結果

問題 No.2672 Subset Xor Sum
コンテスト
ユーザー maspy
提出日時 2024-03-15 21:22:29
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 125 ms / 2,000 ms
コード長 11,202 bytes
コンパイル時間 3,625 ms
コンパイル使用メモリ 270,592 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-09-30 04:12:39
合計ジャッジ時間 6,506 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 2
other AC * 66
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

diff # 

#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

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

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 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); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(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>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

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

#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) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = 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;
    (check(x) ? ok : ng) = 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 "/home/maspy/compro/library/other/io2.hpp"
#define INT(...) \
  int __VA_ARGS__; \
  IN(__VA_ARGS__)
#define LL(...) \
  ll __VA_ARGS__; \
  IN(__VA_ARGS__)
#define STR(...) \
  string __VA_ARGS__; \
  IN(__VA_ARGS__)
#define CHR(...) \
  char __VA_ARGS__; \
  IN(__VA_ARGS__)
#define DBL(...) \
  long double __VA_ARGS__; \
  IN(__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 read(int &a) { cin >> a; }
void read(long long &a) { cin >> a; }
void read(char &a) { cin >> a; }
void read(double &a) { cin >> a; }
void read(long double &a) { cin >> a; }
void read(string &a) { cin >> a; }
template <class T, class S> void read(pair<T, S> &p) { read(p.first), read(p.second); }
template <class T> void read(vector<T> &a) {for(auto &i : a) read(i);}
template <class T> void read(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail> void IN(Head &head, Tail &...tail) {
  read(head);
  IN(tail...);
}

template <typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& A) {
  os << A.fi << " " << A.se;
  return os;
}

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& A) {
  for (size_t i = 0; i < A.size(); i++) {
    if(i) os << " ";
    os << A[i];
  }
  return os;
}

void print() {
  cout << "\n";
  cout.flush();
}

template <class Head, class... Tail>
void print(Head&& head, Tail&&... tail) {
  cout << head;
  if (sizeof...(Tail)) cout << " ";
  print(forward<Tail>(tail)...);
}

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 2 "/home/maspy/compro/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 2 "/home/maspy/compro/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(); }
  int dim() { 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;
  }

  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) { x.add_element(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) {
    normalize();
    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;
  }

  void normalize(bool dec = true) {
    int n = len(dat);
    // 三角化
    FOR(j, n) FOR(i, j) chmin(dat[i], dat[i] ^ dat[j]);
    sort(all(dat));
    if (dec) reverse(all(dat));
  }

private:
  void reduce() {
    SP y;
    for (auto&& e: dat) y.add_element(e);
    (*this) = y;
  }
#undef SP
};
#line 4 "main.cpp"

void solve() {
  LL(N);
  VEC(int, A, N);
  ll s = 0;
  for (auto& x: A) s ^= x;
  if (s != 0) return No();
  Vector_Space<u32> X;
  for (auto& x: A) X.add_element(x);
  ll dim = X.dim();
  Yes(dim < N - 1);
}

signed main() {
  int T = 1;
  // INT(T);
  FOR(T) solve();
  return 0;
}
0