C++ Library for Competitive Programming
View the Project on GitHub emthrm/cp-library
/* * @title グラフ/フロー/マッチング/一般グラフの最大マッチング * * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3032 */ #include <cmath> #include <iostream> #include <vector> #include "emthrm/graph/flow/matching/maximum_matching.hpp" int main() { int n, a, b; std::cin >> n >> a >> b; int ans = 0; std::vector<int> as, bs; while (n--) { int a_i, b_i; std::cin >> a_i >> b_i; const int x = std::abs(a_i - b_i); if (x <= a || (b <= x && x <= 2 * a)) { ++ans; } else { as.emplace_back(a_i); bs.emplace_back(b_i); } } n = as.size(); if (n > 0) { std::vector<std::vector<int>> graph(n); for (int i = 0; i < n; ++i) { for (int j = i + 1; j < n; ++j) { const int x = std::abs((as[i] + as[j]) - (bs[i] + bs[j])); if (x <= a || (b <= x && x <= 2 * a)) { graph[i].emplace_back(j); graph[j].emplace_back(i); } } } ans += emthrm::maximum_matching(graph); } std::cout << ans << '\n'; return 0; }
#line 1 "test/graph/flow/matching/maximum_matching.test.cpp" /* * @title グラフ/フロー/マッチング/一般グラフの最大マッチング * * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3032 */ #include <cmath> #include <iostream> #include <vector> #line 1 "include/emthrm/graph/flow/matching/maximum_matching.hpp" #include <random> #line 6 "include/emthrm/graph/flow/matching/maximum_matching.hpp" #line 1 "include/emthrm/math/matrix/gauss_jordan.hpp" #include <utility> #line 1 "include/emthrm/math/matrix/matrix.hpp" #line 5 "include/emthrm/math/matrix/matrix.hpp" namespace emthrm { template <typename T> struct Matrix { explicit Matrix(const int m, const int n, const T def = 0) : data(m, std::vector<T>(n, def)) {} int nrow() const { return data.size(); } int ncol() const { return data.empty() ? 0 : data.front().size(); } Matrix pow(long long exponent) const { const int n = nrow(); Matrix<T> res(n, n, 0), tmp = *this; for (int i = 0; i < n; ++i) { res[i][i] = 1; } for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } inline const std::vector<T>& operator[](const int i) const { return data[i]; } inline std::vector<T>& operator[](const int i) { return data[i]; } Matrix& operator=(const Matrix& x) = default; Matrix& operator+=(const Matrix& x) { const int m = nrow(), n = ncol(); for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { data[i][j] += x[i][j]; } } return *this; } Matrix& operator-=(const Matrix& x) { const int m = nrow(), n = ncol(); for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { data[i][j] -= x[i][j]; } } return *this; } Matrix& operator*=(const Matrix& x) { const int m = nrow(), l = ncol(), n = x.ncol(); std::vector<std::vector<T>> res(m, std::vector<T>(n, 0)); for (int i = 0; i < m; ++i) { for (int k = 0; k < l; ++k) { for (int j = 0; j < n; ++j) { res[i][j] += data[i][k] * x[k][j]; } } } data.swap(res); return *this; } Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; } Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; } Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; } private: std::vector<std::vector<T>> data; }; } // namespace emthrm #line 7 "include/emthrm/math/matrix/gauss_jordan.hpp" namespace emthrm { template <bool IS_EXTENDED = false, typename T> int gauss_jordan(Matrix<T>* a, const T eps = 1e-8) { const int m = a->nrow(), n = a->ncol(); int rank = 0; for (int col = 0; col < (IS_EXTENDED ? n - 1 : n); ++col) { int pivot = -1; T mx = eps; for (int row = rank; row < m; ++row) { const T abs = ((*a)[row][col] < 0 ? -(*a)[row][col] : (*a)[row][col]); if (abs > mx) { pivot = row; mx = abs; } } if (pivot == -1) continue; std::swap((*a)[rank], (*a)[pivot]); T tmp = (*a)[rank][col]; for (int col2 = 0; col2 < n; ++col2) { (*a)[rank][col2] /= tmp; } for (int row = 0; row < m; ++row) { if (row != rank && ((*a)[row][col] < 0 ? -(*a)[row][col] : (*a)[row][col]) > eps) { tmp = (*a)[row][col]; for (int col2 = 0; col2 < n; ++col2) { (*a)[row][col2] -= (*a)[rank][col2] * tmp; } } } ++rank; } return rank; } } // namespace emthrm #line 1 "include/emthrm/math/modint.hpp" #ifndef ARBITRARY_MODINT # include <cassert> #endif #include <compare> #line 9 "include/emthrm/math/modint.hpp" // #include <numeric> #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 10 "include/emthrm/graph/flow/matching/maximum_matching.hpp" namespace emthrm { int maximum_matching(const std::vector<std::vector<int>>& graph) { constexpr unsigned int P = 1000000007; using ModInt = MInt<P>; ModInt::set_mod(P); static std::mt19937_64 engine(std::random_device {} ()); static std::uniform_int_distribution<> dist(1, P - 1); const int n = graph.size(); Matrix<ModInt> tutte_matrix(n, n, 0); for (int i = 0; i < n; ++i) { for (const int j : graph[i]) { if (j > i) { const ModInt x = ModInt::raw(dist(engine)); tutte_matrix[i][j] = x; tutte_matrix[j][i] = -x; } } } return gauss_jordan(&tutte_matrix, ModInt(0)) / 2; } } // namespace emthrm #line 12 "test/graph/flow/matching/maximum_matching.test.cpp" int main() { int n, a, b; std::cin >> n >> a >> b; int ans = 0; std::vector<int> as, bs; while (n--) { int a_i, b_i; std::cin >> a_i >> b_i; const int x = std::abs(a_i - b_i); if (x <= a || (b <= x && x <= 2 * a)) { ++ans; } else { as.emplace_back(a_i); bs.emplace_back(b_i); } } n = as.size(); if (n > 0) { std::vector<std::vector<int>> graph(n); for (int i = 0; i < n; ++i) { for (int j = i + 1; j < n; ++j) { const int x = std::abs((as[i] + as[j]) - (bs[i] + bs[j])); if (x <= a || (b <= x && x <= 2 * a)) { graph[i].emplace_back(j); graph[j].emplace_back(i); } } } ans += emthrm::maximum_matching(graph); } std::cout << ans << '\n'; return 0; }