MtSaka's Library
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test/yosupo/data_strucuture/unionfind_with_potential_non_commutative_group.test.cpp
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- Last update: 2024-11-14 08:53:04+09:00
- Problem: https://judge.yosupo.jp/problem/unionfind_with_potential_non_commutative_group
Depends on
- Weighted Disjoint Set Union(重み付きUnion Find) (ds/union-find/weighted-union-find.hpp)
- ModInt (math/modular/modint.hpp)
- Matrix(行列) (math/others/matrix.hpp)
- others/monoid.hpp
- template/alias.hpp
- template/func.hpp
- template/in.hpp
- template/macro.hpp
- template/out.hpp
- template/template.hpp
- template/type-traits.hpp
- template/util.hpp
Code
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/unionfind_with_potential_non_commutative_group
#include "../../../template/template.hpp"
#include "../../../ds/union-find/weighted-union-find.hpp"
#include "../../../math/modular/modint.hpp"
#include "../../../math/others/matrix.hpp"
using mint = ModInt<998244353>;
using Mat = Matrix<mint>;
struct Prod {
using value_type = Mat;
static Mat id() { return Mat::I(2); }
static Mat op(const Mat& x, const Mat& y) { return x * y; }
static Mat get_inv(const Mat& x) {
Mat ret(2, 2);
ret[0][0] = x[1][1], ret[0][1] = -x[0][1], ret[1][0] = -x[1][0], ret[1][1] = x[0][0];
ret *= (x[0][0] * x[1][1] - x[0][1] * x[1][0]).inv();
return ret;
}
};
int main() {
INT(n, q);
WeightedUnionFind<Prod> uf(n);
rep(q) {
INT(t, x, y);
if (t == 0) {
Mat a(2, 2);
sc >> a;
if (!uf.merge(x, y, a).second)
print(0);
else
print(1);
} else {
if (!uf.same(x, y))
print(-1);
else {
print(uf.diff(x, y));
}
}
}
}#line 1 "test/yosupo/data_strucuture/unionfind_with_potential_non_commutative_group.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/unionfind_with_potential_non_commutative_group
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#line 3 "template/alias.hpp"
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using i128 = __int128_t;
using u128 = __uint128_t;
using pi = std::pair<int, int>;
using pl = std::pair<ll, ll>;
using vi = std::vector<int>;
using vl = std::vector<ll>;
using vs = std::vector<std::string>;
using vc = std::vector<char>;
using vvl = std::vector<vl>;
using vd = std::vector<double>;
using vp = std::vector<pl>;
using vb = std::vector<bool>;
template <typename T>
struct infinity {
static constexpr T max = std::numeric_limits<T>::max();
static constexpr T min = std::numeric_limits<T>::min();
static constexpr T value = std::numeric_limits<T>::max() / 2;
static constexpr T mvalue = std::numeric_limits<T>::min() / 2;
};
template <typename T>
constexpr T INF = infinity<T>::value;
constexpr ll inf = INF<ll>;
constexpr ld EPS = 1e-8;
constexpr ld PI = 3.1415926535897932384626;
constexpr int dx[8] = {-1, 0, 1, 0, 1, -1, -1, 1};
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
#line 3 "template/macro.hpp"
#ifndef __COUNTER__
#define __COUNTER__ __LINE__
#endif
#define SELECT4(a, b, c, d, e, ...) e
#define SELECT3(a, b, c, d, ...) d
#define REP_1(a, c) for (ll REP_##c = 0; REP_##c < (ll)(a); ++REP_##c)
#define REP1(a) REP_1(a, __COUNTER__)
#define REP2(i, a) for (ll i = 0; i < (ll)(a); ++i)
#define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define rep(...) SELECT4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
#define RREP_1(a, c) for (ll RREP_##c = (ll)(a) - 1; RREP_##c >= 0; --RREP_##c)
#define RREP1(a) RREP_1(a, __COUNTER__)
#define RREP2(i, a) for (ll i = (ll)(a) - 1; i >= 0; --i)
#define RREP3(i, a, b) for (ll i = (ll)(b) - 1; i >= (ll)(a); --i)
#define rrep(...) SELECT3(__VA_ARGS__, RREP3, RREP2, RREP1)(__VA_ARGS__)
#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
#define INT(...) \
int __VA_ARGS__; \
scan(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
scan(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
scan(__VA_ARGS__)
#define CHR(...) \
char __VA_ARGS__; \
scan(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
scan(__VA_ARGS__)
#define LD(...) \
ld __VA_ARGS__; \
scan(__VA_ARGS__)
#define pb push_back
#define eb emplace_back
#line 3 "template/type-traits.hpp"
#line 5 "template/type-traits.hpp"
template <typename T, typename... Args>
struct function_traits_impl {
using return_type = T;
static constexpr std::size_t arg_size = sizeof...(Args);
template <std::size_t idx>
using argument_type = typename std::tuple_element<idx, std::tuple<Args...>>::type;
using argument_types = std::tuple<Args...>;
};
template <typename>
struct function_traits_helper;
template <typename T, typename Tp, typename... Args>
struct function_traits_helper<T (Tp::*)(Args...)> : function_traits_impl<T, Args...> {};
template <typename T, typename Tp, typename... Args>
struct function_traits_helper<T (Tp::*)(Args...) const> : function_traits_impl<T, Args...> {};
template <typename T, typename Tp, typename... Args>
struct function_traits_helper<T (Tp::*)(Args...)&> : function_traits_impl<T, Args...> {};
template <typename T, typename Tp, typename... Args>
