Problem p02649 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <bitset>
#include <cassert>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#define FOR(i, n, m) for (ll i = (n); i < (ll)(m); i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define pb push_back
using namespace std;
using ll = long long;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 1000000007;
constexpr long double eps = 1e-6;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  os << to_string(p.first) << " " << to_string(p.second);
  return os;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  REP(i, v.size()) {
    if (i)
      os << " ";
    os << v[i];
  }
  return os;
}

struct modint {
  ll n;

public:
  modint(const ll n = 0) : n((n % mod + mod) % mod) {}
  static modint pow(modint a, int m) {
    modint r = 1;
    while (m > 0) {
      if (m & 1) {
        r *= a;
      }
      a = (a * a);
      m /= 2;
    }
    return r;
  }
  modint &operator++() {
    *this += 1;
    return *this;
  }
  modint &operator--() {
    *this -= 1;
    return *this;
  }
  modint operator++(int) {
    modint ret = *this;
    *this += 1;
    return ret;
  }
  modint operator--(int) {
    modint ret = *this;
    *this -= 1;
    return ret;
  }
  modint operator~() const { return (this->pow(n, mod - 2)); } // inverse
  friend bool operator==(const modint &lhs, const modint &rhs) {
    return lhs.n == rhs.n;
  }
  friend bool operator<(const modint &lhs, const modint &rhs) {
    return lhs.n < rhs.n;
  }
  friend bool operator>(const modint &lhs, const modint &rhs) {
    return lhs.n > rhs.n;
  }
  friend modint &operator+=(modint &lhs, const modint &rhs) {
    lhs.n += rhs.n;
    if (lhs.n >= mod)
      lhs.n -= mod;
    return lhs;
  }
  friend modint &operator-=(modint &lhs, const modint &rhs) {
    lhs.n -= rhs.n;
    if (lhs.n < 0)
      lhs.n += mod;
    return lhs;
  }
  friend modint &operator*=(modint &lhs, const modint &rhs) {
    lhs.n = (lhs.n * rhs.n) % mod;
    return lhs;
  }
  friend modint &operator/=(modint &lhs, const modint &rhs) {
    lhs.n = (lhs.n * (~rhs).n) % mod;
    return lhs;
  }
  friend modint operator+(const modint &lhs, const modint &rhs) {
    return modint(lhs.n + rhs.n);
  }
  friend modint operator-(const modint &lhs, const modint &rhs) {
    return modint(lhs.n - rhs.n);
  }
  friend modint operator*(const modint &lhs, const modint &rhs) {
    return modint(lhs.n * rhs.n);
  }
  friend modint operator/(const modint &lhs, const modint &rhs) {
    return modint(lhs.n * (~rhs).n);
  }
};
istream &operator>>(istream &is, modint m) {
  is >> m.n;
  return is;
}
ostream &operator<<(ostream &os, modint m) {
  os << m.n;
  return os;
}

#define MAX_N 1010101
long long extgcd(long long a, long long b, long long &x, long long &y) {
  long long d = a;
  if (b != 0) {
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  } else {
    x = 1;
    y = 0;
  }
  return d;
}
long long mod_inverse(long long a, long long m) {
  long long x, y;
  if (extgcd(a, m, x, y) == 1)
    return (m + x % m) % m;
  else
    return -1;
}
vector<long long> fact(MAX_N + 1, inf);
long long mod_fact(long long n, long long &e) {
  if (fact[0] == inf) {
    fact[0] = 1;
    if (MAX_N != 0)
      fact[1] = 1;
    for (ll i = 2; i <= MAX_N; ++i) {
      fact[i] = (fact[i - 1] * i) % mod;
    }
  }
  e = 0;
  if (n == 0)
    return 1;
  long long res = mod_fact(n / mod, e);
  e += n / mod;
  if ((n / mod) % 2 != 0)
    return (res * (mod - fact[n % mod])) % mod;
  return (res * fact[n % mod]) % mod;
}
// return nCk
long long mod_comb(long long n, long long k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  long long e1, e2, e3;
  long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2),
            a3 = mod_fact(n - k, e3);
  if (e1 > e2 + e3)
    return 0;
  return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
}

using mi = modint;

mi mod_pow(mi a, ll n) {
  mi ret = 1;
  mi tmp = a;
  while (n > 0) {
    if (n % 2)
      ret *= tmp;
    tmp = tmp * tmp;
    n /= 2;
  }
  return ret;
}

ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

using ld = long double;

ll comb[55][55];

