#define READ_NUM_TEST_CASES false #define USE_FAST_IO false //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/template.hpp" BEGINS HERE // #include <bits/stdc++.h> using namespace std; //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/abbrevs.hpp" BEGINS HERE // #define UI unsigned int #define LL long long #define ULL unsigned long long #define PII pair<int,int> #define RI ri() #define RUI rui() #define RLL rll() #define RULL rull() #define RSTR rstr() #define FO(i,a,b) for(int i=(a); i<int(b); ++i) #define OF(i,a,b) for(int i=(b)-1; i>=int(a); --i) #define FOR(i,n) FO(i,0,n) #define ROF(i,n) OF(i,0,n) #define MIN(a,b) ((a)<(b) ? (a) : (b)) #define MAX(a,b) ((b)<(a) ? (a) : (b)) #define REMIN(a,b) ((a) = min(a,b)) #define REMAX(a,b) ((a) = max(a,b)) #define ALL(c) (c).begin(),(c).end() #define SQR(x) ((x)*(x)) bool is_pow(int x) { return (x&(x-1)) == 0; } // // AMALGAMATE: "include/abbrevs.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// #if USE_FAST_IO //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/fast-io.hpp" BEGINS HERE // //#define FREAD fread //#define FWRITE fwrite #define FREAD fread_unlocked #define FWRITE fwrite_unlocked struct Buffer { FILE* const stream; const int buffer_size; uint8_t* const buff; int pos = 0; Buffer(FILE* a_stream, int a_buffer_size) : stream( a_stream ), buffer_size( a_buffer_size ), buff( new uint8_t[ buffer_size ] ) { setvbuf(stream, NULL, _IONBF, 0); } ~Buffer() { delete[] buff; } }; class In_Buffer : private Buffer { public: In_Buffer(FILE* a_stream, int a_buffer_size) : Buffer(a_stream, a_buffer_size) { FREAD(buff, 1, buffer_size, stream); } public: void prepare(int num_chars) { auto remaining = buffer_size - pos; if(remaining >= num_chars) return; assert(remaining >= 0); // prevent compiler warning memcpy(buff, buff+pos, remaining); int read = FREAD(buff+remaining, 1, pos, stream); int block_end = remaining + read; memset(buff + block_end, 0, buffer_size - block_end); pos = 0; } public: char get_unchecked() { return buff[ pos++ ]; } }; template<class INT> INT read_unsigned(In_Buffer& buff) { buff.prepare(25); char c = buff.get_unchecked(); while(c < '-') c = buff.get_unchecked(); INT r = 0; for(;;) { if(c < '0') return r; c -= '0'; r = r*10 + c; c = buff.get_unchecked(); } } template<class INT> INT read_signed(In_Buffer& buff) { buff.prepare(25); char c = buff.get_unchecked(); while(c < '-') c = buff.get_unchecked(); bool minus = false; if(c=='-') { c = buff.get_unchecked(); minus = true; } INT r = 0; for(;;) { if(c < '0') return minus ? -r : r; r = r*10 + (c-'0'); c = buff.get_unchecked(); } } In_Buffer& operator>>( In_Buffer& buff, char& c) { buff.prepare(1); c = buff.get_unchecked(); return buff; } In_Buffer& operator>>( In_Buffer& buff, UI& r) { r = read_unsigned<UI>(buff); return buff; } In_Buffer& operator>>( In_Buffer& buff, ULL& r) { r = read_unsigned<ULL>(buff); return buff; } In_Buffer& operator>>( In_Buffer& buff, int& r) { r = read_signed<int>(buff); return buff; } In_Buffer& operator>>( In_Buffer& buff, LL& r) { r = read_signed<LL>(buff); return buff; } In_Buffer& operator>>( In_Buffer& buff, string& r) { r.clear(); char c = buff.get_unchecked(); while(c <= ' ') c = buff.get_unchecked(); do { r.push_back( c ); c = buff.get_unchecked(); } while(c > ' '); return buff; } class Out_Buffer : private Buffer { public: Out_Buffer(FILE* a_stream, int a_buffer_size) : Buffer(a_stream, a_buffer_size) {} ~Out_Buffer() { flush(); } public: void prepare(int num_chars) { if(buffer_size - pos >= num_chars) return; flush(); } void flush() { FWRITE(buff, 1, pos, stream); pos = 0; } public: void put_unchecked(const char& c) { buff[ pos++ ] = c; } void put_unchecked(const char* str, int len) { memcpy(buff+pos, str, len); pos += len; } }; template<class INT> void write_signed(Out_Buffer& buff, const INT& i) { buff.prepare(25); if(i == 0) { buff.put_unchecked('0'); return; } auto ci = i; if(ci < 0) { buff.put_unchecked('-'); ci = -ci; } const int sz = 25; char temp[sz]; int pos = sz; while(ci) { temp[ --pos ] = '0' + ci%10; ci/=10; } buff.put_unchecked(temp+pos, sz-pos); } template<class INT> void write_unsigned(Out_Buffer& buff, const INT& i) { buff.prepare(25); if(i==0) { buff.put_unchecked('0'); return; } const int sz = 25; char temp[sz]; int pos = sz; auto ci = i; while(ci) { temp[ --pos ] = '0' + ci%10; ci/=10; } buff.put_unchecked(temp+pos, sz-pos); } Out_Buffer& operator<<( Out_Buffer& buff, const char& c) { buff.prepare(1); buff.put_unchecked( c ); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const UI& r) { write_unsigned<UI>(buff, r); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const ULL& r) { write_unsigned<ULL>(buff, r); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const int& r) { write_signed<int>(buff, r); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const LL& r) { write_signed<LL>(buff, r); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const char* cstr) { auto len = strlen(cstr); buff.prepare(len); buff.put_unchecked(cstr, len); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const string& str) { buff.prepare( str.size() ); buff.put_unchecked(str.data(), str.size()); return buff; } #define BUFF_SIZE 32768 In_Buffer fast_cin( stdin, BUFF_SIZE ); Out_Buffer fast_cout( stdout, BUFF_SIZE ); //Out_Buffer fast_cerr( stderr, BUFF_SIZE ); char fast_endl = '\n'; // // AMALGAMATE: "include/fast-io.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// #define cin fast_cin #define cout fast_cout #define endl fast_endl #else //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/slow-io.hpp" BEGINS HERE // struct Slow_IO_Singleton { Slow_IO_Singleton() { ios_base::sync_with_stdio( false ); std::cin.tie( nullptr ); std::cout.tie( nullptr ); setlocale(LC_ALL,"C"); const int buffer_size = 32768; static char stdin_buffer[ buffer_size ]; static char stdout_buffer[ buffer_size ]; cin.rdbuf()->pubsetbuf( stdin_buffer, buffer_size ); cout.rdbuf()->pubsetbuf( stdout_buffer, buffer_size ); } ~Slow_IO_Singleton() { } }; Slow_IO_Singleton slow_io_singleton; // // AMALGAMATE: "include/slow-io.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// #ifndef DEBUG #define endl '\n' #endif #endif //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/abbrevs-io.hpp" BEGINS HERE // int ri() { int r; cin >> r; return r; } UI rui() { UI r; cin >> r; return r; } LL rll() { LL r; cin >> r; return r; } ULL rull() { ULL r; cin >> r; return r; } string rstr() {string s; cin >> s; return s; } // // AMALGAMATE: "include/abbrevs-io.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/debug.hpp" BEGINS HERE // #define ASS(x) assert(x) // // AMALGAMATE: "include/debug.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// // // for salgo #define CONTEST_MODE namespace salgo {}; using namespace salgo; // // // AMALGAMATE: "include/template.