struct function_traits_helper<T (Tp::*)(Args...) const&> : function_traits_impl<T, Args...> {};
template <typename F>
using function_traits = function_traits_helper<decltype(&std::remove_reference<F>::type::operator())>;
template <typename F>
using function_return_type = typename function_traits<F>::return_type;
template <typename F, std::size_t idx>
using function_argument_type = typename function_traits<F>::template argument_type<idx>;
template <typename F>
using function_argument_types = typename function_traits<F>::argument_types;
template <class T>
using is_signed_int = std::integral_constant<bool, (std::is_integral<T>::value && std::is_signed<T>::value) || std::is_same<T, __int128_t>::value>;
template <class T>
using is_unsigned_int = std::integral_constant<bool, (std::is_integral<T>::value && std::is_unsigned<T>::value) || std::is_same<T, __uint128_t>::value>;
template <class T>
using is_int = std::integral_constant<bool, is_signed_int<T>::value || is_unsigned_int<T>::value>;
template <typename T, typename = void>
struct is_range : std::false_type {};
template <typename T>
struct is_range<
T,
decltype(all(std::declval<typename std::add_lvalue_reference<T>::type>()), (void)0)> : std::true_type {};
template <std::size_t size>
struct int_least {
static_assert(size <= 128, "size must be less than or equal to 128");
using type = typename std::conditional<
size <= 8, std::int_least8_t,
typename std::conditional<
size <= 16, std::int_least16_t,
typename std::conditional<
size <= 32, std::int_least32_t,
typename std::conditional<size <= 64, std::int_least64_t, __int128_t>::type>::type>::type>::type;
};
template <std::size_t size>
using int_least_t = typename int_least<size>::type;
template <std::size_t size>
struct uint_least {
static_assert(size <= 128, "size must be less than or equal to 128");
using type = typename std::conditional<
size <= 8, std::uint_least8_t,
typename std::conditional<
size <= 16, std::uint_least16_t,
typename std::conditional<
size <= 32, std::uint_least32_t,
typename std::conditional<size <= 64, std::uint_least64_t, __uint128_t>::type>::type>::type>::type;
};
template <std::size_t size>
using uint_least_t = typename uint_least<size>::type;
template <typename T>
using double_size_int = int_least<std::numeric_limits<T>::digits * 2 + 1>;
template <typename T>
using double_size_int_t = typename double_size_int<T>::type;
template <typename T>
using double_size_uint = uint_least<std::numeric_limits<T>::digits * 2>;
template <typename T>
using double_size_uint_t = typename double_size_uint<T>::type;
template <typename T>
using double_size = typename std::conditional<std::is_signed<T>::value, double_size_int<T>, double_size_uint<T>>::type;
template <typename T>
using double_size_t = typename double_size<T>::type;
#line 2 "template/in.hpp"
#include <unistd.h>
#line 5 "template/in.hpp"
namespace fastio {
template <std::size_t BUFF_SIZE = 1 << 17, int decimal_precision = 16>
struct Scanner {
private:
template <typename, typename = void>
struct has_scan : std::false_type {};
template <class T>
struct has_scan<T, decltype(std::declval<T>().scan(std::declval<Scanner&>()), (void)0)> : std::true_type {};
int fd;
char buffer[BUFF_SIZE + 1];
int idx, sz;
bool state;
inline void load() {
int len = sz - idx;
if (idx < len) return;
std::memcpy(buffer, buffer + idx, len);
sz = len + read(fd, buffer + len, BUFF_SIZE - len);
idx = 0;
buffer[sz] = 0;
}
inline char cur() {
if (idx == sz) load();
if (idx == sz) {
state = false;
return '\0';
}
return buffer[idx];
}
inline void next() {
if (idx == sz) load();
if (idx == sz) return;
idx++;
}
public:
Scanner() : Scanner(0) {}
explicit Scanner(int fd) : fd(fd), idx(0), sz(0), state(true) {}
explicit Scanner(FILE* file) : fd(fileno(file)), idx(0), sz(0), state(true) {}
inline char scan_char() {
if (idx == sz) load();
return (idx == sz ? '\0' : buffer[idx++]);
}
Scanner ignore(int n = 1) {
if (idx + n > sz) load();
idx += n;
return (*this);
}
inline void skip_space() {
if (idx == sz) load();
while (('\t' <= cur() && cur() <= '\r') || cur() == ' ') {
if (++idx == sz) load();
}
}
void scan(char& a) {
skip_space();
a = scan_char();
}
void scan(std::string& a) {
skip_space();
a.clear();
while (cur() != '\0' && (buffer[idx] < '\t' || '\r' < buffer[idx]) && buffer[idx] != ' ') {
a += scan_char();
}
}
template <std::size_t len>
void scan(std::bitset<len>& a) {
skip_space();
if (idx + len > sz) load();
rrep(i, len) a[i] = (buffer[idx++] != '0');
}
template <typename T, typename std::enable_if<is_int<T>::value && !has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
skip_space();
bool neg = false;
if constexpr (std::is_signed<T>::value || std::is_same_v<T, __int128_t>) {
if (cur() == '-') {
neg = true;
next();
}
}
if (idx + 40 > sz && (idx == sz || ('0' <= buffer[sz - 1] && buffer[sz - 1] <= '9'))) load();
a = 0;
while ('0' <= buffer[idx] && buffer[idx] <= '9') {
a = a * 10 + (buffer[idx++] & 15);
}
