C++ Library for Competitive Programming
View the Project on GitHub emthrm/cp-library
#include "emthrm/string/wildcard_pattern_matching.hpp"
テキスト長を $N$、パターン長を $M$ とおくと $O((N + M)\log(N + M))$
template <typename T = std::string>
requires requires { typename T::value_type; }
std::vector<int> wildcard_pattern_matching(const T& t, const T& p, const typename T::value_type wildcard);
T[i:i+len(P)] = P
https://atcoder.jp/contests/abc307/submissions/43305941
#ifndef EMTHRM_STRING_WILDCARD_PATTERN_MATCHING_HPP_ #define EMTHRM_STRING_WILDCARD_PATTERN_MATCHING_HPP_ #include <algorithm> #include <cassert> #include <map> #include <numeric> #include <string> #include <tuple> #include <vector> #include "emthrm/math/convolution/number_theoretic_transform.hpp" namespace emthrm { template <typename T = std::string> requires requires { typename T::value_type; } std::vector<int> wildcard_pattern_matching( const T& text, const T& pattern, const typename T::value_type wildcard) { if (text.size() < pattern.size()) [[unlikely]] return {}; const auto generate = [wildcard](const T& str) -> std::tuple<std::vector<long long>, std::vector<long long>, std::vector<long long>> { using Char = T::value_type; static std::map<Char, int> characters{{wildcard, 0}}; std::vector<long long> v1(str.size()); std::ranges::transform( str, v1.begin(), [](const Char c) -> int { if (const auto it = characters.find(c); it != characters.end()) { return it->second; } const int next_index = characters.size(); assert(characters.emplace(c, next_index).second); return next_index; }); std::vector<long long> v2 = v1; std::ranges::transform( v2, v2.begin(), [](const long long ch) -> long long { return ch * ch; }); std::vector<long long> v3 = v1; std::ranges::transform( v3, v3.begin(), [](const long long ch) -> long long { return ch * ch * ch; }); return {v1, v2, v3}; }; const auto [t1, t2, t3] = generate(text); auto [p1, p2, p3] = generate(pattern); std::ranges::reverse(p1); std::ranges::reverse(p2); std::ranges::reverse(p3); const int l = text.size() - pattern.size() + 1; std::vector<int> ans(l); std::iota(ans.begin(), ans.end(), 0); const auto check = [&pattern, &t1, &t2, &t3, &p1, &p2, &p3, l, &ans] <unsigned int M>(NumberTheoreticTransform<M> ntt) -> void { using ModInt = NumberTheoreticTransform<M>::ModInt; static const int offset = pattern.size() - 1; const std::vector<ModInt> t3p1 = ntt.convolution(t3, p1); const std::vector<ModInt> t2p2 = ntt.convolution(t2, p2); const std::vector<ModInt> t1p3 = ntt.convolution(t1, p3); std::vector<int> next_ans; next_ans.reserve(ans.size()); for (const int i : ans) { const ModInt wmatch = t3p1[i + offset] - t2p2[i + offset] * ModInt::raw(2) + t1p3[i + offset]; if (wmatch == 0) next_ans.emplace_back(i); } ans.swap(next_ans); }; check(NumberTheoreticTransform<998244353>()); check(NumberTheoreticTransform<1004535809>()); check(NumberTheoreticTransform<1007681537>()); return ans; } } // namespace emthrm #endif // EMTHRM_STRING_WILDCARD_PATTERN_MATCHING_HPP_
#line 1 "include/emthrm/string/wildcard_pattern_matching.hpp" #include <algorithm> #include <cassert> #include <map> #include <numeric> #include <string> #include <tuple> #include <vector> #line 1 "include/emthrm/math/convolution/number_theoretic_transform.hpp" #if __has_include(<atcoder/convolution>) # include <atcoder/convolution> # include <atcoder/modint> #else #line 9 "include/emthrm/math/convolution/number_theoretic_transform.hpp" # include <bit> #line 11 "include/emthrm/math/convolution/number_theoretic_transform.hpp" # include <iterator> #line 13 "include/emthrm/math/convolution/number_theoretic_transform.hpp" # include <utility> #endif #line 16 "include/emthrm/math/convolution/number_theoretic_transform.hpp" #line 1 "include/emthrm/math/modint.hpp" #ifndef ARBITRARY_MODINT #line 6 "include/emthrm/math/modint.hpp" #endif #include <compare> #include <iostream> // #include <numeric> #include <utility> #line 12 "include/emthrm/math/modint.hpp" namespace emthrm { #ifndef ARBITRARY_MODINT template <unsigned int M> struct MInt { unsigned int v; constexpr MInt() : v(0) {} constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {} static constexpr MInt raw(const int x) { MInt x_; x_.v = x; return x_; } static constexpr int get_mod() { return M; } static constexpr void set_mod(const int divisor) { assert(std::cmp_equal(divisor, M)); } static void init(const int x) { inv<true>(x); fact(x); fact_inv(x); } template <bool MEMOIZES = false> static MInt inv(const int n) { // assert(0 <= n && n < M && std::gcd(n, M) == 1); static std::vector<MInt> inverse{0, 1}; const int prev = inverse.size(); if (n < prev) return inverse[n]; if constexpr (MEMOIZES) { // "n!" and "M" must be disjoint. inverse.resize(n + 1); for (int i = prev; i <= n; ++i) { inverse[i] = -inverse[M % i] * raw(M / i); } return inverse[n]; } int u = 1, v = 0; for (unsigned int a = n, b = M; b;) { const unsigned int q = a / b; std::swap(a -= q * b, b); std::swap(u -= q * v, v); } return u; } static MInt fact(const int n) { static std::vector<MInt> factorial{1}; if (const int prev = factorial.size(); n >= prev) { factorial.resize(n + 1); for (int i = prev; i <= n; ++i) { factorial[i] = factorial[i - 1] * i; } } return factorial[n]; } static MInt fact_inv(const int n) { static std::vector<MInt> f_inv{1}; if (const int prev = f_inv.size(); n >= prev) { f_inv.resize(n + 1); f_inv[n] = inv(fact(n).v); for (int i = n; i > prev; --i) { f_inv[i - 1] = f_inv[i] * i; } } return f_inv[n]; } static MInt nCk(const int n, const int k) { if (n < 0 || n < k || k < 0) [[unlikely]] return MInt(); return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) : fact_inv(n - k) * fact_inv(k)); } static MInt nPk(const int n, const int k) { return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k); } static MInt nHk(const int n, const int k) { return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k)); } static MInt large_nCk(long long n, const int k) { if (n < 0 || n < k || k < 0) [[unlikely]] return MInt(); inv<true>(k); MInt res = 1; for (int i = 1; i <= k; ++i) { res *= inv(i) * n--; } return res; } constexpr MInt pow(long long exponent) const { MInt res = 1, tmp = *this; for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } constexpr MInt& operator+=(const MInt& x) { if ((v += x.v) >= M) v -= M; return *this; } constexpr MInt& operator-=(const MInt& x) { if ((v += M - x.v) >= M) v -= M; return *this; } constexpr MInt& operator*=(const MInt& x) { v = (unsigned long long){v} * x.v % M; return *this; } MInt& operator/=(const MInt& x) { return *this *= inv(x.v); } constexpr auto operator<=>(const MInt& x) const = default; constexpr MInt& operator++() { if (++v == M) [[unlikely]] v = 0; return *this; } constexpr MInt operator++(int) { const MInt res = *this; ++*this; return res; } constexpr MInt& operator--() { v = (v == 0 ? M - 1 : v - 1); return *this; } constexpr MInt operator--(int) { const MInt res = *this; --*this; return res; } constexpr MInt operator+() const { return *this; } constexpr MInt operator-() const { return raw(v ? M - v : 0); } constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; } constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; } constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; } MInt