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// //#define assert(x) // // snippets/int-pow.hpp // template<class T, class E, class OP> T int_pow(T a, E exp, const OP& op, const T& neutral) { // assert(exp >= 0); if(exp < 0) return 1; auto r = neutral; while(exp != 0) { if((exp & 1) != 0) { op(r, a); --exp; } else{ exp >>= 1; op(a, a); } } return r; } template<class T, class E> T int_pow(const T& a, const E& exp) { auto lambda = [](T& aa, const T& bb){ aa *= bb; }; return int_pow<T,E,decltype(lambda)>(a, exp, lambda, T(1)); } // // snippets/modulo.hpp // uint32_t MOD = 1e9 + 7; class Modulo { public: using H = uint32_t; H h = 0; public: Modulo() = default; Modulo(H x) : h( x % MOD ) {} Modulo(const Modulo&) = default; public: Modulo& operator+=(const Modulo& o) { h += o.h; if(h >= MOD) h -= MOD; return *this; } Modulo& operator-=(const Modulo& o) { h = MOD + h - o.h; if(h >= MOD) h -= MOD; return *this; } Modulo& operator*=(const Modulo& o) { h = (1ULL * h * o.h) % MOD; return *this; } Modulo& operator/=(const Modulo& o) { const auto TOTIENT = MOD-1; *this *= int_pow(o, TOTIENT-1); return *this; } bool operator==(const Modulo& o) const { return h == o.h; } bool operator!=(const Modulo& o) const { return h != o.h; } Modulo operator+(const Modulo& o) const { return Modulo(*this) += o; } Modulo operator-(const Modulo& o) const { return Modulo(*this) -= o; } Modulo operator*(const Modulo& o) const { return Modulo(*this) *= o; } Modulo operator/(const Modulo& o) const { return Modulo(*this) /= o; } Modulo& operator--() { if(h == 0) h = MOD; --h; return *this; } Modulo& operator++() { ++h; if(h == MOD) h = 0; return *this; } Modulo operator--(int) { auto m = *this; --(*this); return m; } Modulo operator++(int) { auto m = *this; ++(*this); return m; } explicit operator H() const { return h; } }; ostream& operator<<(ostream& os, const Modulo& modulo) { return os << modulo.h; } struct Range { int fi = -1; int la = -1; bool operator<(const Range& o) const { return pair{fi,la} < pair{o.fi, o.la}; } int num() const { return la-fi+1; } }; struct Test_Case { int n = RI; int m = RI; int num_lake = RI; int num_sea = RI; int num_not_reachable = 0; struct Vert { vector<int> tos; Range range; bool reachable = false; bool vis = false; }; bool is_sea(int iv) { return num_lake <= iv && iv < num_lake + num_sea; } vector<Vert> verts; void dfs0(int iv) { auto& v = verts[iv]; if(v.reachable) return; v.reachable = true; for(auto to : v.tos) { dfs0(to); } } void dfs(int iv) { auto& v = verts[iv]; if(v.vis) return; v.vis = true; deque<Range> ranges; if(is_sea(iv)) ranges.push_back({ iv-num_lake, iv-num_lake }); for(auto& to : v.tos) { dfs(to); auto& r = verts[to].range; if(r.fi != -1) { ranges.push_back(r); } } // auto asd = ranges; if(!ranges.empty()) { sort(ALL(ranges)); while(ranges.size() > 1 && ranges[0].la >= ranges[1].fi - 1) { ranges[1].fi = ranges[0].fi; ranges.pop_front(); } while(ranges.size() > 1 && ranges.back().la - num_sea >= ranges[0].fi - 1) { ranges.back().la = ranges[0].la + num_sea; ranges.pop_front(); } // if(ranges.size() != 1) { // cout << "DBG ranges at vert " << iv << endl; // for(auto& r : asd) cout << r.fi << " -> " << r.la << endl; // cout << endl; // } assert(ranges.size() == 1); if(ranges[0].la - ranges[0].fi + 1 >= num_sea) { v.range = {0, num_sea-1}; } else { v.range = ranges[0]; } } } void subtask_a(const vector<Range>& ranges) { vector<Modulo> dp( ranges.size()+1 ); dp[0] = 0; dp[1] = int_pow(Modulo(2), num_sea - ranges[0].num()); // cout << "dp[1] == " << dp[1] << endl; int i_end = 0; FO(i, 1, ranges.size()) { // int num_new = ranges[i].la - ranges[i-1].la; dp[i+1] = dp[i]; if(i_end >= 0) --i_end; while(i_end+1 < (int)ranges.size() && ranges[i_end+1].la < ranges[i-1].fi) ++i_end; while(i_end == -1 || ranges[i_end].la < ranges[i].fi) { int end_pos = ranges[i].fi-1; if(i_end+1 < (int)ranges.size()) REMIN(end_pos, ranges[i_end+1].la); int start_pos = ranges[i-1].fi; if(i_end >= 0) REMAX(start_pos, ranges[i_end].la + 1); // cout << endl << "dp step i_end == " << i_end << " start_pos == " << start_pos << " end_pos == " << end_pos << endl; dp[i+1] += (int_pow(Modulo(2), num_sea) - dp[i_end+1]) / int_pow(Modulo(2), ranges[i].la - start_pos +1) * (int_pow(Modulo(2), end_pos - start_pos +1) - 1); // cout << "dp += " << (int_pow(Modulo(2), num_sea) - dp[i_end+1]) << " / " << // int_pow(Modulo(2), ranges[i].la - start_pos +1) << " * " << // (int_pow(Modulo(2), end_pos - start_pos +1) - 1) << endl; ++i_end; } // cout << "dp[" << i+1 << "] == " << dp[i+1] << endl; } auto r = int_pow(Modulo(2), num_sea) - dp[ ranges.size() ]; r *= int_pow(Modulo(2), num_not_reachable); cout << r << endl; } void subtask_b(const vector<Range>&) { } void solve() { // cout << "Case #" << icase+1 << ": "; verts.resize(n); FOR(i,m) { int a = RI-1; string edge = RSTR; int b = RI-1; if(edge == "->") { verts[a].tos.push_back(b); } else { verts[a].tos.push_back(b); verts[b].tos.push_back(a); } } FOR(i, num_lake) { dfs0(i); } // delete not-reachable sea settlements n = 0; vector<int> v_remap( verts.size() ); FOR(i, verts.size()) { if(is_sea(i) && !verts[i].reachable) { // delete! ++num_not_reachable; } else { v_remap[i] = n; verts[n] = verts[i]; ++n; } } verts.resize(n); for(auto& v : verts) { for(auto& to : v.tos) { to = v_remap[to]; } } num_sea -= num_not_reachable; // cout << "deleted " << num_not_reachable << " not-reachable sea settlements" << endl; FOR(asd,10) FOR(i,n) { dfs(i); } // cout << "ranges:" << endl; // FOR(i, num_lake) { // cout << i+1 << ": " << verts[i].range.fi << " -> " << verts[i].range.la << endl; // } int full_range_at = -1; auto is_full = [&](const auto& range) { return range.fi == 0 && range.la == num_sea-1; }; FOR(i, num_lake) { if(is_full(verts[i].range)) { full_range_at = i; break; } } vector<Range> ranges; FOR(i, num_lake) ranges.push_back( verts[i].range ); auto cycle = [&](const auto& v, int at) { vector<Range> r; FO(i, at, num_lake) { r.push_back( v[i] ); } FO(i, 0, at) { r.push_back( v[i] ); } return r; }; if(full_range_at != -1) { ranges = cycle(ranges, full_range_at); } { decltype(ranges) res; for(auto& r : ranges) { if(!is_full(r)) res.push_back(r); } ranges = std::move(res); } int num_inc = 0; int num_dec = 0; FOR(i, ranges.size()) { int j = (i+1) % ranges.size(); if(ranges[i].fi < ranges[j].fi) ++num_inc; if(ranges[i].la < ranges[j].la) ++num_inc; if(ranges[i].fi > ranges[j].fi) ++num_dec; if(ranges[i].la > ranges[j].la) ++num_dec; } if(num_dec > num_inc) { reverse(ALL(ranges)); } auto fix = [&](auto& vec) { FO(i, 1, vec.size()) { if(vec[i-1].fi > vec[i].fi) { vec[i].fi += num_sea; vec[i].la += num_sea; } } }; fix(ranges); int break_before = -1; FOR(i, ranges.size()) { int j = (i+1) % ranges.size(); auto i_range = ranges[i]; auto j_range = ranges[j]; if(i_range.fi > j_range.fi || i_range.la > j_range.la) { j_range.fi += num_sea; j_range.la += num_sea; } if(i_range.la < j_range.fi) { break_before = j; break; } } if(break_before != -1) { ranges = cycle(ranges, break_before); } fix(ranges); // cout << "RANGES:" << endl; // for(auto& r : ranges) cout << r.fi << " -> " << r.la << endl; // cout << endl; if(full_range_at != -1 || break_before != -1) { // cout << "SUBTASK A" << endl; subtask_a(ranges); } else { // cout << "SUBTASK B" << endl; subtask_b(ranges); } } int icase = -1; }; // struct Test_Case int main() { int num_cases = READ_NUM_TEST_CASES ? RI : 1; FOR(i, num_cases) { Test_Case tc; tc.icase = i; tc.solve(); } return 0; }
