Hashiryo's Library
This documentation is automatically generated by competitive-verifier/competitive-verifier
test/yukicoder/2277.UFPU.test.cpp
- View this file on GitHub
- Last update: 2024-10-01 17:03:34+09:00
- Problem: https://yukicoder.me/problems/no/2277
Depends on
- Union-Find (ポテンシャル, undo可能) (src/DataStructure/UnionFind_Potentialized_Undoable.hpp)
modintを扱うテンプレート (src/Internal/modint_traits.hpp)- 剰余の高速化 (src/Internal/Remainder.hpp)
- 逆元 ($\mathbb{Z}/m\mathbb{Z}$) (src/Math/mod_inv.hpp)
- ModInt (src/Math/ModInt.hpp)
Code
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/2277
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
// ポテンシャルUF(2SAT+連結成分)
#include <iostream>
#include "src/Math/ModInt.hpp"
#include "src/DataStructure/UnionFind_Potentialized_Undoable.hpp"
using namespace std;
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
using Mint= ModInt<998244353>;
int N, Q;
cin >> N >> Q;
UnionFind_Potentialized_Undoable<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;
}#line 1 "test/yukicoder/2277.UFPU.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/2277
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
// ポテンシャルUF(2SAT+連結成分)
#include <iostream>
#line 2 "src/Math/mod_inv.hpp"
#include <utility>
#include <type_traits>
#include <cassert>
template <class Uint> constexpr inline Uint mod_inv(Uint a, Uint mod) {
std::make_signed_t<Uint> x= 1, y= 0, z= 0;
for (Uint q= 0, b= mod, c= 0; b;) z= x, x= y, y= z - y * (q= a / b), c= a, a= b, b= c - b * q;
return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
#line 2 "src/Internal/Remainder.hpp"
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;
struct MP_Na { // mod < 2^32
u32 mod;
constexpr MP_Na(): mod(0) {}
constexpr MP_Na(u32 m): mod(m) {}
constexpr inline u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
constexpr inline u32 set(u32 n) const { return n; }
constexpr inline u32 get(u32 n) const { return n; }
constexpr inline u32 norm(u32 n) const { return n; }
constexpr inline u32 plus(u64 l, u32 r) const { return l+= r, l < mod ? l : l - mod; }
constexpr inline u32 diff(u64 l, u32 r) const { return l-= r, l >> 63 ? l + mod : l; }
};
template <class u_t, class du_t, u8 B> struct MP_Mo { // mod < 2^32, mod < 2^62
u_t mod;
constexpr MP_Mo(): mod(0), iv(0), r2(0) {}
constexpr MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
constexpr inline u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
constexpr inline u_t set(u_t n) const { return mul(n, r2); }
constexpr inline u_t get(u_t n) const { return n= reduce(n), n >= mod ? n - mod : n; }
constexpr inline u_t norm(u_t n) const { return n >= mod ? n - mod : n; }
constexpr inline u_t plus(u_t l, u_t r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
constexpr inline u_t diff(u_t l, u_t r) const { return l-= r, l >> (B - 1) ? l + (mod << 1) : l; }
private:
u_t iv, r2;
static constexpr u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
constexpr inline u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
using MP_Mo32= MP_Mo<u32, u64, 32>;
using MP_Mo64= MP_Mo<u64, u128, 64>;
struct MP_Br { // 2^20 < mod <= 2^41
u64 mod;
constexpr MP_Br(): mod(0), x(0) {}
constexpr MP_Br(u64 m): mod(m), x((u128(1) << 84) / m) {}
constexpr inline u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
static constexpr inline u64 set(u64 n) { return n; }
constexpr inline u64 get(u64 n) const { return n >= mod ? n - mod : n; }
constexpr inline u64 norm(u64 n) const { return n >= mod ? n - mod : n; }