operator/(const MInt& x) const { return MInt(*this) /= x; } friend std::ostream& operator<<(std::ostream& os, const MInt& x) { return os << x.v; } friend std::istream& operator>>(std::istream& is, MInt& x) { long long v; is >> v; x = MInt(v); return is; } }; #else // ARBITRARY_MODINT template <int ID> struct MInt { unsigned int v; constexpr MInt() : v(0) {} MInt(const long long x) : v(x >= 0 ? x % mod() : x % mod() + mod()) {} static constexpr MInt raw(const int x) { MInt x_; x_.v = x; return x_; } static int get_mod() { return mod(); } static void set_mod(const unsigned int divisor) { mod() = divisor; } static void init(const int x) { inv<true>(x); fact(x); fact_inv(x); } template <bool MEMOIZES = false> static MInt inv(const int n) { // assert(0 <= n && n < mod() && std::gcd(x, mod()) == 1); static std::vector<MInt> inverse{0, 1}; const int prev = inverse.size(); if (n < prev) return inverse[n]; if constexpr (MEMOIZES) { // "n!" and "M" must be disjoint. inverse.resize(n + 1); for (int i = prev; i <= n; ++i) { inverse[i] = -inverse[mod() % i] * raw(mod() / i); } return inverse[n]; } int u = 1, v = 0; for (unsigned int a = n, b = mod(); b;) { const unsigned int q = a / b; std::swap(a -= q * b, b); std::swap(u -= q * v, v); } return u; } static MInt fact(const int n) { static std::vector<MInt> factorial{1}; if (const int prev = factorial.size(); n >= prev) { factorial.resize(n + 1); for (int i = prev; i <= n; ++i) { factorial[i] = factorial[i - 1] * i; } } return factorial[n]; } static MInt fact_inv(const int n) { static std::vector<MInt> f_inv{1}; if (const int prev = f_inv.size(); n >= prev) { f_inv.resize(n + 1); f_inv[n] = inv(fact(n).v); for (int i = n; i > prev; --i) { f_inv[i - 1] = f_inv[i] * i; } } return f_inv[n]; } static MInt nCk(const int n, const int k) { if (n < 0 || n < k || k < 0) [[unlikely]] return MInt(); return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) : fact_inv(n - k) * fact_inv(k)); } static MInt nPk(const int n, const int k) { return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k); } static MInt nHk(const int n, const int k) { return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k)); } static MInt large_nCk(long long n, const int k) { if (n < 0 || n < k || k < 0) [[unlikely]] return MInt(); inv<true>(k); MInt res = 1; for (int i = 1; i <= k; ++i) { res *= inv(i) * n--; } return res; } MInt pow(long long exponent) const { MInt res = 1, tmp = *this; for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } MInt& operator+=(const MInt& x) { if ((v += x.v) >= mod()) v -= mod(); return *this; } MInt& operator-=(const MInt& x) { if ((v += mod() - x.v) >= mod()) v -= mod(); return *this; } MInt& operator*=(const MInt& x) { v = (unsigned long long){v} * x.v % mod(); return *this; } MInt& operator/=(const MInt& x) { return *this *= inv(x.v); } auto operator<=>(const MInt& x) const = default; MInt& operator++() { if (++v == mod()) [[unlikely]] v = 0; return *this; } MInt operator++(int) { const MInt res = *this; ++*this; return res; } MInt& operator--() { v = (v == 0 ? mod() - 1 : v - 1); return *this; } MInt operator--(int) { const MInt res = *this; --*this; return res; } MInt operator+() const { return *this; } MInt operator-() const { return raw(v ? mod() - v : 0); } MInt operator+(const MInt& x) const { return MInt(*this) += x; } MInt operator-(const MInt& x) const { return MInt(*this) -= x; } MInt operator*(const MInt& x) const { return MInt(*this) *= x; } MInt operator/(const MInt& x) const { return MInt(*this) /= x; } friend