    return {};
  vector<int> res(size);
  generate(res.begin(), res.end(), [&]() { return genRandNum(lb, ub); });
  return res;
}
string n2bin(long long n) {
  assert(n >= 0);
  string res = "";
  while (n > 0)
    res += (n % 2LL ? '1' : '0'), n /= 2LL;
  return string(res.rbegin(), res.rend());
}
void test() {
  N = 8;
  VI as = genRandSeq(N, 1, 1 << 3);
  s = genRandSeq(N, 0, 2);
  vector<II> states(N);
  REP(i, N) states[i] = {s[i], as[i]};
  sort(ALL(states));

  VI ress;
  do {
    MINUS(memo);
    REP(i, N) A[i] = states[i].second, s[i] = states[i].first;
    bool res = f(0, 0);
    if (!res) {
      vector<pair<int, string>> xs;
      FORR(p, states) xs.emplace_back(p.first, n2bin(p.second));
      dumpc(xs);
    }
    ress.push_back(res);
  } while (next_permutation(ALL(states)));

  set<int> S;
  FORR(s, ress) S.emplace(s);
  int ands[2] = {(1 << N) - 1, (1 << N) - 1}, ors[2] = {0, 0};
  FORR(p, states) ands[p.first] &= p.second, ors[p.first] |= p.second;
  if (SZ(S) == 2) {
    dump(n2bin(ands[0] ^ ors[0]), n2bin(ands[1] ^ ors[1]));
    dumpc(ress);
    dumpc(states);
  }
  assert(SZ(S) == 1);

  dumpc(ress);
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << setprecision(12) << fixed;

  // while(true) test();

  int t;
  cin >> t;
  while (t--) {
    cin >> N;
    REP(i, N) cin >> A[i];
    cin >> S;
    cout << solve() << endl;
  }

  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
// type alias
typedef long long LL;
typedef pair<int, int> II;
typedef tuple<int, int, int> III;
typedef vector<int> VI;
typedef vector<string> VS;
typedef unordered_map<int, int> MAPII;
typedef unordered_set<int> SETI;
template <class T> using VV = vector<vector<T>>;
// minmax
template <class T> inline T SMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
template <class T> inline T SMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
// repetition
#define FORE(i, a, b) for (int i = (a); i <= (b); ++i)
#define REPE(i, n) for (int i = 0; i <= (n); ++i)
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define FORR(x, arr) for (auto &x : arr)
#define SZ(a) int((a).size())
// collection
#define ALL(c) (c).begin(), (c).end()
// DP
#define MINUS(dp) memset(dp, -1, sizeof(dp))
#define ZERO(dp) memset(dp, 0, sizeof(dp))
// stdout
#define println(args...) fprintf(stdout, ##args), putchar('\\n');
// debug cerr
template <class Iter> void __kumaerrc(Iter begin, Iter end) {
  for (; begin != end; ++begin) {
    cerr << *begin << ',';
  }
  cerr << endl;
}
void __kumaerr(istream_iterator<string> it) {
  (void)it;
  cerr << endl;
}
template <typename T, typename... Args>
void __kumaerr(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << "=" << a << ", ", __kumaerr(++it, args...);
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &_os, const std::pair<S, T> &_p) {
  return _os << "{" << _p.first << ',' << _p.second << "}";
}
#define __KUMATRACE__ true
#ifdef __KUMATRACE__
#define dump(args...)                                                          \\
  {                                                                            \\
    string _s = #args;                                                         \\
    replace(_s.begin(), _s.end(), ',', ' ');                                   \\
    stringstream _ss(_s);                                                      \\
    istream_iterator<string> _it(_ss);                                         \\
    __kumaerr(_it, args);                                                      \\
  }
#define dumpc(ar)                                                              \\
  {                                                                            \\
    cerr << #ar << ": ";                                                       \\
    FORR(x, (ar)) { cerr << x << ','; }                                        \\
    cerr << endl;                                                              \\
  }
#define dumpC(beg, end)                                                        \\
  {                                                                            \\
    cerr << "~" << #end << ": ";                                               \\
    __kumaerrc(beg, end);                                                      \\
  }
#else
#define dump(args...)
#define dumpc(ar)
#define dumpC(beg, end)
#endif

