結果

問題 No.2277 Honest or Dishonest ?
コンテスト
ユーザー hashiryo
提出日時 2024-09-03 20:11:02
言語 C++17
(gcc 13.3.0 + boost 1.89.0)
結果
AC  
実行時間 32 ms / 2,000 ms
コード長 10,752 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 2,280 ms
コンパイル使用メモリ 203,524 KB
最終ジャッジ日時 2025-02-24 03:48:09
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 50
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 #
raw source code 

// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
// clang-format off
std::ostream&operator<<(std::ostream&os,std::int8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,std::uint8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,const __int128_t &u){if(!u)os<<"0";__int128_t tmp=u<0?(os<<"-",-u):u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
std::ostream&operator<<(std::ostream&os,const __uint128_t &u){if(!u)os<<"0";__uint128_t tmp=u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
#define checkpoint() (void(0))
#define debug(...) (void(0))
#define debugArray(x,n) (void(0))
#define debugMatrix(x,h,w) (void(0))
// clang-format on
#include <type_traits>
template <class Int> constexpr inline Int mod_inv(Int a, Int mod) {
 static_assert(std::is_signed_v<Int>);
 Int x= 1, y= 0, b= mod;
 for (Int q= 0, z= 0; b;) z= x, x= y, y= z - y * (q= a / b), z= a, a= b, b= z - b * q;
 return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
#define CE constexpr
#define IL inline
#define NORM \
 if (n >= mod) n-= mod; \
 return n
#define PLUS(U, M) \
 CE IL U plus(U l, U r) const { return l+= r, l < (M) ? l : l - (M); }
#define DIFF(U, C, M) \
 CE IL U diff(U l, U r) const { return l-= r, l >> C ? l + (M) : l; }
#define SGN(U) \
 static CE IL U set(U n) { return n; } \
 static CE IL U get(U n) { return n; } \
 static CE IL U norm(U n) { return n; }
template <class u_t, class du_t, u8 B, u8 A> struct MP_Mo {
 u_t mod;
 CE MP_Mo(): mod(0), iv(0), r2(0) {}
 CE MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
 CE IL u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
 PLUS(u_t, mod << 1)
 DIFF(u_t, A, mod << 1)
 CE IL u_t set(u_t n) const { return mul(n, r2); }
 CE IL u_t get(u_t n) const {
  n= reduce(n);
  NORM;
 }
 CE IL u_t norm(u_t n) const { NORM; }
private:
 u_t iv, r2;
 static CE u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
 CE IL u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
struct MP_Na {
 u32 mod;
 CE MP_Na(): mod(0){};
 CE MP_Na(u32 m): mod(m) {}
 CE IL u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
 PLUS(u32, mod) DIFF(u32, 31, mod) SGN(u32)
};
struct MP_Br {  // mod < 2^31
 u32 mod;
 CE MP_Br(): mod(0), s(0), x(0) {}
 CE MP_Br(u32 m): mod(m), s(95 - __builtin_clz(m - 1)), x(((u128(1) << s) + m - 1) / m) {}
 CE IL u32 mul(u32 l, u32 r) const { return rem(u64(l) * r); }
 PLUS(u32, mod) DIFF(u32, 31, mod) SGN(u32) private: u8 s;
 u64 x;
 CE IL u64 quo(u64 n) const { return (u128(x) * n) >> s; }
 CE IL u32 rem(u64 n) const { return n - quo(n) * mod; }
};
struct MP_Br2 {  // 2^20 < mod <= 2^41
 u64 mod;
 CE MP_Br2(): mod(0), x(0) {}
 CE MP_Br2(u64 m): mod(m), x((u128(1) << 84) / m) {}
 CE IL u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
 PLUS(u64, mod << 1)
 DIFF(u64, 63, mod << 1)
 static CE IL u64 set(u64 n) { return n; }
 CE IL u64 get(u64 n) const { NORM; }
 CE IL u64 norm(u64 n) const { NORM; }
private:
 u64 x;
 CE IL u128 quo(const u128 &n) const { return (n * x) >> 84; }
 CE IL u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
struct MP_D2B1 {
 u8 s;
 u64 mod, d, v;
