//Andrzej Jabłoński #include "bits/stdc++.h" #define forx(i,b,e) for(std::common_type<decltype(b, e)>::type i = (b), ie = (e); i < ie; i++) #define pow2(x) (1ll<<(x)) #define all(x) begin(x), end(x) #define until(x) while(!(x)) #define len(x) (int)size(x) using namespace std; using llong = long long; template<class T> void __echo(const T& x, string sep) { cerr << x << sep; } void __echo(const string& x, string sep) { cerr << "\"" << x << "\"" << sep; } void __echo(const char& x, string sep = ", ") { cerr << "\'" << x << "\'" << sep; } template<class T> void __echo(const vector<T>& x, string sep) { cerr << "{"; for (size_t i = 0; i < x.size(); i++) __echo(x[i], i + 1 == x.size() ? "" : ", "); cerr << "}" << sep; } template<class T1, class T2> void __echo(const pair<T1, T2>& x, string sep = ", ") { cerr << "("; __echo(x.first, ", "); __echo(x.second, ""); cerr << ")" << sep; } void __echo(istringstream& stream) { cerr << "\n"; } template<size_t> struct Int {}; template<class Tuple, size_t Pos> void print_tuple(const Tuple& x, Int<Pos>) { __echo(get<tuple_size<Tuple>::value - Pos>(x), ", "); print_tuple(x, Int<Pos - 1>()); } template<class Tuple> void print_tuple(const Tuple& x, Int<1>) { cerr << get<tuple_size<Tuple>::value - 1>(x); } template<class... Args> void print_tuple(const tuple<Args...>& x) { print_tuple(x, Int<sizeof... (Args)>()); } template<class... Args> void __echo(const tuple<Args...>& x, string sep) { cerr << "("; print_tuple(x); cerr << ")" << sep; } template<class T> bool _char_const(const T& x) { return false; } bool _char_const(const char* x) { cerr << x; return true; } template<class T> bool isCharConst(const T& x) { return false; } bool isCharConst(const char* x) { return true; } string trim(string x) { return string(begin(x) + x.find_first_not_of(' '), begin(x) + x.find_last_not_of(' ') + 1); } template<class T, class... Args> void __echo(istringstream& stream, const T& x, Args... args) { static int cnt[200] = { 0 };//no bo po co to tworzyc od nowa? string name; do { string s; getline(stream, s, ','); for (auto c : s) cnt[(int)c]++; name += s + ','; } while (not(cnt['('] == cnt[')'] && cnt['['] == cnt[']'] && cnt['{'] == cnt['}'] && cnt['\"'] % 2 == 0 && cnt['\''] % 2 == 0)); name.pop_back();//usuwamy ',' if (!_char_const(x)) { cerr << trim(name) << " = "; __echo(x, "; "); } __echo(stream, args...); } #define echo(...) if(DBG) {istringstream str(#__VA_ARGS__); __echo(str, __VA_ARGS__); } ///////////////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////////////// #define TESTSETS 0 #define DBG 0 constexpr int mod = int(1000'000'000 + 7); map<string, bool> ok; bool test(const string& s) { auto it = ok.find(s); if (it != ok.end()) return it->second; forx(i, 0, size(s) - 1) { if (s[i] == s[i + 1]) { string t = s.substr(0, i) + (s[i] == 'C' ? 'Z' : 'C') + s.substr(i + 2); if (test(t)) { ok[s] = true; return true; } } } ok[s] = false; return false; } int rnd(int a, int b) { return rand() % (b - a + 1) + a; } void brut_gen() { ok["C"] = ok["Z"] = true; int a = 3, b = 8; int n = 1; while (n < 20) { string s = string(n, '#'); forx(msk, 0, pow2(n)) { forx(b, 0, n) { s[b] = "CZ"[(msk & pow2(b)) == 0]; } int c = (int)count(all(s), 'C'); int z = n - c; bool git = test(s); if ((c - z) % 3 != 0 && !git) cout << s << ": " << git << "\n"; } n++; } } void solve_n_1(int n, int q, string s) { cout << 1 + (s[0] == 'N') << "\n"; while (q--) { int k; cin >> k >> s[0]; cout << 1 + (s[0] == 'N') << "\n"; } } void solve() { int n, q; string