if constexpr (std::is_signed<T>::value || std::is_same<T, __int128_t>::value) {
if (neg) a = -a;
}
}
template <typename T, typename std::enable_if<std::is_floating_point<T>::value && !has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
skip_space();
bool neg = false;
if (cur() == '-') {
neg = true;
next();
}
a = 0;
while ('0' <= cur() && cur() <= '9') {
a = a * 10 + (scan_char() & 15);
}
if (cur() == '.') {
next();
T n = 0, d = 1;
for (int i = 0; '0' <= cur() && cur() <= '9' && i < decimal_precision; ++i) {
n = n * 10 + (scan_char() & 15);
d *= 10;
}
while ('0' <= cur() && cur() <= '9') next();
a += n / d;
}
if (neg) a = -a;
}
private:
template <std::size_t i, typename... Args>
void scan(std::tuple<Args...>& a) {
if constexpr (i < sizeof...(Args)) {
scan(std::get<i>(a));
scan<i + 1, Args...>(a);
}
}
public:
template <typename... Args>
void scan(std::tuple<Args...>& a) {
scan<0, Args...>(a);
}
template <typename T, typename U>
void scan(std::pair<T, U>& a) {
scan(a.first);
scan(a.second);
}
template <typename T, typename std::enable_if<is_range<T>::value && !has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
for (auto& i : a) scan(i);
}
template <typename T, typename std::enable_if<has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
a.scan(*this);
}
void operator()() {}
template <typename Head, typename... Tail>
void operator()(Head& head, Tail&... tail) {
scan(head);
operator()(std::forward<Tail&>(tail)...);
}
template <typename T>
Scanner& operator>>(T& a) {
scan(a);
return *this;
}
explicit operator bool() const { return state; }
friend Scanner& getline(Scanner& sc, std::string& a) {
a.clear();
char c;
if ((c = sc.scan_char()) == '\0' || c == '\n') return sc;
a += c;
while ((c = sc.scan_char()) != '\0' && c != '\n') a += c;
return sc;
}
};
Scanner<> sc;
} // namespace fastio
using fastio::sc;
#line 6 "template/out.hpp"
namespace fastio {
struct Pre {
char buffer[10000][4];
constexpr Pre() : buffer() {
for (int i = 0; i < 10000; ++i) {
int n = i;
for (int j = 3; j >= 0; --j) {
buffer[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
template <std::size_t BUFF_SIZE = 1 << 17, bool debug = false>
struct Printer {
private:
template <typename, bool = debug, class = void>
struct has_print : std::false_type {};
template <typename T>
struct has_print<T, false, decltype(std::declval<T>().print(std::declval<Printer&>()), (void)0)> : std::true_type {};
template <typename T>
struct has_print<T, true, decltype(std::declval<T>().debug(std::declval<Printer&>()), (void)0)> : std::true_type {};
int fd;
char buffer[BUFF_SIZE];
int idx;
std::size_t decimal_precision;
public:
Printer() : Printer((debug ? 2 : 1)) {}
explicit Printer(int fd) : fd(fd), idx(0), decimal_precision(16) {}
explicit Printer(FILE* file) : fd(fileno(file)), idx(0), decimal_precision(16) {}
~Printer() {
flush();
}
void set_decimal_precision(std::size_t n) { decimal_precision = n; }
inline void print_char(char c) {
buffer[idx++] = c;
if (idx == BUFF_SIZE) flush();
}
inline void flush() {
idx = write(fd, buffer, idx);
idx = 0;
}
void print(char a) {
if constexpr (debug) print_char('\'');
print_char(a);
if constexpr (debug) print_char('\'');
}
void print(bool a) {
if constexpr (debug) print_char('\'');
print_char('0' + a);
if constexpr (debug) print_char('\'');
}
void print(const char* a) {
if constexpr (debug) print_char('\"');
for (; *a != '\0'; ++a) print_char(*a);
if constexpr (debug) print_char('\"');
}
template <std::size_t N>
void print(const char (&a)[N]) {
if constexpr (debug) print_char('\"');
for (auto i : a) print_char(i);
if constexpr (debug) print_char('\"');
}
void print(const std::string& a) {
if constexpr (debug) print_char('\"');
for (auto i : a) print_char(i);
if constexpr (debug) print_char('\"');
}
template <std::size_t len>
void print(const std::bitset<len>& a) {
for (int i = len - 1; i >= 0; --i) print_char('0' + a[i]);
}
template <typename T, typename std::enable_if<is_int<T>::value && !has_print<T>::value>::type* = nullptr>
void print(T a) {
if (!a) {
print_char('0');
return;
}
if constexpr (is_signed_int<T>::value) {
if (a < 0) {
print_char('-');
a = -a;
}
}
if (static_cast<size_t>(idx + 40) >= BUFF_SIZE) flush();
static char stk[40];
int top = 40;
while (a >= 10000) {
int i = a % 10000;
a /= 10000;
top -= 4;
std::memcpy(stk + top, pre.buffer[i], 4);
}
if (a >= 1000) {
std::memcpy(buffer + idx, pre.buffer[a], 4);
idx += 4;
} else if (a >= 100) {
std::memcpy(buffer + idx, pre.buffer[a] + 1, 3);
idx += 3;
} else if (a >= 10) {
std::memcpy(buffer + idx, pre.buffer[a] + 2, 2);
idx += 2;
} else {
buffer[idx++] = '0' | a;
}
std::memcpy(buffer + idx, stk + top, 40 - top);
idx += 40 - top;
}
template <typename T, typename std::enable_if<std::is_floating_point<T>::value && !has_print<T>::value>::type* = nullptr>
void print(T a) {
if (a == infinity<T>::max || a == infinity<T>::value) {
print("inf");
return;
}
if (a == infinity<T>::min || a == infinity<T>::mvalue) {
print("-inf");
return;
}
if (std::isnan(a)) {
print("nan");
return;
}