std::ostream& operator<<(std::ostream& os, const MInt& x) { return os << x.v; } friend std::istream& operator>>(std::istream& is, MInt& x) { long long v; is >> v; x = MInt(v); return is; } private: static unsigned int& mod() { static unsigned int divisor = 0; return divisor; } }; #endif // ARBITRARY_MODINT } // namespace emthrm #line 18 "include/emthrm/math/convolution/number_theoretic_transform.hpp" namespace emthrm { #if __has_include(<atcoder/convolution>) template <unsigned int T> struct NumberTheoreticTransform { using ModInt = MInt<T>; NumberTheoreticTransform() = default; template <typename U> std::vector<ModInt> dft(const std::vector<U>& a); void idft(std::vector<ModInt>* a); template <typename U> std::vector<ModInt> convolution( const std::vector<U>& a, const std::vector<U>& b) const { const int a_size = a.size(), b_size = b.size(); std::vector<atcoder::static_modint<T>> c(a_size), d(b_size); for (int i = 0; i < a_size; ++i) { c[i] = atcoder::static_modint<T>::raw(ModInt(a[i]).v); } for (int i = 0; i < b_size; ++i) { d[i] = atcoder::static_modint<T>::raw(ModInt(b[i]).v); } c = atcoder::convolution(c, d); const int c_size = c.size(); std::vector<ModInt> res(c_size); for (int i = 0; i < c_size; ++i) { res[i] = ModInt::raw(c[i].val()); } return res; } }; #else // __has_include(<atcoder/convolution>) template <unsigned int T> struct NumberTheoreticTransform { using ModInt = MInt<T>; NumberTheoreticTransform() : n_max(1 << init().first), root(ModInt::raw(init().second)) {} template <typename U> std::vector<ModInt> dft(const std::vector<U>& a) { std::vector<ModInt> b(std::bit_ceil(a.size()), 0); std::ranges::copy(a, b.begin()); calc(&b); return b; } void idft(std::vector<ModInt>* a) { assert(std::has_single_bit(a->size())); calc(a); std::reverse(std::next(a->begin()), a->end()); const int n = a->size(); const ModInt inv_n = ModInt::inv(n); for (int i = 0; i < n; ++i) { (*a)[i] *= inv_n; } } template <typename U> std::vector<ModInt> convolution( const std::vector<U>& a, const std::vector<U>& b) { const int a_size = a.size(), b_size = b.size(); const int c_size = a_size + b_size - 1; if (std::min(a_size, b_size) <= 60) { std::vector<ModInt> c(c_size, 0); if (a_size > b_size) { for (int i = 0; i < a_size; ++i) { for (int j = 0; j < b_size; ++j) { c[i + j] += ModInt(a[i]) * b[j]; } } } else { for (int j = 0; j < b_size; ++j) { for (int i = 0; i < a_size; ++i) { c[i + j] += ModInt(b[j]) * a[i]; } } } return c; } const int n = std::bit_ceil(static_cast<unsigned int>(c_size)); std::vector<ModInt> c(n, 0), d(n, 0); std::ranges::copy(a, c.begin()); calc(&c); std::ranges::copy(b, d.begin()); calc(&d); for (int i = 0; i < n; ++i) { c[i] *= d[i]; } idft(&c); c.resize(c_size); return c; } private: static std::pair<int, int> init() { static const std::map<int, std::pair<int, int>> primes{ {16957441, {14, 102066830}}, // 329 {17006593, {15, 608991743}}, // 26 {19529729, {17, 927947839}}, // 770 {167772161, {25, 243}}, // 3 {469762049, {26, 2187}}, // 3 {645922817, {23, 680782677}}, // 3 {897581057, {23, 126991183}}, // 3 {924844033, {21, 480100938}}, // 5 {935329793, {22, 945616399}}, // 3 {943718401, {22, 39032610}}, // 7 {950009857, {21, 912960248}}, // 7 {962592769, {21, 762567211}}, // 7 {975175681, {21, 973754139}}, // 17 {976224257, {20, 168477898}}, // 3 {985661441, {22, 157780640}}, // 3 {998244353, {23, 15311432}}, // 3 {1004535809, {21, 840453100}}, // 3 {1007681537, {20, 283888334}}, // 3 {1012924417, {21, 428116421}}, // 5 {1045430273, {20, 328125745}}, // 3 {1051721729, {20, 234350985}}, // 6 {1053818881, {20, 309635616}}, // 7 {1224736769, {24, 304180829}}}; // 3 return primes.at(T); } const int n_max; const ModInt root; std::vector<int> butterfly{0}; std::vector<std::vector<ModInt>> omega{{1}}; void calc(std::vector<ModInt>* a) { const int n = a->size(), prev_n = butterfly.size(); if (n > prev_n) { assert(n <= n_max); butterfly.resize(n); const int prev_lg = omega.size(), lg = std::countr_zero(a->size()); for (int i = 1; i < prev_n; ++i) { butterfly[i] <<= lg - prev_lg; } for (int i = prev_n; i < n; ++i) { butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1)); } omega.resize(lg); for (int i = prev_lg; i < lg; ++i) { omega[i].resize(1 << i); const ModInt tmp = root.pow((ModInt::get_mod() - 1) >> (i + 1)); for (int j = 0; j < (1 << (i - 1)); ++j) { omega[i][j << 1] = omega[i - 1][j]; omega[i][(j << 1) + 1] = omega[i - 1][j] * tmp; } } } const int shift = std::countr_zero(butterfly.size()) - std::countr_zero(a->size()); for (int i = 0; i < n; ++i) { const int j = butterfly[i] >> shift; if (i < j) std::swap((*a)[i], (*a)[j]); } for (int block = 1, den = 0; block < n; block <<= 1, ++den) { for (int i = 0; i < n; i += (block << 1)) { for (int j = 0; j < block; ++j) { const ModInt tmp = (*a)[i + j + block] * omega[den][j]; (*a)[i + j + block] = (*a)[i + j] - tmp; (*a)[i + j] += tmp; } } } } }; #endif // __has_include(<atcoder/convolution>) } // namespace emthrm #line 13 "include/emthrm/string/wildcard_pattern_matching.hpp" namespace emthrm { template <typename T = std::string> requires requires { typename T::value_type; } std::vector<int> wildcard_pattern_matching( const T& text, const T& pattern, const typename T::value_type wildcard) { if (text.size() < pattern.size()) [[unlikely]] return {}; const auto generate = [wildcard](const T& str) -> std::tuple<std::vector<long long>, std::vector<long long>, std::vector<long long>> { using Char = T::value_type; static std::map<Char, int> characters{{wildcard, 0}}; std::vector<long long> v1(str.size()); std::ranges::transform( str, v1.begin(), [](const Char c) -> int { if (const auto it = characters.find(c); it != characters.end()) { return it->second; } const int next_index = characters.size(); assert(characters.emplace(c, next_index).second); return next_index; }); std::vector<long long> v2 = v1; std::ranges::transform( v2, v2.begin(), [](const long long ch) -> long long { return ch * ch; }); std::vector<long long> v3 = v1; std::ranges::transform( v3, v3.begin(), [](const long long ch) -> long long { return ch * ch * ch; }); return {v1, v2, v3}; }; const auto [t1, t2, t3] = generate(text); auto [p1, p2, p3] = generate(pattern); std::ranges::reverse(p1); std::ranges::reverse(p2); std::ranges::reverse(p3); const int l = text.size() - pattern.size() + 1; std::vector<int> ans(l); std::iota(ans.begin(), ans.end(), 0); const auto check = [&pattern, &t1, &t2, &t3, &p1, &p2, &p3, l, &ans] <unsigned int M>(NumberTheoreticTransform<M> ntt) -> void { using ModInt = NumberTheoreticTransform<M>::ModInt; static const int offset = pattern.size() - 1; const std::vector<ModInt> t3p1 = ntt.convolution(t3, p1); const std::vector<ModInt> t2p2 = ntt.convolution(t2, p2); const std::vector<ModInt> t1p3 = ntt.convolution(t1, p3); std::vector<int> next_ans; next_ans.reserve(ans.size()); for (const int i : ans) { const ModInt wmatch = t3p1[i + offset] - t2p2[i + offset] * ModInt::raw(2) + t1p3[i + offset]; if (wmatch == 0) next_ans.emplace_back(i); } ans.swap(next_ans); }; check(NumberTheoreticTransform<998244353>()); check(NumberTheoreticTransform<1004535809>()); check(NumberTheoreticTransform<1007681537>()); return ans; } } // namespace emthrm