s; cin >> n >> q >> s; if (n == 1) { solve_n_1(n, q, s); return; } int cCZ = 0; //liczba dobrze ustawionych pozycji do ciagu CZCZCZCZC int cZC = 0; int free = 0; //liczba wolnych pozycji, czyli liczba czastek N int cntC = 0; int cntZ = 0; auto ok_CZ = [&](int idx, char value)->bool { if (idx % 2 == 0 && value != 'Z') return true; if (idx % 2 == 1 && value != 'C') return true; return false; }; auto ok_ZC = [&](int idx, char value)->bool { if (idx % 2 == 0 && value != 'C') return true; if (idx % 2 == 1 && value != 'Z') return true; return false; }; auto update_s = [&](int i, char c) { if (s[i] == c) return; // Na pozycje i wpisz znak c // i zaktualizuj info o CZCZC... i ZCZCZ... if (ok_CZ(i, s[i]) && !ok_CZ(i, c)) cCZ--; if (!ok_CZ(i, s[i]) && ok_CZ(i, c)) cCZ++; if (ok_ZC(i, s[i]) && !ok_ZC(i, c)) cZC--; if (!ok_ZC(i, s[i]) && ok_ZC(i, c)) cZC++; // oraz o ilosci N (free), Z (cntZ), C (cntC) if (s[i] == 'N') free--; if (s[i] == 'Z') cntZ--; if (s[i] == 'C') cntC--; if (c == 'N') free++; if (c == 'Z') cntZ++; if (c == 'C') cntC++; s[i] = c; }; forx(i, 0, n) { if (s[i] == 'N') free++; if (s[i] == 'Z') cntZ++; if (s[i] == 'C') cntC++; if (ok_CZ(i, s[i])) cCZ++; if (ok_ZC(i, s[i])) cZC++; } auto seqCZ = [&]() { return cCZ == n; };//czy da sie stworzyc ciag CZC... auto seqZC = [&]() { return cZC == n; }; // ------------- preprocessing [3][3] --------------- vector<int> p2mod(n + 42, 1); forx(i, 1, n + 42) p2mod[i] = (p2mod[i - 1] * 2ll) % mod; constexpr int inv3 = 333333336; constexpr int inv2 = 500000004; auto n1p = [&](int n) { return (n % 2 ? mod - 1 : 1); //(-1)^n modulo }; auto mmul = [&](int a, int b)->int { a %= mod; b %= mod; llong res = (((llong)a * b) % mod + mod) % mod; return res % mod; }; auto madd = [&](int a, int b)->int { a %= mod; b %= mod; return (((llong)a + b) % mod + mod) % mod; }; auto seq = [&](int N, int r) { int n = N / 3; //podloga int magic = 0; if (N % 3 == 0) { if (r % 3 == 0) { magic = mmul(inv3, madd(mmul(2, n1p(n)), p2mod[3 * n])); } else if (r % 3 == 1) { magic = mmul(inv3, madd(n1p(n + 1), p2mod[3 * n])); } else { magic = mmul(inv3, madd(n1p(n + 1), p2mod[3 * n])); } } else if (N % 3 == 1) { if (r % 3 == 0) { magic = mmul(inv3, madd(n1p(n), p2mod[3 * n + 1])); } else if (r % 3 == 1) { magic = mmul(inv3, madd(n1p(n), p2mod[3 * n + 1])); } else { magic = mmul(mmul(-2, inv3), madd(n1p(n), -p2mod[3 * n])); } } else { if (r % 3 == 0) { magic = mmul(inv3, madd(n1p(n + 1), p2mod[3 * n + 2])); } else if (r % 3 == 1) { magic = mmul(mmul(2, inv3), madd(n1p(n), p2mod[3 * n + 1])); } else { magic = mmul(inv3, madd(n1p(n + 1), p2mod[3 * n + 2])); } } if (DBG) echo(N, r, p2mod[N], magic); return madd(p2mod[N], -magic); }; auto good_seq = [&]()->int { if (free == 0) { // odpowiedz to zawsze 1 lub 0 return ((cntC - cntZ) % 3 != 0) && !seqCZ() && !seqZC(); } else { int bad_mod = (2 * (cntZ - cntC + free) % 3 + 3) % 3;// r (bad_mod) int special_combinations = (n % 2 == 1 ? seqCZ() + seqZC() : 0); //moze byc jednak dwie na raz (NNNN) int good_mod_combinations = seq(free, bad_mod); int ans = madd(good_mod_combinations, -special_combinations); return ans; } }; // -------------------- odpowiedzi na zapytania --------------------- int ans0 = good_seq(); cout << ans0 << "\n"; forx(query, 0, q) { int idx; char c; cin >> idx >> c; idx -= 1; update_s(idx, c); int ans = good_seq(); cout << ans << "\n"; } } int main() { ios::sync_with_stdio(0); cin.tie(0); int t = 1; if (TESTSETS) cin >> t; while (t--) solve(); }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 | //Andrzej Jabłoński #include "bits/stdc++.h" #define forx(i,b,e) for(std::common_type<decltype(b, e)>::type i = (b), ie = (e); i < ie; i++) #define pow2(x) (1ll<<(x)) #define all(x) begin(x), end(x) #define until(x) while(!