結果
問題 | No.2536 同値性と充足可能性 |
ユーザー | Gandalfr |
提出日時 | 2023-11-10 22:52:50 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 110 ms / 2,000 ms |
コード長 | 22,500 bytes |
コンパイル時間 | 2,400 ms |
コンパイル使用メモリ | 215,364 KB |
実行使用メモリ | 6,064 KB |
最終ジャッジ日時 | 2024-09-26 02:03:36 |
合計ジャッジ時間 | 4,901 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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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 | 2 ms
5,376 KB |
testcase_09 | AC | 2 ms
5,376 KB |
testcase_10 | AC | 2 ms
5,376 KB |
testcase_11 | AC | 2 ms
5,376 KB |
testcase_12 | AC | 2 ms
5,376 KB |
testcase_13 | AC | 2 ms
5,376 KB |
testcase_14 | AC | 2 ms
5,376 KB |
testcase_15 | AC | 2 ms
5,376 KB |
testcase_16 | AC | 2 ms
5,376 KB |
testcase_17 | AC | 3 ms
5,376 KB |
testcase_18 | AC | 3 ms
5,376 KB |
testcase_19 | AC | 2 ms
5,376 KB |
testcase_20 | AC | 8 ms
5,376 KB |
testcase_21 | AC | 9 ms
5,376 KB |
testcase_22 | AC | 9 ms
5,376 KB |
testcase_23 | AC | 76 ms
5,376 KB |
testcase_24 | AC | 76 ms
5,376 KB |
testcase_25 | AC | 109 ms
5,940 KB |
testcase_26 | AC | 108 ms
6,028 KB |
testcase_27 | AC | 109 ms
5,860 KB |
testcase_28 | AC | 105 ms
5,948 KB |
testcase_29 | AC | 110 ms
5,884 KB |
testcase_30 | AC | 105 ms
6,064 KB |
ソースコード
#line 1 "playspace/main.cpp" #include <bits/stdc++.h> #line 8 "library/gandalfr/other/io_supporter.hpp" #line 1 "library/atcoder/modint.hpp" #line 6 "library/atcoder/modint.hpp" #include <type_traits> #ifdef _MSC_VER #include <intrin.h> #endif #line 1 "library/atcoder/internal_math.hpp" #line 5 "library/atcoder/internal_math.hpp" #ifdef _MSC_VER #include <intrin.h> #endif namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast modular multiplication by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m < 2^31` explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template <int n> constexpr bool is_prime = is_prime_constexpr(n); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template <int m> constexpr int primitive_root = primitive_root_constexpr(m); // @param n `n < 2^32` // @param m `1 <= m < 2^32` // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64) unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; // y_max < m * (n + 1) // floor(y_max / m) <= n n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #line 1 "library/atcoder/internal_type_traits.hpp" #line 7 "library/atcoder/internal_type_traits.hpp" namespace atcoder { namespace internal { #ifndef _MSC_VER template <class T> using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type; template <class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>; template <class T> using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional< is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type; #else template <class T> using is_integral = typename std::is_integral<T>; template <class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type; #endif template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>; template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>; template <class T> using to_unsigned_t = typename to_unsigned<T>::type; } // namespace internal } // namespace atcoder #line 14 "library/atcoder/modint.hpp" namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template <class T> using is_modint = std::is_base_of<modint_base, T>; template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>; } // namespace internal template <int m, std::enable_if_t<(1 <= m)>* = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime<m>; }; template <int id> struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template <int id> internal::barrett dynamic_modint<id>::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template <class T> using is_static_modint = std::is_base_of<internal::static_modint_base, T>; template <class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>; template <class> struct is_dynamic_modint : public std::false_type {}; template <int id> struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {}; template <class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>; } // namespace internal } // namespace atcoder #line 10 "library/gandalfr/other/io_supporter.hpp" template <typename T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) { for (int i = 0; i < (int)v.size(); i++) os << v[i] << (i + 1 != (int)v.size() ? " " : ""); return os; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::set<T> &st) { for (const T &x : st) { std::cout << x << " "; } return os; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::multiset<T> &st) { for (const T &x : st) { std::cout << x << " "; } return os; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::deque<T> &dq) { for (const T &x : dq) { std::cout << x << " "; } return os; } template <typename T1, typename T2> std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &p) { os << p.first << ' ' << p.second; return os; } template <typename T> std::ostream &operator<<(std::ostream &os, std::queue<T> q) { while (!q.empty()) { os << q.front(); q.pop(); } return os; } template <typename _Tp, typename _Sequence, typename _Compare> std::ostream &operator<<(std::ostream &os, std::priority_queue<_Tp, _Sequence, _Compare> q) { while (!q.empty()) { os << q.top(); q.pop(); } return os; } namespace atcoder { template <int m> std::ostream &operator<<(std::ostream &os, const static_modint<m> &mi) { os << mi.val(); return os; } template <int m> std::ostream &operator<<(std::ostream &os, const dynamic_modint<m> &mi) { os << mi.val(); return os; } } // namespace atcoder template <typename T> std::istream &operator>>(std::istream &is, std::vector<T> &v) { for (T &in : v) is >> in; return is; } template <typename T1, typename T2> std::istream &operator>>(std::istream &is, std::pair<T1, T2> &p) { is >> p.first >> p.second; return is; } namespace atcoder { template <int m> std::istream &operator>>(std::istream &is, static_modint<m> &mi) { long long n; is >> n; mi = n; return is; } template <int m> std::istream &operator>>(std::istream &is, dynamic_modint<m> &mi) { long long n; is >> n; mi = n; return is; } } // namespace atcoder #line 3 "library/gandalfr/data_structure/union_find.hpp" #line 6 "library/gandalfr/data_structure/union_find.hpp" class union_find { private: int N; mutable std::vector<int> par; std::vector<int> nxt; int group_num; // 集合の数 public: union_find() : N(0), group_num(0) {} union_find(int n) : N(n), par(n, -1), nxt(n), group_num(n) { std::iota(nxt.begin(), nxt.end(), 0); } /** * @brief 頂点を n 個に増やす * @attention 小さくはできない */ void expand(int n) { if (n <= N) return; par.resize(n, -1); nxt.resize(n); for (int i = N; i < n; ++i) nxt[i] = i; group_num += n - N; N = n; } int leader(int x) const { return (par[x] < 0 ? x : par[x] = leader(par[x])); } bool same(int x, int y) const { return leader(x) == leader(y); } bool merge(int x, int y) { if ((x = leader(x)) == (y = leader(y))) return false; if (-par[x] > -par[y]) std::swap(x, y); par[x] += par[y]; par[y] = x; std::swap(nxt[x], nxt[y]); group_num--; return true; } /** * @brief x の属するグループのサイズを返す */ int size(int x) const { return -par[leader(x)]; } /** * @brief すべてのノードの数 */ int size() const { return N; } std::vector<int> group_containing_node(int x) const { std::vector<int> ret{x}; for (int cu = nxt[x]; cu != ret[0]; cu = nxt[cu]) ret.push_back(cu); return ret; } int count_groups() const { return group_num; } std::vector<std::vector<int>> all_groups() const { std::vector<std::vector<int>> result; result.reserve(group_num); std::vector<bool> used(N, false); for (int i = 0; i < N; ++i) { if (!used[i]) { result.emplace_back(group_containing_node(i)); for (int x : result.back()) { used[x] = true; } } } return result; } }; #line 4 "playspace/main.cpp" using namespace std; using ll = long long; const int INF = 1001001001; const ll INFLL = 1001001001001001001; const ll MOD = 1000000007; const ll _MOD = 998244353; #define rep(i, j, n) for(ll i = (ll)(j); i < (ll)(n); i++) #define rrep(i, j, n) for(ll i = (ll)(n-1); i >= (ll)(j); i--) #define all(a) (a).begin(),(a).end() #define LF cout << endl #define debug(a) std::cerr << #a << ": " << a << std::endl template<typename T1, typename T2> inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template<typename T1, typename T2> inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } void Yes(bool ok){ std::cout << (ok ? "Yes" : "No") << std::endl; } int main(void){ int N, M; cin >> N >> M; union_find G(N * 2); rep(i,0,M) { int a, b; string S; cin >> a >> S >> b; if (S == "<==>") { G.merge(a-1, b-1); G.merge(a-1+N, b-1+N); } else { G.merge(a-1, b-1+N); G.merge(a-1+N, b-1); } } rep(i,0,N) { if (G.same(i, i+N)) { Yes(0); return 0; } } vector<int> ans; vector<int> seen(N, false); rep(i,0,N) { vector<int> buf1, buf2; if (seen[i]) continue; for (auto x: G.group_containing_node(i)) { if (x < N) { buf1.push_back(x + 1); seen[x] = true; } else { buf2.push_back(x + 1 - N); seen[x - N] = true; } } if (buf1.size() > buf2.size()) { ans.insert(ans.end(), all(buf1)); } else { ans.insert(ans.end(), all(buf2)); } } sort(all(ans)); Yes(1); cout << ans.size() << endl; cout << ans << endl; }