 CE MP_D2B1(): s(0), mod(0), d(0), v(0) {}
 CE MP_D2B1(u64 m): s(__builtin_clzll(m)), mod(m), d(m << s), v(u128(-1) / d) {}
 CE IL u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
 PLUS(u64, mod) DIFF(u64, 63, mod) SGN(u64) private: CE IL u64 rem(const u128 &u) const {
  u128 q= (u >> 64) * v + u;
  u64 r= u64(u) - (q >> 64) * d - d;
  if (r > u64(q)) r+= d;
  if (r >= d) r-= d;
  return r;
 }
};
template <class u_t, class MP> CE u_t pow(u_t x, u64 k, const MP &md) {
 for (u_t ret= md.set(1);; x= md.mul(x, x))
  if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
#undef NORM
#undef PLUS
#undef DIFF
#undef SGN
#undef CE
}
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
namespace math_internal {
#define CE constexpr
template <class MP, u64 MOD> struct SB: s_b {
protected:
 static CE MP md= MP(MOD);
};
template <class Int, class U, class B> struct MInt: public B {
 using Uint= U;
 static CE inline auto mod() { return B::md.mod; }
 CE MInt(): x(0) {}
 template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> CE MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
 CE MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
 CE MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
 CE MInt name const { \
  MInt ret; \
  return ret.x= op, ret; \
 }
 FUNC(operator+(const MInt & r), B::md.plus(x, r.x))
 FUNC(operator-(const MInt & r), B::md.diff(x, r.x))
 FUNC(operator*(const MInt & r), B::md.mul(x, r.x))
 FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
 CE MInt operator/(const MInt& r) const { return *this * r.inv(); }
 CE MInt& operator+=(const MInt& r) { return *this= *this + r; }
 CE MInt& operator-=(const MInt& r) { return *this= *this - r; }
 CE MInt& operator*=(const MInt& r) { return *this= *this * r; }
 CE MInt& operator/=(const MInt& r) { return *this= *this / r; }
 CE bool operator==(const MInt& r) const { return B::md.norm(x) == B::md.norm(r.x); }
 CE bool operator!=(const MInt& r) const { return !(*this == r); }
 CE bool operator<(const MInt& r) const { return B::md.norm(x) < B::md.norm(r.x); }
 CE inline MInt inv() const { return mod_inv<Int>(val(), B::md.mod); }
 CE inline Uint val() const { return B::md.get(x); }
 friend ostream& operator<<(ostream& os, const MInt& r) { return os << r.val(); }
 friend istream& operator>>(istream& is, MInt& r) {
  i64 v;
  return is >> v, r= MInt(v), is;
 }
private:
 Uint x;
};
template <u64 MOD> using ModInt= conditional_t < (MOD < (1 << 30)) & MOD, MInt<int, u32, SB<MP_Mo<u32, u64, 32, 31>, MOD>>, conditional_t < (MOD < (1ull << 62)) & MOD, MInt<i64, u64, SB<MP_Mo<u64, u128, 64, 63>, MOD>>, conditional_t<MOD<(1u << 31), MInt<int, u32, SB<MP_Na, MOD>>, conditional_t<MOD<(1ull << 32), MInt<i64, u32, SB<MP_Na, MOD>>, conditional_t<MOD <= (1ull << 41), MInt<i64, u64, SB<MP_Br2, MOD>>, MInt<i64, u64, SB<MP_D2B1, MOD>>>>>>>;
#undef CE
}
using math_internal::ModInt;
template <bool undoable= false, class weight_t= void> class UnionFind {
 std::vector<int> par;
 std::vector<weight_t> val;
public:
 UnionFind(int n): par(n, -1), val(n) {}
 int leader(int u) {
  if (par[u] < 0) return u;
  int r= leader(par[u]);
  if constexpr (std::is_same_v<weight_t, bool>) val[u]= val[u] ^ val[par[u]];
  else val[u]+= val[par[u]];
  return par[u]= r;
 }
 //  p(v) - p(u) = w
 bool unite(int u, int v, weight_t w) {
  int u_= leader(u), v_= leader(v);
  if constexpr (std::is_same_v<weight_t, bool>) w^= val[u] ^ val[v];
  else w+= val[u] - val[v];
  if (u_ == v_) return w == weight_t();