if (a < 0) {
print_char('-');
a = -a;
}
T b = a;
if (b < 1) {
print_char('0');
} else {
std::string s;
while (b >= 1) {
s += (char)('0' | (int)std::fmod(b, 10.0));
b /= 10;
}
for (auto i = s.rbegin(); i != s.rend(); ++i) {
print_char(*i);
}
}
print_char('.');
for (std::size_t _ = 0; _ < decimal_precision; ++_) {
a *= 10;
print_char('0' | (int)std::fmod(a, 10.0));
}
}
private:
template <std::size_t i, typename... Args>
void print(const std::tuple<Args...>& a) {
if constexpr (i < sizeof...(Args)) {
if constexpr (debug) print_char(',');
print_char(' ');
print(std::get<i>(a));
print<i + 1>(a);
}
}
public:
template <typename... Args>
void print(const std::tuple<Args...>& a) {
if constexpr (debug) print_char('(');
if constexpr (sizeof...(Args) != 0) {
print(std::get<0>(a));
}
print<1, Args...>(a);
if constexpr (debug) print_char(')');
}
template <typename T, typename U>
void print(const std::pair<T, U>& a) {
if constexpr (debug) print_char('(');
print(a.first);
if constexpr (debug) print_char(',');
print_char(' ');
print(a.second);
if constexpr (debug) print_char(')');
}
template <typename T, typename std::enable_if<is_range<T>::value>::type* = nullptr>
void print(const T& a) {
if constexpr (debug) print_char('{');
auto it = std::begin(a);
if (it != std::end(a)) {
print(*it);
while (++it != std::end(a)) {
if constexpr (debug) print_char(',');
print_char(' ');
print(*it);
}
}
if constexpr (debug) print_char('}');
}
template <typename T, typename std::enable_if<has_print<T>::value && !debug>::type* = nullptr>
void print(const T& a) {
a.print(*this);
}
template <typename T, typename std::enable_if<has_print<T>::value && debug>::type* = nullptr>
void print(const T& a) {
a.debug(*this);
}
void operator()() {}
template <typename Head, typename... Tail>
void operator()(const Head& head, const Tail&... tail) {
print(head);
operator()(std::forward<const Tail&>(tail)...);
}
template <typename T>
Printer& operator<<(const T& a) {
print(a);
return *this;
}
Printer& operator<<(Printer& (*f)(Printer&)) {
return f(*this);
}
};
template <std::size_t BUFF_SIZE, bool debug>
Printer<BUFF_SIZE, debug>& endl(Printer<BUFF_SIZE, debug>& out) {
out.print_char('\n');
out.flush();
return out;
}
template <std::size_t BUFF_SIZE, bool debug>
Printer<BUFF_SIZE, debug>& flush(Printer<BUFF_SIZE, debug>& out) {
out.flush();
return out;
}
Printer<> pr;
Printer<1 << 17, true> prd;
} // namespace fastio
using fastio::endl;
using fastio::flush;
using fastio::pr;
using fastio::prd;
#line 3 "template/func.hpp"
#line 8 "template/func.hpp"
inline constexpr int msb(ull x) {
int res = x ? 0 : -1;
if (x & 0xffffffff00000000) x &= 0xffffffff00000000, res += 32;
if (x & 0xffff0000ffff0000) x &= 0xffff0000ffff0000, res += 16;
if (x & 0xff00ff00ff00ff00) x &= 0xff00ff00ff00ff00, res += 8;
if (x & 0xf0f0f0f0f0f0f0f0) x &= 0xf0f0f0f0f0f0f0f0, res += 4;
if (x & 0xcccccccccccccccc) x &= 0xcccccccccccccccc, res += 2;
return res + (x & 0xaaaaaaaaaaaaaaaa ? 1 : 0);
}
inline constexpr int ceil_log2(ull x) { return x ? msb(x - 1) + 1 : 0; }
inline constexpr ull reverse(ull x) {
x = ((x & 0x5555555555555555) << 1) | ((x & 0xaaaaaaaaaaaaaaaa) >> 1);
x = ((x & 0x3333333333333333) << 2) | ((x & 0xcccccccccccccccc) >> 2);
x = ((x & 0x0f0f0f0f0f0f0f0f) << 4) | ((x & 0xf0f0f0f0f0f0f0f0) >> 4);
x = ((x & 0x00ff00ff00ff00ff) << 8) | ((x & 0xff00ff00ff00ff00) >> 8);
x = ((x & 0x0000ffff0000ffff) << 16) | ((x & 0xffff0000ffff0000) >> 16);
return (x << 32) | (x >> 32);
}
inline constexpr ull reverse(ull x, int len) { return reverse(x) >> (64 - len); }
inline constexpr int popcnt(ull x) {
#if __cplusplus >= 202002L
return std::popcount(x);
#endif
x = (x & 0x5555555555555555) + ((x >> 1) & 0x5555555555555555);
x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333);
x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f0f0f0f0f);
x = (x & 0x00ff00ff00ff00ff) + ((x >> 8) & 0x00ff00ff00ff00ff);
x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff);
return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff);
}
template <typename T, typename U>
inline constexpr bool chmin(T& a, U b) { return a > b && (a = b, true); }
template <typename T, typename U>
inline constexpr bool chmax(T& a, U b) { return a < b && (a = b, true); }
inline constexpr ll gcd(ll a, ll b) {
if (a < 0) a = -a;
if (b < 0) b = -b;
while (b) {
const ll c = b;
b = a % b;
a = c;
}
return a;
}
inline constexpr ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
inline constexpr bool is_prime(ll n) {
if (n <= 1) return false;
for (ll i = 2; i * i <= n; i++) {
if (n % i == 0) return false;
}
return true;
}
inline constexpr ll my_pow(ll a, ll b) {
ll res = 1;
while (b) {
if (b & 1) res *= a;
a *= a;
b >>= 1;
}
return res;
}
inline constexpr ll mod_pow(ll a, ll b, const ll& mod) {
if (mod == 1) return 0;
a %= mod;
ll res = 1;
while (b) {
if (b & 1) (res *= a) %= mod;
(a *= a) %= mod;
b >>= 1;
}
return res;
}
inline ll mod_inv(ll a, const ll& mod) {
ll b = mod, x = 1, u = 0, t;
while (b) {
