#836708 (C++23) No.184 たのしい排他的論理和(HARD)

提出ソース
結果

問題	No.184 たのしい排他的論理和(HARD)
ユーザー	maspy
提出日時	2023-02-03 03:18:42
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	15 ms / 5,000 ms
コード長	17,731 bytes
コンパイル時間	3,928 ms
コンパイル使用メモリ	272,772 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-07-02 11:28:00
合計ジャッジ時間	6,992 ms
ジャッジサーバーID （参考情報）	judge1 / judge5
このコードへのチャレンジ
（要ログイン）
テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	11 ms 5,376 KB
testcase_09	AC	4 ms 5,376 KB
testcase_10	AC	9 ms 5,376 KB
testcase_11	AC	8 ms 5,376 KB
testcase_12	AC	13 ms 5,376 KB
testcase_13	AC	14 ms 5,376 KB
testcase_14	AC	9 ms 5,376 KB
testcase_15	AC	15 ms 5,376 KB
testcase_16	AC	13 ms 5,376 KB
testcase_17	AC	14 ms 5,376 KB
testcase_18	AC	2 ms 5,376 KB
testcase_19	AC	2 ms 5,376 KB
testcase_20	AC	4 ms 5,376 KB
testcase_21	AC	15 ms 5,376 KB
testcase_22	AC	15 ms 5,376 KB
testcase_23	AC	2 ms 5,376 KB
testcase_24	AC	2 ms 5,376 KB
testcase_25	AC	2 ms 5,376 KB
testcase_26	AC	2 ms 5,376 KB
testcase_27	AC	2 ms 5,376 KB
testcase_28	AC	10 ms 5,376 KB
testcase_29	AC	13 ms 5,376 KB
testcase_30	AC	11 ms 5,376 KB
testcase_31	AC	11 ms 5,376 KB
testcase_32	AC	12 ms 5,376 KB
testcase_33	AC	15 ms 5,376 KB
testcase_34	AC	15 ms 5,376 KB
testcase_35	AC	15 ms 5,376 KB
testcase_36	AC	15 ms 5,376 KB
権限があれば一括ダウンロードができます
ソースコード

raw source code
#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/184"
#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  assert(!que.empty());
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  assert(!que.empty());
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.write(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};

struct has_read_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.read(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <typename T,
            typename enable_if<has_read<T>::value>::type * = nullptr>
  inline bool read_single(T &x) {
    x.read();
    return true;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <size_t N = 0, typename T>
  void read_single_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
      auto &x = std::get<N>(t);
      read_single(x);
      read_single_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool read_single(tuple<T...> &tpl) {
    read_single_tuple(tpl);
    return true;
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <typename T,
            typename enable_if<has_write<T>::value>::type * = nullptr>
  inline void write(T x) {
    x.write();
  }
  template <class T>
  void write(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <size_t N = 0, typename T>
  void write_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
      if constexpr (N > 0) { write(' '); }
      const auto x = std::get<N>(t);
      write(x);
      write_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool write(tuple<T...> tpl) {
    write_tuple(tpl);
    return true;
  }
  template <class T, size_t S>
  void write(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if (val < 0) {
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if (negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 1 "library/linalg/xor/solve_linear.hpp"
// solve Ax = b を解く。[0] に特殊解、[1]～ に Ker A の基底が入る。解なしは
// empty。 A の行ベクトルを UINT で持たせる。
template <typename UINT>
vc<UINT> solve_linear(int n, int m, vc<UINT>& A, UINT b) {
  assert(max(n, m) <= numeric_limits<UINT>::digits);
  assert(len(A) == n);
  int rk = 0;
  FOR(j, m) {
    if (rk == n) break;
    FOR(i, rk, n) if (A[i] >> j & 1) {
      if (i == rk) break;
      swap(A[rk], A[i]);
      if ((b >> rk & 1) != (b >> i & 1)) b ^= (UINT(1) << rk) | (UINT(1) << i);
      break;
    }
    if (!(A[rk] >> j & 1)) continue;
    FOR(i, n) if (i != rk) {
      if (A[i] >> j & 1) {
        A[i] ^= A[rk];
        b ^= (b >> rk & 1) << i;
      }
    }
    ++rk;
  }
  if (b >> rk) { return {}; }
  vc<UINT> res(1);
  vc<int> pivot(m, -1);
  int p = 0;
  FOR(i, rk) {
    while (!(A[i] >> p & 1)) ++p;
    res[0] |= (b >> i & 1) << p;
    pivot[p] = i;
  }
  FOR(j, m) if (pivot[j] == -1) {
    UINT x = 0;
    x |= UINT(1) << j;
    FOR(k, j) if (pivot[k] != -1 && (A[pivot[k]] >> j & 1)) {
      x |= UINT(1) << k;
    }
    res.eb(x);
  }
  return res;
}
#line 2 "library/linalg/xor/transpose.hpp"