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(a) : (b)) #define MAX(a,b) ((b)<(a) ? (a) : (b)) #define REMIN(a,b) ((a) = min(a,b)) #define REMAX(a,b) ((a) = max(a,b)) #define ALL(c) (c).begin(),(c).end() #define SQR(x) ((x)*(x)) bool is_pow(int x) { return (x&(x-1)) == 0; } // // AMALGAMATE: "include/abbrevs.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// #if USE_FAST_IO //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/fast-io.hpp" BEGINS HERE // //#define FREAD fread //#define FWRITE fwrite #define FREAD fread_unlocked #define FWRITE fwrite_unlocked struct Buffer { FILE* const stream; const int buffer_size; uint8_t* const buff; int pos = 0; Buffer(FILE* a_stream, int a_buffer_size) : stream( a_stream ), buffer_size( a_buffer_size ), buff( new uint8_t[ buffer_size ] ) { setvbuf(stream, NULL, _IONBF, 0); } ~Buffer() { delete[] buff; } }; class In_Buffer : private Buffer { public: In_Buffer(FILE* a_stream, int a_buffer_size) : Buffer(a_stream, a_buffer_size) { FREAD(buff, 1, buffer_size, stream); } public: void prepare(int num_chars) { auto remaining = buffer_size - pos; if(remaining >= num_chars) return; assert(remaining >= 0); // prevent compiler warning memcpy(buff, buff+pos, remaining); int read = FREAD(buff+remaining, 1, pos, stream); int block_end = remaining + read; memset(buff + block_end, 0, buffer_size - block_end); pos = 0; } public: char get_unchecked() { return buff[ pos++ ]; } }; template<class INT> INT read_unsigned(In_Buffer& buff) { buff.prepare(25); char c = buff.get_unchecked(); while(c < '-') c = buff.get_unchecked(); INT r = 0; for(;;) { if(c < '0') return r; c -= '0'; r = r*10 + c; c = buff.get_unchecked(); } } template<class INT> INT read_signed(In_Buffer& buff) { buff.prepare(25); char c = buff.get_unchecked(); while(c < '-') c = buff.get_unchecked(); bool minus = false; if(c=='-') { c = buff.get_unchecked(); minus = true; } INT r = 0; for(;;) { if(c < '0') return minus ? -r : r; r = r*10 + (c-'0'); c = buff.get_unchecked(); } } In_Buffer& operator>>( In_Buffer& buff, char& c) { buff.prepare(1); c = buff.get_unchecked(); return buff; } In_Buffer& operator>>( In_Buffer& buff, UI& r) { r = read_unsigned<UI>(buff); return buff; } In_Buffer& operator>>( In_Buffer& buff, ULL& r) { r = read_unsigned<ULL>(buff); return buff; } In_Buffer& operator>>( In_Buffer& buff, int& r) { r = read_signed<int>(buff); return buff; } In_Buffer& operator>>( In_Buffer& buff, LL& r) { r = read_signed<LL>(buff); return buff; } In_Buffer& operator>>( In_Buffer& buff, string& r) { r.clear(); char c = buff.get_unchecked(); while(c <= ' ') c = buff.get_unchecked(); do { r.push_back( c ); c = buff.get_unchecked(); } while(c > ' '); return buff; } class Out_Buffer : private Buffer { public: Out_Buffer(FILE* a_stream, int a_buffer_size) : Buffer(a_stream, a_buffer_size) {} ~Out_Buffer() { flush(); } public: void prepare(int num_chars) { if(buffer_size - pos >= num_chars) return; flush(); } void flush() { FWRITE(buff, 1, pos, stream); pos = 0; } public: void put_unchecked(const char& c) { buff[ pos++ ] = c; } void put_unchecked(const char* str, int len) { memcpy(buff+pos, str, len); pos += len; } }; template<class INT> void write_signed(Out_Buffer& buff, const INT& i) { buff.prepare(25); if(i == 0) { buff.put_unchecked('0'); return; } auto ci = i; if(ci < 0) { buff.put_unchecked('-'); ci = -ci; } const int sz = 25; char temp[sz]; int pos = sz; while(ci) { temp[ --pos ] = '0' + ci%10; ci/=10; } buff.put_unchecked(temp+pos, sz-pos); } template<class INT> void write_unsigned(Out_Buffer& buff, const INT& i) { buff.prepare(25); if(i==0) { buff.put_unchecked('0'); return; } const int sz = 25; char temp[sz]; int pos = sz; auto ci = i; while(ci) { temp[ --pos ] = '0' + ci%10; ci/=10; } buff.put_unchecked(temp+pos, sz-pos); } Out_Buffer& operator<<( Out_Buffer& buff, const char& c) { buff.prepare(1); buff.put_unchecked( c ); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const UI& r) { write_unsigned<UI>(buff, r); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const ULL& r) { write_unsigned<ULL>(buff, r); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const int& r) { write_signed<int>(buff, r); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const LL& r) { write_signed<LL>(buff, r); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const char* cstr) { auto len = strlen(cstr); buff.prepare(len); buff.put_unchecked(cstr, len); return buff; } Out_Buffer& operator<<( Out_Buffer& buff, const string& str) { buff.prepare( str.size() ); buff.put_unchecked(str.data(), str.size()); return buff; } #define BUFF_SIZE 32768 In_Buffer fast_cin( stdin, BUFF_SIZE ); Out_Buffer fast_cout( stdout, BUFF_SIZE ); //Out_Buffer fast_cerr( stderr, BUFF_SIZE ); char fast_endl = '\n'; // // AMALGAMATE: "include/fast-io.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// #define cin fast_cin #define cout fast_cout #define endl fast_endl #else //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/slow-io.hpp" BEGINS HERE // struct Slow_IO_Singleton { Slow_IO_Singleton() { ios_base::sync_with_stdio( false ); std::cin.tie( nullptr ); std::cout.tie( nullptr ); setlocale(LC_ALL,"C"); const int buffer_size = 32768; static char stdin_buffer[ buffer_size ]; static char stdout_buffer[ buffer_size ]; cin.rdbuf()->pubsetbuf( stdin_buffer, buffer_size ); cout.rdbuf()->pubsetbuf( stdout_buffer, buffer_size ); } ~Slow_IO_Singleton() { } }; Slow_IO_Singleton slow_io_singleton; // // AMALGAMATE: "include/slow-io.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// #ifndef DEBUG #define endl '\n' #endif #endif //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/abbrevs-io.hpp" BEGINS HERE // int ri() { int r; cin >> r; return r; } UI rui() { UI r; cin >> r; return r; } LL rll() { LL r; cin >> r; return r; } ULL rull() { ULL r; cin >> r; return r; } string rstr() {string s; cin >> s; return s; } // // AMALGAMATE: "include/abbrevs-io.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// // AMALGAMATE: "include/debug.hpp" BEGINS HERE // #define ASS(x) assert(x) // // AMALGAMATE: "include/debug.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// // // for salgo #define CONTEST_MODE namespace salgo {}; using namespace salgo; // // // AMALGAMATE: "include/template.hpp" ENDS HERE //////////////////////////////////////////////////////////////////////////////// //#define assert(x) // // snippets/int-pow.hpp // template<class T, class E, class OP> T int_pow(T a, E exp, const OP& op, const T& neutral) { // assert(exp >= 0); if(exp < 0) return 1; auto r = neutral; while(exp != 0) { if((exp & 1) != 0) { op(r, a); --exp; } else{ exp >>= 1; op(a, a); } } return r; } template<class T, class E> T int_pow(const T& a, const E& exp) { auto lambda = [](T& aa, const