t = a / b;
std::swap(a -= t * b, b);
std::swap(x -= t * u, u);
}
if (x < 0) x += mod;
return x;
}
template <typename T, typename U>
std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
std::istream& operator>>(std::istream& is, std::pair<T, U>& p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
for (auto it = std::begin(v); it != std::end(v);) {
os << *it << ((++it) != std::end(v) ? " " : "");
}
return os;
}
template <typename T>
std::istream& operator>>(std::istream& is, std::vector<T>& v) {
for (T& in : v) {
is >> in;
}
return is;
}
inline void scan() {}
template <class Head, class... Tail>
inline void scan(Head& head, Tail&... tail) {
sc >> head;
scan(tail...);
}
template <class T>
inline void print(const T& t) { pr << t << '\n'; }
template <class Head, class... Tail>
inline void print(const Head& head, const Tail&... tail) {
pr << head << ' ';
print(tail...);
}
template <class... T>
inline void fin(const T&... a) {
print(a...);
exit(0);
}
template <typename T>
inline void dump(const T& a) { prd << a; }
inline void trace() { prd << endl; }
template <typename Head, typename... Tail>
inline void trace(const Head& head, const Tail&... tail) {
dump(head);
if (sizeof...(tail)) prd.print_char(','), prd.print_char(' ');
trace(tail...);
}
#ifdef ONLINE_JUDGE
#define dbg(...) (void(0))
#else
#define dbg(...) \
do { \
prd << #__VA_ARGS__; \
prd.print_char(' '), prd.print_char('='), prd.print_char(' '); \
trace(__VA_ARGS__); \
} while (0)
#endif
#line 3 "template/util.hpp"
#line 6 "template/util.hpp"
template <typename F>
struct REC {
private:
F f;
public:
explicit constexpr REC(F&& f_) : f(std::forward<F>(f_)) {}
template <typename... Args>
constexpr auto operator()(Args&&... args) const {
return f(*this, std::forward<Args>(args)...);
}
};
template <typename T, typename Comp = std::less<T>>
struct compressor {
private:
std::vector<T> data;
Comp cmp;
bool sorted = false;
public:
compressor() : compressor(Comp()) {}
compressor(const Comp& cmp) : cmp(cmp) {}
compressor(const std::vector<T>& dat, const Comp& cmp = Comp()) : data(dat), cmp(cmp) {}
compressor(std::vector<T>&& dat, const Comp& cmp = Comp()) : data(std::move(dat)), cmp(cmp) {}
compressor(std::initializer_list<T> li, const Comp& cmp = Comp()) : data(li.begin(), li.end()), cmp(cmp) {}
void push_back(const T& v) {
assert(!sorted);
data.push_back(v);
}
void push_back(T&& v) {
assert(!sorted);
data.push_back(std::move(v));
}
template <typename... Args>
void emplace_back(Args&&... args) {
assert(!sorted);
data.emplace_back(std::forward<Args>(args)...);
}
void push(const std::vector<T>& v) {
assert(!sorted);
const int n = data.size();
data.resize(v.size() + n);
for (int i = 0; i < (int)v.size(); i++) data[i + n] = v[i];
}
void build() {
assert(!sorted);
sorted = 1;
std::sort(data.begin(), data.end(), cmp);
data.erase(unique(data.begin(), data.end(), [&](const T& l, const T& r) -> bool { return !cmp(l, r) && !cmp(r, l); }), data.end());
}
const T& operator[](int k) const& {
assert(sorted);
return data[k];
}
int get_index(const T& v) const {
assert(sorted);
return int(lower_bound(data.begin(), data.end(), v, cmp) - data.begin());
}
void press(std::vector<T>& v) const {
assert(sorted);
for (auto&& i : v) i = get_index(i);
}
std::vector<int> pressed(const std::vector<T>& v) const {
assert(sorted);
std::vector<int> ret(v.size());
for (int i = 0; i < (int)v.size(); i++) ret[i] = get_index(v[i]);
return ret;
}
int size() const {
assert(sorted);
return data.size();
}
};
#line 11 "template/template.hpp"
using namespace std;
#line 3 "others/monoid.hpp"
namespace Monoid {
template <typename M, typename = void>
struct has_op : false_type {};
template <typename M>
struct has_op<M, decltype((void)M::op)> : true_type {};
template <typename M, typename = void>
struct has_id : false_type {};
template <typename M>
struct has_id<M, decltype((void)M::id)> : true_type {};
template <typename M, typename = void>
struct has_inv : false_type {};
template <typename M>
struct has_inv<M, decltype((void)M::inv)> : true_type {};
template <typename M, typename = void>
struct has_get_inv : false_type {};
template <typename M>
struct has_get_inv<M, decltype((void)M::get_inv)> : true_type {};
template <typename A, typename = void>
struct has_mul_op : false_type {};
template <typename A>
struct has_mul_op<A, decltype((void)A::mul_op)> : true_type {};
template <typename T, typename = void>
struct is_semigroup : false_type {};
template <typename T>
struct is_semigroup<T, decltype(declval<typename T::value_type>(), (void)T::op)> : true_type {};
template <typename T, typename = void>
struct is_monoid : false_type {};
template <typename T>
struct is_monoid<T, decltype(declval<typename T::value_type>(), (void)T::op, (void)T::id)> : true_type {};
template <typename T, typename = void>
struct is_group : false_type {};
template <typename T>
struct is_group<T, decltype(declval<typename T::value_type>(), (void)T::op, (void)T::id, (void)T::get_inv)> : true_type {};