  if (par[u_] > par[v_]) std::swap(u_, v_), w= -w;
  return par[u_]+= par[v_], par[v_]= u_, val[v_]= w, true;
 }
 bool connected(int u, int v) { return leader(u) == leader(v); }
 int size(int u) { return -par[leader(u)]; }
 weight_t potential(int u) { return leader(u), val[u]; }
 //  p(v) - p(u)
 weight_t diff(int u, int v) {
  if constexpr (std::is_same_v<weight_t, bool>) return potential(u) ^ potential(v);
  else return potential(v) - potential(u);
 }
};
template <> class UnionFind<false, void> {
 std::vector<int> par;
public:
 UnionFind(int n): par(n, -1) {}
 int leader(int u) { return par[u] < 0 ? u : par[u]= leader(par[u]); }
 bool unite(int u, int v) {
  if ((u= leader(u)) == (v= leader(v))) return false;
  if (par[u] > par[v]) std::swap(u, v);
  return par[u]+= par[v], par[v]= u, true;
 }
 bool connected(int u, int v) { return leader(u) == leader(v); }
 int size(int u) { return -par[leader(u)]; }
};
template <class T> class UnionFind<true, T> {
 std::vector<int> par;
 std::vector<T> val;
 std::vector<std::tuple<int, int, T>> his;
public:
 UnionFind(int n): par(n, -1), val(n) {}
 int leader(int u) const { return par[u] < 0 ? u : leader(par[u]); }
 //  p(v) - p(u) = w
 bool unite(int u, int v, T w) {
  int u_= leader(u), v_= leader(v);
  if constexpr (std::is_same_v<T, bool>) w^= val[u] ^ val[v];
  else w+= val[u] - val[v];
  if (u_ == v_) return w == T();
  if (par[u_] > par[v_]) std::swap(u_, v_), w= -w;
  return his.emplace_back(v_, par[v_], val[v_]), par[u_]+= par[v_], par[v_]= u_, val[v_]= w, true;
 }
 bool connected(int u, int v) const { return leader(u) == leader(v); }
 int size(int u) const { return -par[leader(u)]; }
 T potential(int u) {
  if constexpr (std::is_same_v<T, bool>) return par[u] < 0 ? val[u] : val[u] ^ potential(par[u]);
  else return par[u] < 0 ? val[u] : val[u] + potential(par[u]);
 }
 //  p(v) - p(u)
 T diff(int u, int v) {
  if constexpr (std::is_same_v<T, bool>) return potential(v) ^ potential(u);
  else return potential(v) - potential(u);
 }
 int time() const { return his.size(); }
 void undo() {
  if (his.empty()) return;
  auto [u, s, v]= his.back();
  his.pop_back(), par[par[u]]-= s, par[u]= s, val[u]= v;
 }
 void rollback(int t) {
  for (assert(t <= time()); time() > t;) undo();
 }
};
template <> class UnionFind<true, void> {
 std::vector<int> par;
 std::vector<std::pair<int, int>> his;
public:
 UnionFind(int n): par(n, -1) {}
 int leader(int u) const { return par[u] < 0 ? u : leader(par[u]); }
 bool unite(int u, int v) {
  if ((u= leader(u)) == (v= leader(v))) return false;
  if (par[u] > par[v]) std::swap(u, v);
  return his.emplace_back(v, par[v]), par[u]+= par[v], par[v]= u, true;
 }
 bool connected(int u, int v) const { return leader(u) == leader(v); }
 int size(int u) const { return -par[leader(u)]; }
 int time() const { return his.size(); }
 void undo() {
  if (his.empty()) return;
  auto [u, s]= his.back();
  his.pop_back(), par[par[u]]-= s, par[u]= s;
 }
 void rollback(int t) {
  for (assert(t <= time()); time() > t;) undo();
 }
};
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<998244353>;
 int N, Q;
 cin >> N >> Q;
 UnionFind<false, bool> uf(N);
 bool isok= true;
 for (int i= 0; i < Q; ++i) {
  int A, B, C;
  cin >> A >> B >> C, --A, --B;
  isok&= uf.unite(A, B, C);
 }
 if (!isok) return cout << 0 << '\n', 0;
 int cnt= 0;
 for (int i= 0; i < N; ++i) cnt+= uf.leader(i) == i;
 cout << Mint(2).pow(cnt) << '\n';
 return 0;
}
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