constexpr inline u64 plus(u64 l, u64 r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
constexpr inline u64 diff(u64 l, u64 r) const { return l-= r, l >> 63 ? l + (mod << 1) : l; }
private:
u64 x;
constexpr inline u128 quo(const u128 &n) const { return (n * x) >> 84; }
constexpr inline u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
template <class du_t, u8 B> struct MP_D2B1 { // mod < 2^63, mod < 2^64
u64 mod;
constexpr MP_D2B1(): mod(0), s(0), d(0), v(0) {}
constexpr MP_D2B1(u64 m): mod(m), s(__builtin_clzll(m)), d(m << s), v(u128(-1) / d) {}
constexpr inline u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
constexpr inline u64 set(u64 n) const { return n; }
constexpr inline u64 get(u64 n) const { return n; }
constexpr inline u64 norm(u64 n) const { return n; }
constexpr inline u64 plus(du_t l, u64 r) const { return l+= r, l < mod ? l : l - mod; }
constexpr inline u64 diff(du_t l, u64 r) const { return l-= r, l >> B ? l + mod : l; }
private:
u8 s;
u64 d, v;
constexpr inline 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;
}
};
using MP_D2B1_1= MP_D2B1<u64, 63>;
using MP_D2B1_2= MP_D2B1<u128, 127>;
template <class u_t, class MP> constexpr 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;
}
}
#line 3 "src/Internal/modint_traits.hpp"
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>;
#line 6 "src/Math/ModInt.hpp"
namespace math_internal {
template <class MP, u64 MOD> struct SB: s_b {
protected:
static constexpr MP md= MP(MOD);
};
template <class U, class B> struct MInt: public B {
using Uint= U;
static constexpr inline auto mod() { return B::md.mod; }
constexpr MInt(): x(0) {}
template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> constexpr MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
constexpr MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
constexpr MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
constexpr 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
constexpr MInt operator/(const MInt &r) const { return *this * r.inv(); }
constexpr MInt &operator+=(const MInt &r) { return *this= *this + r; }
constexpr MInt &operator-=(const MInt &r) { return *this= *this - r; }
constexpr MInt &operator*=(const MInt &r) { return *this= *this * r; }
constexpr MInt &operator/=(const MInt &r) { return *this= *this / r; }
constexpr bool operator==(const MInt &r) const { return B::md.norm(x) == B::md.norm(r.x); }
constexpr bool operator!=(const MInt &r) const { return !(*this == r); }
constexpr bool operator<(const MInt &r) const { return B::md.norm(x) < B::md.norm(r.x); }
constexpr inline MInt inv() const { return mod_inv<U>(val(), B::md.mod); }
constexpr 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 MP_B= conditional_t < (MOD < (1 << 30)) & MOD, MP_Mo32, conditional_t < MOD < (1ull << 32), MP_Na, conditional_t<(MOD < (1ull << 62)) & MOD, MP_Mo64, conditional_t<MOD<(1ull << 41), MP_Br, conditional_t<MOD<(1ull << 63), MP_D2B1_1, MP_D2B1_2>>>>>;
template <u64 MOD> using ModInt= MInt < conditional_t<MOD<(1 << 30), u32, u64>, SB<MP_B<MOD>, MOD>>;
}
using math_internal::ModInt;
#line 2 "src/DataStructure/UnionFind_Potentialized_Undoable.hpp"
#include <vector>
#include <algorithm>
#line 5 "src/DataStructure/UnionFind_Potentialized_Undoable.hpp"
template <class weight_t> class UnionFind_Potentialized_Undoable {
std::vector<int> par;
std::vector<weight_t> val;
std::vector<std::tuple<int, int, weight_t, int>> his;
int cur;
public:
UnionFind_Potentialized_Undoable(int n): par(n, -1), val(n), his{{-1, -1, weight_t(), 1}}, cur(0) { his.reserve(n + 1); }
int leader(int u) const { return par[u] < 0 ? u : leader(par[u]); }
// -p(v) + p(u) = w
bool unite(int u, int v, weight_t w) {
if constexpr (std::is_same_v<weight_t, bool>) w^= potential(v) ^ potential(u);
else w= potential(v) + w - potential(u);
if (++cur; (u= leader(u)) == (v= leader(v))) return ++std::get<3>(his.back()), w == weight_t();
if (par[v] > par[u]) std::swap(u, v), w= -w;
return his.emplace_back(u, par[u], val[u], 1), par[v]+= par[u], par[u]= v, val[u]= 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) {
if (par[u] < 0) return val[u];
if constexpr (std::is_same_v<weight_t, bool>) return potential(par[u]) ^ val[u];
else return potential(par[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);
}
int time() const { return cur; }
void undo() {
if (assert(cur > 0), --cur; --std::get<3>(his.back()) == 0) {
auto [u, p, v, _]= his.back();
par[par[u]]-= p, par[u]= p, val[u]= v, his.pop_back();
}
}
void rollback(int t) {
assert(0 <= t), assert(t <= cur);
if (t == cur) return;
for (;;) {
auto &[u, p, v, i]= his.back();
if (cur-= i; cur < t) {
i= t - cur, cur= t;
break;
}
par[par[u]]-= p, par[u]= p, val[u]= v, his.pop_back();
}
}
};
#line 8 "test/yukicoder/2277.UFPU.test.cpp"
using namespace std;
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
using Mint= ModInt<998244353>;
int N, Q;
cin >> N >> Q;
UnionFind_Potentialized_Undoable<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;
}
Test cases
| Env | Name | Status | Elapsed | Memory |
|---|---|---|---|---|
| g++-13 | 01_sample_1.txt |
AC |
5 ms | 3 MB |
| g++-13 | 01_sample_2.txt |
AC |
4 ms | 4 MB |
| g++-13 | 01_sample_3.txt |
AC |
5 ms | 3 MB |
| g++-13 | 02_random_1.txt |
AC |
21 ms | 4 MB |
| g++-13 | 02_random_10.txt |
AC |
14 ms | 4 MB |
| g++-13 | 02_random_11.txt |
AC |
21 ms | 4 MB |
| g++-13 | 02_random_12.txt |
AC |
16 ms | 4 MB |
| g++-13 | 02_random_13.txt |
AC |
9 ms | 4 MB |
| g++-13 | 02_random_14.txt |
AC |
16 ms | 4 MB |
| g++-13 | 02_random_15.txt |
AC |
11 ms | 4 MB |
| g++-13 | 02_random_16.txt |
AC |
19 ms | 5 MB |
| g++-13 | 02_random_17.txt |
AC |
20 ms | 5 MB |
| g++-13 | 02_random_18.txt |
AC |
18 ms | 4 MB |
| g++-13 | 02_random_19.txt |
AC |
17 ms | 4 MB |
| g++-13 | 02_random_2.txt |
AC |
21 ms | 5 MB |
| g++-13 | 02_random_20.txt |
AC |
16 ms | 4 MB |
| g++-13 | 02_random_3.txt |
AC |
10 ms | 4 MB |
| g++-13 | 02_random_4.txt |
AC |
20 ms | 4 MB |
| g++-13 | 02_random_5.txt |
AC |
17 ms | 4 MB |
| g++-13 | 02_random_6.txt |
AC |
9 ms | 4 MB |
| g++-13 | 02_random_7.txt |
AC |
15 ms | 4 MB |
| g++-13 | 02_random_8.txt |
AC |
14 ms | 4 MB |
| g++-13 | 02_random_9.txt |
AC |
9 ms | 4 MB |
| g++-13 | 03_random_1.txt |
AC |
22 ms | 4 MB |
| g++-13 | 03_random_10.txt |
AC |
12 ms | 4 MB |
| g++-13 | 03_random_11.txt |
AC |
21 ms | 5 MB |
| g++-13 | 03_random_12.txt |
AC |
22 ms | 4 MB |
| g++-13 | 03_random_13.txt |
AC |
6 ms | 4 MB |
| g++-13 | 03_random_14.txt |
AC |
15 ms | 4 MB |
| g++-13 | 03_random_15.txt |
AC |
22 ms | 4 MB |
| g++-13 | 03_random_16.txt |
AC |
9 ms | 4 MB |
| g++-13 | 03_random_17.txt |
AC |
10 ms | 4 MB |
| g++-13 | 03_random_18.txt |
AC |
6 ms | 4 MB |
| g++-13 | 03_random_19.txt |
AC |
23 ms | 5 MB |
| g++-13 | 03_random_2.txt |
AC |
14 ms | 4 MB |
| g++-13 | 03_random_20.txt |
AC |
17 ms | 4 MB |
| g++-13 | 03_random_3.txt |
AC |
16 ms | 5 MB |
| g++-13 | 03_random_4.txt |
AC |
7 ms | 4 MB |