template <typename T, typename = void>
struct is_action : false_type {};
template <typename T>
struct is_action<T, typename enable_if<is_monoid<typename T::M>::value && is_semigroup<typename T::E>::value && (has_op<T>::value || has_mul_op<T>::value)>::type> : true_type {};
template <typename T, typename = void>
struct is_distributable_action : false_type {};
template <typename T>
struct is_distributable_action<T, typename enable_if<is_action<T>::value && !has_mul_op<T>::value>::type> : true_type {};
template <typename T>
struct Sum {
using value_type = T;
static constexpr T op(const T& x, const T& y) { return x + y; }
static constexpr T id() { return T(0); }
static constexpr T inv(const T& x, const T& y) { return x - y; }
static constexpr T get_inv(const T& x) { return -x; }
};
template <typename T, T max_value = infinity<T>::value>
struct Min {
using value_type = T;
static constexpr T op(const T& x, const T& y) { return x < y ? x : y; }
static constexpr T id() { return max_value; }
};
template <typename T, T min_value = infinity<T>::mvalue>
struct Max {
using value_type = T;
static constexpr T op(const T& x, const T& y) { return x < y ? y : x; }
static constexpr T id() { return min_value; }
};
template <typename T>
struct Assign {
using value_type = T;
static constexpr T op(const T&, const T& x) { return x; }
};
template <typename T, T max_value = infinity<T>::value>
struct AssignMin {
using M = Min<T, max_value>;
using E = Assign<T>;
static constexpr T op(const T& x, const T&) { return x; }
};
template <typename T, T min_value = infinity<T>::mvalue>
struct AssignMax {
using M = Max<T, min_value>;
using E = Assign<T>;
static constexpr T op(const T& x, const T&) { return x; }
};
template <typename T>
struct AssignSum {
using M = Sum<T>;
using E = Assign<T>;
static constexpr T mul_op(const T& x, int sz, const T&) { return x * sz; }
};
template <typename T, T max_value = infinity<T>::value>
struct AddMin {
using M = Min<T, max_value>;
using E = Sum<T>;
static constexpr T op(const T& a, const T& b) { return b + a; }
};
template <typename T, T min_value = infinity<T>::mvalue>
struct AddMax {
using M = Max<T, min_value>;
using E = Sum<T>;
static constexpr T op(const T& a, const T& b) { return b + a; }
};
template <typename T>
struct AddSum {
using M = Sum<T>;
using E = Sum<T>;
static constexpr T mul_op(const T& x, int sz, const T& y) { return y + x * sz; }
};
template <typename T, T max_value = infinity<T>::value>
struct ChminMin {
using M = Min<T, max_value>;
using E = Min<T>;
static constexpr T op(const T& x, const T& y) { return y < x ? y : x; }
};
template <typename T, T min_value = infinity<T>::mvalue>
struct ChminMax {
using M = Max<T, min_value>;
using E = Min<T>;
static constexpr T op(const T& x, const T& y) { return y < x ? y : x; }
};
template <typename T, T max_value = infinity<T>::value>
struct ChmaxMin {
using M = Min<T, max_value>;
using E = Max<T>;
static constexpr T op(const T& x, const T& y) { return x < y ? y : x; }
};
template <typename T, T min_value = infinity<T>::mvalue>
struct ChmaxMax {
using M = Max<T, min_value>;
using E = Max<T>;
static constexpr T op(const T& x, const T& y) { return x < y ? y : x; }
};
template <typename E_>
struct AttachMonoid {
using M = E_;
using E = E_;
using T = typename E_::value_type;
static T op(const T& x, const T& y) { return E_::op(y, x); }
};
} // namespace Monoid
#line 4 "ds/union-find/weighted-union-find.hpp"
template <typename M, bool = Monoid::is_monoid<M>::value>
struct WeightedUnionFind {
private:
using T = typename M::value_type;
vector<int> par;
vector<T> val; // a_r^{-1} a_i
public:
WeightedUnionFind() {}
WeightedUnionFind(int n) : par(n, -1), val(n, M::id()) {}
int root(int x) {
if (par[x] < 0) return x;
const int r = root(par[x]);
val[x] = M::op(val[par[x]], val[x]);
return par[x] = r;
}
T weight(int x) { return root(x), val[x]; }
bool same(int x, int y) { return root(x) == root(y); }
int size(int x) { return -par[root(x)]; }
pair<bool, bool> merge(int x, int y, T w) {
w = M::op(weight(x), M::get_inv(M::op(weight(y), w)));
x = root(x), y = root(y);
if (x == y) {
if (w == M::id()) return {false, true};
return {false, false};
}
if (par[x] > par[y]) swap(x, y), w = M::get_inv(w);
par[x] += par[y];
par[y] = x;
val[y] = w;
return {true, true};
}
// a_y^{-1} a_x
T diff(int x, int y) { return M::op(M::get_inv(weight(y)), weight(x)); }
};
/**
* @brief Weighted Disjoint Set Union(重み付きUnion Find)
*/
#line 3 "math/modular/modint.hpp"
namespace internal {
struct modint_base {};
} // namespace internal
template <typename T>
using is_modint = is_base_of<internal::modint_base, T>;
template <typename T, T mod>
struct StaticModInt : internal::modint_base {
static_assert(is_integral<T>::value, "T must be integral");
static_assert(is_unsigned<T>::value, "T must be unsgined");
static_assert(mod > 0, "mod must be positive");
static_assert(mod <= INF<T>, "mod*2 must be less than or equal to T::max()");
private:
using large_t = typename double_size_uint<T>::type;