(x)) #define len(x) (int)size(x) using namespace std; using llong = long long; template<class T> void __echo(const T& x, string sep) { cerr << x << sep; } void __echo(const string& x, string sep) { cerr << "\"" << x << "\"" << sep; } void __echo(const char& x, string sep = ", ") { cerr << "\'" << x << "\'" << sep; } template<class T> void __echo(const vector<T>& x, string sep) { cerr << "{"; for (size_t i = 0; i < x.size(); i++) __echo(x[i], i + 1 == x.size() ? "" : ", "); cerr << "}" << sep; } template<class T1, class T2> void __echo(const pair<T1, T2>& x, string sep = ", ") { cerr << "("; __echo(x.first, ", "); __echo(x.second, ""); cerr << ")" << sep; } void __echo(istringstream& stream) { cerr << "\n"; } template<size_t> struct Int {}; template<class Tuple, size_t Pos> void print_tuple(const Tuple& x, Int<Pos>) { __echo(get<tuple_size<Tuple>::value - Pos>(x), ", "); print_tuple(x, Int<Pos - 1>()); } template<class Tuple> void print_tuple(const Tuple& x, Int<1>) { cerr << get<tuple_size<Tuple>::value - 1>(x); } template<class... Args> void print_tuple(const tuple<Args...>& x) { print_tuple(x, Int<sizeof... (Args)>()); } template<class... Args> void __echo(const tuple<Args...>& x, string sep) { cerr << "("; print_tuple(x); cerr << ")" << sep; } template<class T> bool _char_const(const T& x) { return false; } bool _char_const(const char* x) { cerr << x; return true; } template<class T> bool isCharConst(const T& x) { return false; } bool isCharConst(const char* x) { return true; } string trim(string x) { return string(begin(x) + x.find_first_not_of(' '), begin(x) + x.find_last_not_of(' ') + 1); } template<class T, class... Args> void __echo(istringstream& stream, const T& x, Args... args) { static int cnt[200] = { 0 };//no bo po co to tworzyc od nowa? string name; do { string s; getline(stream, s, ','); for (auto c : s) cnt[(int)c]++; name += s + ','; } while (not(cnt['('] == cnt[')'] && cnt['['] == cnt[']'] && cnt['{'] == cnt['}'] && cnt['\"'] % 2 == 0 && cnt['\''] % 2 == 0)); name.pop_back();//usuwamy ',' if (!_char_const(x)) { cerr << trim(name) << " = "; __echo(x, "; "); } __echo(stream, args...); } #define echo(...) if(DBG) {istringstream str(#__VA_ARGS__); __echo(str, __VA_ARGS__); } ///////////////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////////////// #define TESTSETS 0 #define DBG 0 constexpr int mod = int(1000'000'000 + 7); map<string, bool> ok; bool test(const string& s) { auto it = ok.find(s); if (it != ok.end()) return it->second; forx(i, 0, size(s) - 1) { if (s[i] == s[i + 1]) { string t = s.substr(0, i) + (s[i] == 'C' ? 'Z' : 'C') + s.substr(i + 2); if (test(t)) { ok[s] = true; return true; } } } ok[s] = false; return false; } int rnd(int a, int b) { return rand() % (b - a + 1) + a; } void brut_gen() { ok["C"] = ok["Z"] = true; int a = 3, b = 8; int n = 1; while (n < 20) { string s = string(n, '#'); forx(msk, 0, pow2(n)) { forx(b, 0, n) { s[b] = "CZ"[(msk & pow2(b)) == 0]; } int c = (int)count(all(s), 'C'); int z = n - c; bool git = test(s); if ((c - z) % 3 != 0 && !git) cout << s << ": " << git << "\n"; } n++; } } void solve_n_1(int n, int q, string s) { cout << 1 + (s[0] == 'N') << "\n"; while (q--) { int k; cin >> k >> s[0]; cout << 1 + (s[0] == 'N') << "\n"; } } void