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  REP(i, 55) REP(j, 55) {
    if (j == 0 || j == i)
      comb[i][j] = 1;
    else
      comb[i][j] = comb[i - 1][j] + comb[i - 1][j - 1];
  }
  REP(i, 55) REP(j, 55) if (j) comb[i][j] += comb[i][j - 1];
  int n, k, s, t;
  cin >> n >> k >> s >> t;
  if ((s & t) != s) {
    cout << 0 << endl;
    return 0;
  }
  bitset<20> bs_s(s);
  bitset<20> bs_t(t);
  int d = 0;
  REP(i, 20) if (bs_s[i] == 0 && bs_t[i] == 1) d++;
  vector<int> a(n);
  vector<int> b;
  REP(i, n) cin >> a[i];
  REP(i, n) {
    if ((s & a[i]) != s)
      continue;
    if ((a[i] & t) != a[i])
      continue;
    bitset<20> bs_a(a[i]);
    bitset<20> new_num(0);
    int crt_digit = 0;
    REP(j, 20) {
      if (bs_s[j] == 0 && bs_t[j] == 1) {
        new_num[crt_digit] = bs_a[j];
        crt_digit++;
      }
    }
    b.pb(new_num.to_ulong());
  }
  n = (int)b.size();
  k = min(n, k);
  if (n == 0) {
    cout << 0 << endl;
    return 0;
  }
  if (d == 0) {
    cout << comb[n][k] - 1 << endl;
    return 0;
  }
  vector<map<int, int>> valid_term((1 << d));
  vector<set<int>> st((1 << 18));
  REP(i, n) FOR(j, 1, (1 << d)) { valid_term[j][j & b[i]]++; }
  ll ans = (comb[n][k] - 1);
  for (int mask = 0; mask < (1 << d); mask++)
    for (auto [tgt, cnt_cand] : valid_term[mask]) {
      int popc = __builtin_popcount(mask);
      if (popc & 1)
        ans -= (comb[cnt_cand][min(k, cnt_cand)] - 1);
      else
        ans += (comb[cnt_cand][min(k, cnt_cand)] - 1);
    }
  cout << ans << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <bitset>
#include <cassert>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#define FOR(i, n, m) for (ll i = (n); i < (ll)(m); i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define pb push_back
using namespace std;
using ll = long long;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 1000000007;
constexpr long double eps = 1e-6;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  os << to_string(p.first) << " " << to_string(p.second);
  return os;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  REP(i, v.size()) {
    if (i)
      os << " ";
    os << v[i];
  }
  return os;
}

struct modint {
  ll n;

public:
  modint(const ll n = 0) : n((n % mod + mod) % mod) {}
  static modint pow(modint a, int m) {
    modint r = 1;
    while (m > 0) {
      if (m & 1) {
        r *= a;
      }
      a = (a * a);
      m /= 2;
    }
    return r;
  }
  modint &operator++() {
    *this += 1;
    return *this;
  }
  modint &operator--() {
    *this -= 1;
    return *this;
  }
  modint operator++(int) {
    modint ret = *this;
    *this += 1;
    return ret;
  }
  modint operator--(int) {
    modint ret = *this;
    *this -= 1;
    return ret;
  }
  modint operator~() const { return (this->pow(n, mod - 2)); } // inverse
  friend bool operator==(const modint &lhs, const modint &rhs) {
    return lhs.n == rhs.n;
  }
  friend bool operator<(const modint &lhs, const modint &rhs) {
    return lhs.n < rhs.n;
  }
  friend bool operator>(const modint &lhs, const modint &rhs) {
    return lhs.n > rhs.n;
  }
  friend modint &operator+=(modint &lhs, const modint &rhs) {
    lhs.n += rhs.n;
    if (lhs.n >= mod)
      lhs.n -= mod;
    return lhs;
  }
  friend modint &operator-=(modint &lhs, const modint &rhs) {
    lhs.n -= rhs.n;
    if (lhs.n < 0)
      lhs.n += mod;
    return lhs;
  }
  friend modint &operator*=(modint &lhs, const modint &rhs) {
    lhs.n = (lhs.n * rhs.n) % mod;
    return lhs;
  }
  friend modint &operator/=(modint &lhs, const modint &rhs) {
    lhs.n = (lhs.n * (~rhs).n) % mod;
    return lhs;
  }
  friend modint operator+(const modint &lhs, const modint &rhs) {
    return modint(lhs.n + rhs.n);
  }
  friend modint operator-(const modint &lhs, const modint &rhs) {
    return modint(lhs.n - rhs.n);
  }
  friend modint operator*(const modint &lhs, const modint &rhs) {
    return modint(lhs.n * rhs.n);
  }
  friend modint operator/(const modint &lhs, const modint &rhs) {
    return modint(lhs.n * (~rhs).n);
  }
};
istream &operator>>(istream &is, modint m) {
  is >> m.n;
  return is;
}
ostream &operator<<(ostream &os, modint m) {
  os << m.n;
  return os;
}