using signed_t = typename make_signed<T>::type;
T val;
public:
constexpr StaticModInt() : val(0) {}
template <typename U, typename enable_if<is_integral<U>::value && is_unsigned<U>::value>::type* = nullptr>
constexpr StaticModInt(U x) : val(x % mod) {}
template <typename U, typename enable_if<is_integral<U>::value && is_signed<U>::value>::type* = nullptr>
constexpr StaticModInt(U x) : val{} {
x %= static_cast<signed_t>(mod);
if (x < 0) x += static_cast<signed_t>(mod);
val = static_cast<T>(x);
}
constexpr T get() const { return val; }
static constexpr T get_mod() { return mod; }
static constexpr StaticModInt raw(T v) {
StaticModInt res;
res.val = v;
return res;
}
constexpr StaticModInt inv() const {
return mod_inv(val, mod);
}
constexpr StaticModInt& operator++() {
++val;
if (val == mod) val = 0;
return *this;
}
constexpr StaticModInt operator++(int) {
StaticModInt res = *this;
++*this;
return res;
}
constexpr StaticModInt& operator--() {
if (val == 0) val = mod;
--val;
return *this;
}
constexpr StaticModInt operator--(int) {
StaticModInt res = *this;
--*this;
return res;
}
constexpr StaticModInt& operator+=(const StaticModInt& x) {
val += x.val;
if (val >= mod) val -= mod;
return *this;
}
constexpr StaticModInt& operator-=(const StaticModInt& x) {
if (val < x.val) val += mod;
val -= x.val;
return *this;
}
constexpr StaticModInt& operator*=(const StaticModInt& x) {
val = static_cast<T>((static_cast<large_t>(val) * x.val) % mod);
return *this;
}
constexpr StaticModInt& operator/=(const StaticModInt& x) {
return *this *= x.inv();
}
friend constexpr StaticModInt operator+(const StaticModInt& l, const StaticModInt& r) { return StaticModInt(l) += r; }
friend constexpr StaticModInt operator-(const StaticModInt& l, const StaticModInt& r) { return StaticModInt(l) -= r; }
friend constexpr StaticModInt operator*(const StaticModInt& l, const StaticModInt& r) { return StaticModInt(l) *= r; }
friend constexpr StaticModInt operator/(const StaticModInt& l, const StaticModInt& r) { return StaticModInt(l) /= r; }
constexpr StaticModInt operator+() const { return StaticModInt(*this); }
constexpr StaticModInt operator-() const { return StaticModInt() - *this; }
friend constexpr bool operator==(const StaticModInt& l, const StaticModInt& r) { return l.val == r.val; }
friend constexpr bool operator!=(const StaticModInt& l, const StaticModInt& r) { return l.val != r.val; }
constexpr StaticModInt pow(ll a) const {
StaticModInt v = *this, res = 1;
while (a) {
if (a & 1) res *= v;
v *= v;
a >>= 1;
}
return res;
}
template <typename Sc>
void scan(Sc& a) {
ll x;
a.scan(x);
*this = x;
}
template <typename Pr>
void print(Pr& a) const {
a.print(val);
}
template <typename Pr>
void debug(Pr& a) const {
a.print(val);
}
};
template <unsigned int p>
using ModInt = StaticModInt<unsigned int, p>;
template <typename T, int id>
struct DynamicModInt {
static_assert(is_integral<T>::value, "T must be integral");
static_assert(is_unsigned<T>::value, "T must be unsigned");
private:
using large_t = typename double_size_uint<T>::type;
using signed_t = typename make_signed<T>::type;
T val;
static T mod;
public:
constexpr DynamicModInt() : val(0) {}
template <typename U, typename enable_if<is_integral<U>::value && is_unsigned<U>::value>::type* = nullptr>
constexpr DynamicModInt(U x) : val(x % mod) {}
template <typename U, typename enable_if<is_integral<U>::value && is_signed<U>::value>::type* = nullptr>
constexpr DynamicModInt(U x) : val{} {
x %= static_cast<signed_t>(mod);
if (x < 0) x += static_cast<signed_t>(mod);
val = static_cast<T>(x);
}
T get() const { return val; }
static T get_mod() { return mod; }
static void set_mod(T x) {
mod = x;
assert(mod > 0);
assert(mod <= INF<T>);
}
static DynamicModInt raw(T v) {
DynamicModInt res;
res.val = v;
return res;
}
DynamicModInt inv() const {
return mod_inv(val, mod);
}
DynamicModInt& operator++() {
++val;
if (val == mod) val = 0;
return *this;
}
DynamicModInt operator++(int) {
DynamicModInt res = *this;
++*this;
return res;
}
DynamicModInt& operator--() {
if (val == 0) val = mod;
--val;
return *this;
}
DynamicModInt operator--(int) {
DynamicModInt res = *this;
--*this;
return res;
}
DynamicModInt& operator+=(const DynamicModInt& x) {
val += x.val;
if (val >= mod) val -= mod;
return *this;
}
DynamicModInt& operator-=(const DynamicModInt& x) {
if (val < x.val) val += mod;
val -= x.val;
return *this;
}
DynamicModInt& operator*=(const DynamicModInt& x) {
val = static_cast<T>((static_cast<large_t>(val) * x.val) % mod);
return *this;
}
DynamicModInt& operator/=(const DynamicModInt& x) {
return *this *= x.inv();
}
friend DynamicModInt operator+(const DynamicModInt& l, const DynamicModInt& r) { return DynamicModInt(l) += r; }
friend DynamicModInt operator-(const DynamicModInt& l, const DynamicModInt& r) { return DynamicModInt(l) -= r; }
friend DynamicModInt operator*(const DynamicModInt& l, const DynamicModInt& r) { return DynamicModInt(l) *= r; }