// n x m 行列の transpose。O((n+m)log(n+m)) 時間。
// https://github.com/dsnet/matrix-transpose
template <typename UINT>
vc<UINT> transpose(int n, int m, vc<UINT>& A, bool keep_A = 1) {
  assert(max(n, m) <= numeric_limits<UINT>::digits);
  assert(len(A) == n);
  vc<UINT> tmp;
  if (keep_A) tmp = A;
  int LOG = 0;
  while ((1 << LOG) < max(n, m)) ++LOG;
  A.resize(1 << LOG);
  int width = 1 << LOG;
  UINT mask = 1;
  FOR(i, LOG) mask = mask | (mask << (1 << i));
  FOR(t, LOG) {
    width >>= 1;
    mask = mask ^ (mask >> width);
    FOR(i, 1 << t) {
      FOR(j, width) {
        UINT* x = &A[width * (2 * i + 0) + j];
        UINT* y = &A[width * (2 * i + 1) + j];
        *x = ((*y << width) & mask) ^ *x;
        *y = ((*x & mask) >> width) ^ *y;
        *x = ((*y << width) & mask) ^ *x;
      }
    }
  }
  A.resize(m);
  if (!keep_A) return A;
  swap(A, tmp);
  return tmp;
}
#line 3 "library/linalg/xor/vector_space.hpp"

template <typename UINT>
struct Vector_Space {
#define SP Vector_Space
  vc<UINT> dat;

  Vector_Space() {}
  Vector_Space(vc<UINT> dat, bool is_reduced = false) : dat(dat) {
    if (!is_reduced) reduce();
  }

  int size() { return dat.size(); }

  bool add_element(UINT v) {
    for (auto&& e: dat) {
      if (e == 0 || v == 0) break;
      chmin(v, v ^ e);
    }
    if (v) {
      dat.eb(v);
      return true;
    }
    return false;
  }

  void reduce() {
    SP y;
    for (auto&& e: dat) y.add_element(e);
    (*this) = y;
  }

  bool contain(UINT v) {
    for (auto&& w: dat) {
      if (v == 0) break;
      chmin(v, v ^ w);
    }
    return v == 0;
  }

  UINT get_max(UINT xor_val = 0) {
    UINT res = xor_val;
    for (auto&& x: dat) chmax(res, res ^ x);
    return res;
  }

  UINT get_min(UINT xor_val) {
    UINT res = xor_val;
    for (auto&& x: dat) chmin(res, res ^ x);
    return res;
  }

  static SP merge(SP x, SP y) {
    if (len(x) < len(y)) swap(x, y);
    for (auto v: y.dat) { add_element(x, v); }
    return x;
  }

  static SP intersection(SP& x, SP& y, int max_dim) {
    SP xx = x.orthogonal_space(max_dim);
    SP yy = y.orthogonal_space(max_dim);
    xx = merge(xx, yy);
    return xx.orthogonal_space(max_dim);
  }

  SP orthogonal_space(int max_dim) {
    int n = len(dat);
    // 三角化
    FOR(j, n) FOR(i, j) chmin(dat[i], dat[i] ^ dat[j]);
    int m = max_dim;
    // pivot[k] == k となるように行の順番を変える
    vc<u64> tmp(m);
    FOR(i, len(dat)) tmp[topbit(dat[i])] = dat[i];
    tmp = transpose(m, m, tmp, 0);
    SP res;
    FOR(j, m) {
      if (tmp[j] >> j & 1) continue;
      res.add_element(tmp[j] | UINT(1) << j);
    }
    return res;
  }
#undef SP
};
#line 2 "library/alg/monoid/merge_vector_space.hpp"

template <typename UINT>
struct Merge_Vector_Space {
  using value_type = Vector_Space<UINT>;
  using X = value_type;
  static X op(X x, X y) { return Vector_Space<UINT>::merge(x, y); }
  static constexpr X unit() { return {}; }
  static constexpr bool commute = 1;
};
#line 5 "main.cpp"

void solve() {
  LL(N);
  VEC(ll, A, N);
  using Mono = Merge_Vector_Space<u64>;
  using SP = typename Mono::value_type;
  SP X;
  for (auto&& a: A) { X.add_element(a); }
  print(1LL << len(X));
}

signed main() {
  solve();
  return 0;
}