// $ cp-batch XorBattle | diff XorBattle.out -
// $ g++ -std=c++14 -Wall -O2 -D_GLIBCXX_DEBUG -fsanitize=address XorBattle.cpp
// && ./a.out
template <class T> void gf2_GE(vector<T> &V) {
  // gaussian elimination in GF(2)
  int N = V.size();
  for (int i = 0; i < N; ++i) {
    sort(V.begin() + i, V.end(), greater<T>());
    if (V[i] == 0)
      break;
    T msb = 1;
    while ((msb << 1) <= V[i])
      msb <<= 1;
    for (int j = i + 1; j < N; ++j)
      if (V[j] & msb)
        V[j] ^= V[i];
  }
}
template <class T> int gf2_rank(vector<T> &V) {
  gf2_GE<T>(V);
  return (int)V.size() - count(V.begin(), V.end(), 0);
}
/*

 6/7/2020

 5:00-6:30 give up

 16:00-18:15, 21:50-

 https://twitter.com/hanseilimak/status/1269799620579692549

 https://twitter.com/satanic0258/status/1269638393975107587
 https://twitter.com/satanic0258/status/1269654741346217984
 https://twitter.com/chokudai/status/1269662729712750592
 https://twitter.com/ngtkana/status/1269638258486464513
 https://twitter.com/noshi91/status/1269660771086041088
 https://twitter.com/kyort0n/status/1269712783852986368

 */

const int MAX_N = 1e3 + 1;
LL A[MAX_N];
int N;
string S;

int solve() {
  VI V(1, 0);
  for (int i = N - 1; i >= 0; --i) {
    if (S[i] == '0') {
      V.push_back(A[i]);
      gf2_GE(V);
    } else {
      int rank = gf2_rank(V);
      V.push_back(A[i]);
      int rank2 = gf2_rank(V);
      if (rank2 > rank)
        return 1;
    }
  }
  return 0;
}

VI s;
int memo[MAX_N][1 << 5];

int f(int i, int cur) {
  int &res = memo[i][cur];
  if (res >= 0)
    return res;
  if (i == N) {
    return cur != 0;
  }

  bool res1 = f(i + 1, cur);
  bool res2 = f(i + 1, cur ^ A[i]);

  if (s[i] == 0) {
    res = (!res1 || !res2) ? false : true;
  } else {
    res = (res1 || res2);
  }
  return res;
}

mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
int genRandNum(int lb, int ub) {
  assert(lb < ub);
  // Helper to generate random integer in range [lb, ub)
  int x = rnd() % (int)(ub - lb);
  return x + lb;
}
vector<int> genRandSeq(int size, int lb, int ub) {
  if (size == 0)
    return {};
  vector<int> res(size);
  generate(res.begin(), res.end(), [&]() { return genRandNum(lb, ub); });
  return res;
}
string n2bin(long long n) {
  assert(n >= 0);
  string res = "";
  while (n > 0)
    res += (n % 2LL ? '1' : '0'), n /= 2LL;
  return string(res.rbegin(), res.rend());
}
void test() {
  N = 8;
  VI as = genRandSeq(N, 1, 1 << 3);
  s = genRandSeq(N, 0, 2);
  vector<II> states(N);
  REP(i, N) states[i] = {s[i], as[i]};
  sort(ALL(states));

  VI ress;
  do {
    MINUS(memo);
    REP(i, N) A[i] = states[i].second, s[i] = states[i].first;
    bool res = f(0, 0);
    if (!res) {
      vector<pair<int, string>> xs;
      FORR(p, states) xs.emplace_back(p.first, n2bin(p.second));
      dumpc(xs);
    }
    ress.push_back(res);
  } while (next_permutation(ALL(states)));

  set<int> S;
  FORR(s, ress) S.emplace(s);
  int ands[2] = {(1 << N) - 1, (1 << N) - 1}, ors[2] = {0, 0};
  FORR(p, states) ands[p.first] &= p.second, ors[p.first] |= p.second;
  if (SZ(S) == 2) {
    dump(n2bin(ands[0] ^ ors[0]), n2bin(ands[1] ^ ors[1]));
    dumpc(ress);
    dumpc(states);
  }
  assert(SZ(S) == 1);

  dumpc(ress);
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << setprecision(12) << fixed;

  // while(true) test();

  int t;
  cin >> t;
  while (t--) {
    cin >> N;
    REP(i, N) cin >> A[i];
    cin >> S;
    cout << solve() << endl;
  }

  return 0;
}