friend DynamicModInt operator/(const DynamicModInt& l, const DynamicModInt& r) { return DynamicModInt(l) /= r; }
DynamicModInt operator+() const { return DynamicModInt(*this); }
DynamicModInt operator-() const { return DynamicModInt() - *this; }
friend bool operator==(const DynamicModInt& l, const DynamicModInt& r) { return l.val == r.val; }
friend bool operator!=(const DynamicModInt& l, const DynamicModInt& r) { return l.val != r.val; }
DynamicModInt pow(ll a) const {
DynamicModInt v = *this, res = 1;
while (a) {
if (a & 1) res *= v;
v *= v;
a >>= 1;
}
return res;
}
template <typename Sc>
void scan(Sc& a) {
ll x;
a.scan(x);
*this = x;
}
template <typename Pr>
void print(Pr& a) const {
a.print(val);
}
template <typename Pr>
void debug(Pr& a) const {
a.print(val);
}
};
template <typename T, int id>
T DynamicModInt<T, id>::mod = 998244353;
template <int id>
using dynamic_modint = DynamicModInt<unsigned int, id>;
using modint = dynamic_modint<-1>;
/**
* @brief ModInt
*/
#line 3 "math/others/matrix.hpp"
template <typename T>
struct Matrix : vector<vector<T>> {
private:
using Base = vector<vector<T>>;
public:
Matrix() {}
Matrix(int n, int m) : Base(n, vector<T>(m, T())) {}
Matrix(int n) : Base(n, vector<T>(n, T())) {};
Matrix(const vector<vector<T>>& a) : Base(a) {}
size_t height() const { return this->size(); }
size_t width() const { return (this->size() ? (*this)[0].size() : 0); }
static Matrix I(int n) {
Matrix mat(n);
for (int i = 0; i < n; i++) mat[i][i] = 1;
return mat;
}
Matrix& operator+=(const Matrix& r) {
const int n = height(), m = width();
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) (*this)[i][j] += r[i][j];
return *this;
}
Matrix& operator-=(const Matrix& r) {
const int n = height(), m = width();
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) (*this)[i][j] -= r[i][j];
return *this;
}
Matrix& operator*=(const Matrix& r) {
const int n = height(), m = r.width(), p = width();
vector<vector<T>> res(n, vector<T>(m, T()));
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
for (int k = 0; k < p; k++) res[i][j] += (*this)[i][k] * r[k][j];
return *this = move(res);
}
Matrix& operator*=(const T& r) {
const int n = height(), m = width();
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) (*this)[i][j] *= r;
return *this;
}
Matrix& operator^=(long long k) {
Matrix res = Matrix::I(height());
Matrix tmp = *this;
while (k > 0) {
if (k & 1) res *= tmp;
tmp *= tmp;
k >>= 1LL;
}
return *this = move(res);
}
Matrix pow(long long k) const {
Matrix res = Matrix::I(height());
Matrix tmp = *this;
while (k > 0) {
if (k & 1) res *= tmp;
tmp *= tmp;
k >>= 1LL;
}
return res;
}
friend Matrix operator+(const Matrix& l, const Matrix& r) { return Matrix(l) += r; }
friend Matrix operator-(const Matrix& l, const Matrix& r) { return Matrix(l) -= r; }
friend Matrix operator*(const Matrix& l, const Matrix& r) { return Matrix(l) *= r; }
friend Matrix operator*(const Matrix& l, const T& r) { return Matrix(l) *= r; }
T determinant() const {
Matrix b(*this);
const int n = height();
if (n == 0) return 1;
T res = 1;
rep(i, n) {
if (b[i][i] == T(0)) {
rep(j, i + 1, n) {
if (b[j][i] != 0) {
swap(b[i], b[j]);
res = -res;
break;
}
}
}
if (b[i][i] == T(0)) return T(0);
{
const T s = b[i][i];
res *= s;
const T invs = T(1) / s;
rep(j, n) b[i][j] *= invs;
}
rep(j, i + 1, n) {
const T s = b[j][i];
rep(k, n) b[j][k] -= b[i][k] * s;
}
}
rep(i, n) res *= b[i][i];
return res;
}
};
/**
* @brief Matrix(行列)
*/
#line 6 "test/yosupo/data_strucuture/unionfind_with_potential_non_commutative_group.test.cpp"
using mint = ModInt<998244353>;
using Mat = Matrix<mint>;
struct Prod {
using value_type = Mat;
static Mat id() { return Mat::I(2); }
static Mat op(const Mat& x, const Mat& y) { return x * y; }
static Mat get_inv(const Mat& x) {
Mat ret(2, 2);
ret[0][0] = x[1][1], ret[0][1] = -x[0][1], ret[1][0] = -x[1][0], ret[1][1] = x[0][0];
ret *= (x[0][0] * x[1][1] - x[0][1] * x[1][0]).inv();
return ret;
}
};
int main() {
INT(n, q);
WeightedUnionFind<Prod> uf(n);
rep(q) {
INT(t, x, y);
if (t == 0) {
Mat a(2, 2);
sc >> a;
if (!uf.merge(x, y, a).second)
print(0);
else
print(1);
} else {
if (!uf.same(x, y))
print(-1);
else {
print(uf.diff(x, y));
}
}
}
}
Test cases
| Env | Name | Status | Elapsed | Memory |
|---|---|---|---|---|
| g++ | example_00 |
AC |
6 ms | 3 MB |
| g++ | max_random_00 |
AC |
258 ms | 23 MB |
| g++ | max_random_01 |
AC |
250 ms | 26 MB |
| g++ | max_random_02 |
AC |
294 ms | 12 MB |
| g++ | path_00 |
AC |
303 ms | 34 MB |
| g++ | path_01 |
AC |
230 ms | 34 MB |
| g++ | path_02 |
AC |
366 ms | 34 MB |
| g++ | path_03 |
AC |
360 ms | 34 MB |
| g++ | random_00 |
AC |
148 ms | 23 MB |
| g++ | random_01 |
AC |
145 ms | 26 MB |
| g++ | random_02 |
AC |
144 ms | 12 MB |
| g++ | random_03 |
AC |
46 ms | 29 MB |
| g++ | random_04 |
AC |
155 ms | 6 MB |
| g++ | random_05 |
AC |
178 ms | 11 MB |
| g++ | random_06 |
AC |
112 ms | 33 MB |
| g++ | random_07 |
AC |
26 ms | 18 MB |
| g++ | random_08 |
AC |
80 ms | 5 MB |
| g++ | random_09 |
AC |
227 ms | 20 MB |