T& bb){ aa *= bb; }; return int_pow<T,E,decltype(lambda)>(a, exp, lambda, T(1)); } // // snippets/modulo.hpp // uint32_t MOD = 1e9 + 7; class Modulo { public: using H = uint32_t; H h = 0; public: Modulo() = default; Modulo(H x) : h( x % MOD ) {} Modulo(const Modulo&) = default; public: Modulo& operator+=(const Modulo& o) { h += o.h; if(h >= MOD) h -= MOD; return *this; } Modulo& operator-=(const Modulo& o) { h = MOD + h - o.h; if(h >= MOD) h -= MOD; return *this; } Modulo& operator*=(const Modulo& o) { h = (1ULL * h * o.h) % MOD; return *this; } Modulo& operator/=(const Modulo& o) { const auto TOTIENT = MOD-1; *this *= int_pow(o, TOTIENT-1); return *this; } bool operator==(const Modulo& o) const { return h == o.h; } bool operator!=(const Modulo& o) const { return h != o.h; } Modulo operator+(const Modulo& o) const { return Modulo(*this) += o; } Modulo operator-(const Modulo& o) const { return Modulo(*this) -= o; } Modulo operator*(const Modulo& o) const { return Modulo(*this) *= o; } Modulo operator/(const Modulo& o) const { return Modulo(*this) /= o; } Modulo& operator--() { if(h == 0) h = MOD; --h; return *this; } Modulo& operator++() { ++h; if(h == MOD) h = 0; return *this; } Modulo operator--(int) { auto m = *this; --(*this); return m; } Modulo operator++(int) { auto m = *this; ++(*this); return m; } explicit operator H() const { return h; } }; ostream& operator<<(ostream& os, const Modulo& modulo) { return os << modulo.h; } struct Range { int fi = -1; int la = -1; bool operator<(const Range& o) const { return pair{fi,la} < pair{o.fi, o.la}; } int num() const { return la-fi+1; } }; struct Test_Case { int n = RI; int m = RI; int num_lake = RI; int num_sea = RI; int num_not_reachable = 0; struct Vert { vector<int> tos; Range range; bool reachable = false; bool vis = false; }; bool is_sea(int iv) { return num_lake <= iv && iv < num_lake + num_sea; } vector<Vert> verts; void dfs0(int iv) { auto& v = verts[iv]; if(v.reachable) return; v.reachable = true; for(auto to : v.tos) { dfs0(to); } } void dfs(int iv) { auto& v = verts[iv]; if(v.vis) return; v.vis = true; deque<Range> ranges; if(is_sea(iv)) ranges.push_back({ iv-num_lake, iv-num_lake }); for(auto& to : v.tos) { dfs(to); auto& r = verts[to].range; if(r.fi != -1) { ranges.push_back(r); } } // auto asd = ranges; if(!ranges.empty()) { sort(ALL(ranges)); while(ranges.size() > 1 && ranges[0].la >= ranges[1].fi - 1) { ranges[1].fi = ranges[0].fi; ranges.pop_front(); } while(ranges.size() > 1 && ranges.back().la - num_sea >= ranges[0].fi - 1) { ranges.back().la = ranges[0].la + num_sea; ranges.pop_front(); } // if(ranges.size() != 1) { // cout << "DBG ranges at vert " << iv << endl; // for(auto& r : asd) cout << r.fi << " -> " << r.la << endl; // cout << endl; // } assert(ranges.size() == 1); if(ranges[0].la - ranges[0].fi + 1 >= num_sea) { v.range = {0, num_sea-1}; } else { v.range = ranges[0]; } } } void subtask_a(const vector<Range>& ranges) { vector<Modulo> dp( ranges.size()+1 ); dp[0] = 0; dp[1] = int_pow(Modulo(2), num_sea - ranges[0].num()); // cout << "dp[1] == " << dp[1] << endl; int i_end = 0; FO(i, 1, ranges.size()) { // int num_new = ranges[i].la - ranges[i-1].la; dp[i+1] = dp[i]; if(i_end >= 0) --i_end; while(i_end+1 < (int)ranges.size() && ranges[i_end+1].la < ranges[i-1].fi) ++i_end; while(i_end == -1 || ranges[i_end].la < ranges[i].fi) { int end_pos = ranges[i].fi-1; if(i_end+1 < (int)ranges.size()) REMIN(end_pos, ranges[i_end+1].la); int start_pos = ranges[i-1].fi; if(i_end >= 