| g++-13 | 03_random_5.txt |
AC |
13 ms | 4 MB |
| g++-13 | 03_random_6.txt |
AC |
9 ms | 4 MB |
| g++-13 | 03_random_7.txt |
AC |
12 ms | 4 MB |
| g++-13 | 03_random_8.txt |
AC |
12 ms | 4 MB |
| g++-13 | 03_random_9.txt |
AC |
17 ms | 4 MB |
| g++-13 | 04_max_1.txt |
AC |
23 ms | 5 MB |
| g++-13 | 04_max_10.txt |
AC |
24 ms | 5 MB |
| g++-13 | 04_max_2.txt |
AC |
25 ms | 5 MB |
| g++-13 | 04_max_3.txt |
AC |
25 ms | 5 MB |
| g++-13 | 04_max_4.txt |
AC |
25 ms | 5 MB |
| g++-13 | 04_max_5.txt |
AC |
26 ms | 5 MB |
| g++-13 | 04_max_6.txt |
AC |
25 ms | 5 MB |
| g++-13 | 04_max_7.txt |
AC |
24 ms | 5 MB |
| g++-13 | 04_max_8.txt |
AC |
24 ms | 5 MB |
| g++-13 | 04_max_9.txt |
AC |
24 ms | 5 MB |
| clang++-18 | 01_sample_1.txt |
AC |
5 ms | 4 MB |
| clang++-18 | 01_sample_2.txt |
AC |
5 ms | 4 MB |
| clang++-18 | 01_sample_3.txt |
AC |
4 ms | 4 MB |
| clang++-18 | 02_random_1.txt |
AC |
21 ms | 4 MB |
| clang++-18 | 02_random_10.txt |
AC |
14 ms | 4 MB |
| clang++-18 | 02_random_11.txt |
AC |
21 ms | 4 MB |
| clang++-18 | 02_random_12.txt |
AC |
16 ms | 4 MB |
| clang++-18 | 02_random_13.txt |
AC |
9 ms | 4 MB |
| clang++-18 | 02_random_14.txt |
AC |
16 ms | 4 MB |
| clang++-18 | 02_random_15.txt |
AC |
11 ms | 4 MB |
| clang++-18 | 02_random_16.txt |
AC |
20 ms | 5 MB |
| clang++-18 | 02_random_17.txt |
AC |
22 ms | 5 MB |
| clang++-18 | 02_random_18.txt |
AC |
18 ms | 4 MB |
| clang++-18 | 02_random_19.txt |
AC |
17 ms | 4 MB |
| clang++-18 | 02_random_2.txt |
AC |
21 ms | 5 MB |
| clang++-18 | 02_random_20.txt |
AC |
16 ms | 4 MB |
| clang++-18 | 02_random_3.txt |
AC |
10 ms | 4 MB |
| clang++-18 | 02_random_4.txt |
AC |
20 ms | 4 MB |
| clang++-18 | 02_random_5.txt |
AC |
17 ms | 4 MB |
| clang++-18 | 02_random_6.txt |
AC |
8 ms | 4 MB |
| clang++-18 | 02_random_7.txt |
AC |
15 ms | 4 MB |
| clang++-18 | 02_random_8.txt |
AC |
14 ms | 4 MB |
| clang++-18 | 02_random_9.txt |
AC |
9 ms | 4 MB |
| clang++-18 | 03_random_1.txt |
AC |
22 ms | 4 MB |
| clang++-18 | 03_random_10.txt |
AC |
12 ms | 4 MB |
| clang++-18 | 03_random_11.txt |
AC |
21 ms | 5 MB |
| clang++-18 | 03_random_12.txt |
AC |
22 ms | 4 MB |
| clang++-18 | 03_random_13.txt |
AC |
7 ms | 4 MB |
| clang++-18 | 03_random_14.txt |
AC |
15 ms | 4 MB |
| clang++-18 | 03_random_15.txt |
AC |
22 ms | 4 MB |
| clang++-18 | 03_random_16.txt |
AC |
9 ms | 4 MB |
| clang++-18 | 03_random_17.txt |
AC |
10 ms | 4 MB |
| clang++-18 | 03_random_18.txt |
AC |
6 ms | 4 MB |
| clang++-18 | 03_random_19.txt |
AC |
23 ms | 5 MB |
| clang++-18 | 03_random_2.txt |
AC |
15 ms | 4 MB |
| clang++-18 | 03_random_20.txt |
AC |
18 ms | 4 MB |
| clang++-18 | 03_random_3.txt |
AC |
16 ms | 5 MB |
| clang++-18 | 03_random_4.txt |
AC |
7 ms | 4 MB |
| clang++-18 | 03_random_5.txt |
AC |
13 ms | 4 MB |
| clang++-18 | 03_random_6.txt |
AC |
9 ms | 4 MB |
| clang++-18 | 03_random_7.txt |
AC |
12 ms | 4 MB |
| clang++-18 | 03_random_8.txt |
AC |
12 ms | 4 MB |
| clang++-18 | 03_random_9.txt |
AC |
17 ms | 4 MB |
| clang++-18 | 04_max_1.txt |
AC |
24 ms | 5 MB |
| clang++-18 | 04_max_10.txt |
AC |
24 ms | 5 MB |
| clang++-18 | 04_max_2.txt |
AC |
26 ms | 5 MB |
| clang++-18 | 04_max_3.txt |
AC |
27 ms | 5 MB |
| clang++-18 | 04_max_4.txt |
AC |
26 ms | 5 MB |
| clang++-18 | 04_max_5.txt |
AC |
26 ms | 5 MB |
| clang++-18 | 04_max_6.txt |
AC |
26 ms | 5 MB |
| clang++-18 | 04_max_7.txt |
AC |
25 ms | 5 MB |
| clang++-18 | 04_max_8.txt |
AC |
24 ms | 5 MB |
| clang++-18 | 04_max_9.txt |
AC |
24 ms | 5 MB |