#define MAX_N 1010101
long long extgcd(long long a, long long b, long long &x, long long &y) {
  long long d = a;
  if (b != 0) {
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  } else {
    x = 1;
    y = 0;
  }
  return d;
}
long long mod_inverse(long long a, long long m) {
  long long x, y;
  if (extgcd(a, m, x, y) == 1)
    return (m + x % m) % m;
  else
    return -1;
}
vector<long long> fact(MAX_N + 1, inf);
long long mod_fact(long long n, long long &e) {
  if (fact[0] == inf) {
    fact[0] = 1;
    if (MAX_N != 0)
      fact[1] = 1;
    for (ll i = 2; i <= MAX_N; ++i) {
      fact[i] = (fact[i - 1] * i) % mod;
    }
  }
  e = 0;
  if (n == 0)
    return 1;
  long long res = mod_fact(n / mod, e);
  e += n / mod;
  if ((n / mod) % 2 != 0)
    return (res * (mod - fact[n % mod])) % mod;
  return (res * fact[n % mod]) % mod;
}
// return nCk
long long mod_comb(long long n, long long k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  long long e1, e2, e3;
  long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2),
            a3 = mod_fact(n - k, e3);
  if (e1 > e2 + e3)
    return 0;
  return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
}

using mi = modint;

mi mod_pow(mi a, ll n) {
  mi ret = 1;
  mi tmp = a;
  while (n > 0) {
    if (n % 2)
      ret *= tmp;
    tmp = tmp * tmp;
    n /= 2;
  }
  return ret;
}

ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

using ld = long double;

ll comb[55][55];

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  REP(i, 55) REP(j, 55) {
    if (j == 0 || j == i)
      comb[i][j] = 1;
    else
      comb[i][j] = comb[i - 1][j] + comb[i - 1][j - 1];
  }
  REP(i, 55) REP(j, 55) if (j) comb[i][j] += comb[i][j - 1];
  int n, k, s, t;
  cin >> n >> k >> s >> t;
  if ((s & t) != s) {
    cout << 0 << endl;
    return 0;
  }
  bitset<20> bs_s(s);
  bitset<20> bs_t(t);
  int d = 0;
  REP(i, 20) if (bs_s[i] == 0 && bs_t[i] == 1) d++;
  vector<int> a(n);
  vector<int> b;
  REP(i, n) cin >> a[i];
  REP(i, n) {
    if ((s & a[i]) != s)
      continue;
    if ((a[i] & t) != a[i])
      continue;
    bitset<20> bs_a(a[i]);
    bitset<20> new_num(0);
    int crt_digit = 0;
    REP(j, 20) {
      if (bs_s[j] == 0 && bs_t[j] == 1) {
        new_num[crt_digit] = bs_a[j];
        crt_digit++;
      }
    }
    b.pb(new_num.to_ulong());
  }
  n = (int)b.size();
  k = min(n, k);
  if (n == 0) {
    cout << 0 << endl;
    return 0;
  }
  if (d == 0) {
    cout << comb[n][k] - 1 << endl;
    return 0;
  }
  vector<vector<int>> valid_term((1 << d));
  vector<set<int>> st((1 << 18));
  REP(i, n) FOR(j, 1, (1 << d)) {
    if (!st[j].count(j & b[i])) {
      valid_term[j].pb(j & b[i]);
      st[j].insert(j & b[i]);
    }
  }
  ll ans = (comb[n][k] - 1);
  for (int mask = 0; mask < (1 << d); mask++)
    for (auto tgt : valid_term[mask]) {
      int cnt_cand = 0;
      REP(i, n) {
        if ((mask & b[i]) == tgt)
          cnt_cand++;
      }
      int popc = __builtin_popcount(mask);
      if (popc & 1)
        ans -= (comb[cnt_cand][min(k, cnt_cand)] - 1);
      else
        ans += (comb[cnt_cand][min(k, cnt_cand)] - 1);
    }
  cout << ans << endl;
  return 0;
}