solve() { int n, q; string s; cin >> n >> q >> s; if (n == 1) { solve_n_1(n, q, s); return; } int cCZ = 0; //liczba dobrze ustawionych pozycji do ciagu CZCZCZCZC int cZC = 0; int free = 0; //liczba wolnych pozycji, czyli liczba czastek N int cntC = 0; int cntZ = 0; auto ok_CZ = [&](int idx, char value)->bool { if (idx % 2 == 0 && value != 'Z') return true; if (idx % 2 == 1 && value != 'C') return true; return false; }; auto ok_ZC = [&](int idx, char value)->bool { if (idx % 2 == 0 && value != 'C') return true; if (idx % 2 == 1 && value != 'Z') return true; return false; }; auto update_s = [&](int i, char c) { if (s[i] == c) return; // Na pozycje i wpisz znak c // i zaktualizuj info o CZCZC... i ZCZCZ... if (ok_CZ(i, s[i]) && !ok_CZ(i, c)) cCZ--; if (!ok_CZ(i, s[i]) && ok_CZ(i, c)) cCZ++; if (ok_ZC(i, s[i]) && !ok_ZC(i, c)) cZC--; if (!ok_ZC(i, s[i]) && ok_ZC(i, c)) cZC++; // oraz o ilosci N (free), Z (cntZ), C (cntC) if (s[i] == 'N') free--; if (s[i] == 'Z') cntZ--; if (s[i] == 'C') cntC--; if (c == 'N') free++; if (c == 'Z') cntZ++; if (c == 'C') cntC++; s[i] = c; }; forx(i, 0, n) { if (s[i] == 'N') free++; if (s[i] == 'Z') cntZ++; if (s[i] == 'C') cntC++; if (ok_CZ(i, s[i])) cCZ++; if (ok_ZC(i, s[i])) cZC++; } auto seqCZ = [&]() { return cCZ == n; };//czy da sie stworzyc ciag CZC... auto seqZC = [&]() { return cZC == n; }; // ------------- preprocessing [3][3] --------------- vector<int> p2mod(n + 42, 1); forx(i, 1, n + 42) p2mod[i] = (p2mod[i - 1] * 2ll) % mod; constexpr int inv3 = 333333336; constexpr int inv2 = 500000004; auto n1p = [&](int n) { return (n % 2 ? mod - 1 : 1); //(-1)^n modulo }; auto mmul = [&](int a, int b)->int { a %= mod; b %= mod; llong res = (((llong)a * b) % mod + mod) % mod; return res % mod; }; auto madd = [&](int a, int b)->int { a %= mod; b %= mod; return (((llong)a + b) % mod + mod) % mod; }; auto seq = [&](int N, int r) { int n = N / 3; //podloga int magic = 0; if (N % 3 == 0) { if (r % 3 == 0) { magic = mmul(inv3, madd(mmul(2, n1p(n)), p2mod[3 * n])); } else if (r % 3 == 1) { magic = mmul(inv3, madd(n1p(n + 1), p2mod[3 * n])); } else { magic = mmul(inv3, madd(n1p(n + 1), p2mod[3 * n])); } } else if (N % 3 == 1) { if (r % 3 == 0) { magic = mmul(inv3, madd(n1p(n), p2mod[3 * n + 1])); } else if (r % 3 == 1) { magic = mmul(inv3, madd(n1p(n), p2mod[3 * n + 1])); } else { magic = mmul(mmul(-2, inv3), madd(n1p(n), -p2mod[3 * n])); } } else { if (r % 3 == 0) { magic = mmul(inv3, madd(n1p(n + 1), p2mod[3 * n + 2])); } else if (r % 3 == 1) { magic = mmul(mmul(2, inv3), madd(n1p(n), p2mod[3 * n + 1])); } else { magic = mmul(inv3, madd(n1p(n + 1), p2mod[3 * n + 2])); } } if (DBG) echo(N, r, p2mod[N], magic); return madd(p2mod[N], -magic); }; auto good_seq = [&]()->int { if (free == 0) { // odpowiedz to zawsze 1 lub 0 return ((cntC - cntZ) % 3 != 0) && !seqCZ() && !seqZC(); } else { int bad_mod = (2 * (cntZ - cntC + free) % 3 + 3) % 3;// r (bad_mod) int special_combinations = (n % 2 == 1 ? seqCZ() + seqZC() : 0); //moze byc jednak dwie na raz (NNNN) int good_mod_combinations = seq(free, bad_mod); int ans = madd(good_mod_combinations, -special_combinations); return ans; } }; // -------------------- odpowiedzi na zapytania --------------------- int ans0 = good_seq(); cout << ans0 << "\n"; forx(query, 0, q) { int idx; char c; cin >> idx >> c; idx -= 1; update_s(idx, c); int ans = good_seq(); cout << ans << "\n"; } } int main() { ios::sync_with_stdio(0); cin.tie(0); int t = 1; if (TESTSETS) cin >> t; while (t--) solve(); } |