0) REMAX(start_pos, ranges[i_end].la + 1); // cout << endl << "dp step i_end == " << i_end << " start_pos == " << start_pos << " end_pos == " << end_pos << endl; dp[i+1] += (int_pow(Modulo(2), num_sea) - dp[i_end+1]) / int_pow(Modulo(2), ranges[i].la - start_pos +1) * (int_pow(Modulo(2), end_pos - start_pos +1) - 1); // cout << "dp += " << (int_pow(Modulo(2), num_sea) - dp[i_end+1]) << " / " << // int_pow(Modulo(2), ranges[i].la - start_pos +1) << " * " << // (int_pow(Modulo(2), end_pos - start_pos +1) - 1) << endl; ++i_end; } // cout << "dp[" << i+1 << "] == " << dp[i+1] << endl; } auto r = int_pow(Modulo(2), num_sea) - dp[ ranges.size() ]; r *= int_pow(Modulo(2), num_not_reachable); cout << r << endl; } void subtask_b(const vector<Range>&) { } void solve() { // cout << "Case #" << icase+1 << ": "; verts.resize(n); FOR(i,m) { int a = RI-1; string edge = RSTR; int b = RI-1; if(edge == "->") { verts[a].tos.push_back(b); } else { verts[a].tos.push_back(b); verts[b].tos.push_back(a); } } FOR(i, num_lake) { dfs0(i); } // delete not-reachable sea settlements n = 0; vector<int> v_remap( verts.size() ); FOR(i, verts.size()) { if(is_sea(i) && !verts[i].reachable) { // delete! ++num_not_reachable; } else { v_remap[i] = n; verts[n] = verts[i]; ++n; } } verts.resize(n); for(auto& v : verts) { for(auto& to : v.tos) { to = v_remap[to]; } } num_sea -= num_not_reachable; // cout << "deleted " << num_not_reachable << " not-reachable sea settlements" << endl; FOR(asd,10) FOR(i,n) { dfs(i); } // cout << "ranges:" << endl; // FOR(i, num_lake) { // cout << i+1 << ": " << verts[i].range.fi << " -> " << verts[i].range.la << endl; // } int full_range_at = -1; auto is_full = [&](const auto& range) { return range.fi == 0 && range.la == num_sea-1; }; FOR(i, num_lake) { if(is_full(verts[i].range)) { full_range_at = i; break; } } vector<Range> ranges; FOR(i, num_lake) ranges.push_back( verts[i].range ); auto cycle = [&](const auto& v, int at) { vector<Range> r; FO(i, at, num_lake) { r.push_back( v[i] ); } FO(i, 0, at) { r.push_back( v[i] ); } return r; }; if(full_range_at != -1) { ranges = cycle(ranges, full_range_at); } { decltype(ranges) res; for(auto& r : ranges) { if(!is_full(r)) res.push_back(r); } ranges = std::move(res); } int num_inc = 0; int num_dec = 0; FOR(i, ranges.size()) { int j = (i+1) % ranges.size(); if(ranges[i].fi < ranges[j].fi) ++num_inc; if(ranges[i].la < ranges[j].la) ++num_inc; if(ranges[i].fi > ranges[j].fi) ++num_dec; if(ranges[i].la > ranges[j].la) ++num_dec; } if(num_dec > num_inc) { reverse(ALL(ranges)); } auto fix = [&](auto& vec) { FO(i, 1, vec.size()) { if(vec[i-1].fi > vec[i].fi) { vec[i].fi += num_sea; vec[i].la += num_sea; } } }; fix(ranges); int break_before = -1; FOR(i, ranges.size()) { int j = (i+1) % ranges.size(); auto i_range = ranges[i]; auto j_range = ranges[j]; if(i_range.fi > j_range.fi || i_range.la > j_range.la) { j_range.fi += num_sea; j_range.la += num_sea; } if(i_range.la < j_range.fi) { break_before = j; break; } } if(break_before != -1) { ranges = cycle(ranges, break_before); } fix(ranges); // cout << "RANGES:" << endl; // for(auto& r : ranges) cout << r.fi << " -> " << r.la << endl; // cout << endl; if(full_range_at != -1 || break_before != -1) { // cout << "SUBTASK A" << endl; subtask_a(ranges); } else { // cout << "SUBTASK B" << endl; subtask_b(ranges); } } int icase = -1; }; // struct Test_Case int main() { int num_cases = READ_NUM_TEST_CASES ? RI : 1; FOR(i, num_cases) { Test_Case tc; tc.icase = i; tc.solve(); } return 0; } |