C++ Library for Competitive Programming
View the Project on GitHub emthrm/cp-library
/* * @title 数学/基底 * * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2416 */ #include <bitset> #include <iostream> #include <vector> #include "emthrm/graph/edge.hpp" #include "emthrm/math/basis.hpp" int main() { constexpr int D = 60; int n, m, q; std::cin >> n >> m >> q; std::vector<std::vector<emthrm::Edge<long long>>> graph(n); while (m--) { int f, t; long long p; std::cin >> f >> t >> p; graph[f].emplace_back(f, t, p); graph[t].emplace_back(t, f, p); } std::vector<long long> x(n, -1); x[0] = 0; emthrm::Basis<D> basis; const auto dfs = [&graph, &x, &basis](auto dfs, const int par, const int ver) -> void { for (const emthrm::Edge<long long>& e : graph[ver]) { if (e.dst != par) { if (x[e.dst] == -1) { x[e.dst] = x[ver] ^ e.cost; dfs(dfs, ver, e.dst); } else { basis.add(x[ver] ^ x[e.dst] ^ e.cost); } } } }; dfs(dfs, -1, 0); while (q--) { int a, b; std::cin >> a >> b; std::bitset<D> ans(x[a] ^ x[b]); for (int i = 0; i < basis.rank(); ++i) { if (!ans[basis.msb[i]]) ans ^= basis.v[i]; } std::cout << ans.to_ulong() << '\n'; } return 0; }
#line 1 "test/math/basis.test.cpp" /* * @title 数学/基底 * * verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2416 */ #include <bitset> #include <iostream> #include <vector> #line 1 "include/emthrm/graph/edge.hpp" /** * @title 辺 */ #ifndef EMTHRM_GRAPH_EDGE_HPP_ #define EMTHRM_GRAPH_EDGE_HPP_ #include <compare> namespace emthrm { template <typename CostType> struct Edge { CostType cost; int src, dst; explicit Edge(const int src, const int dst, const CostType cost = 0) : cost(cost), src(src), dst(dst) {} auto operator<=>(const Edge& x) const = default; }; } // namespace emthrm #endif // EMTHRM_GRAPH_EDGE_HPP_ #line 1 "include/emthrm/math/basis.hpp" #include <algorithm> #line 6 "include/emthrm/math/basis.hpp" #include <iterator> #line 8 "include/emthrm/math/basis.hpp" namespace emthrm { template <int D> struct Basis { std::vector<std::bitset<D>> v; std::vector<int> msb; Basis() = default; bool add(std::bitset<D> val) { const int n = rank(); if (n == D) return false; for (int i = 0; i < n; ++i) { if (val[msb[i]]) val ^= v[i]; } if (val.none()) return false; int m = D - 1; while (!val[m]) --m; if (v.empty()) [[unlikely]] { v.emplace_back(val); msb.emplace_back(m); return true; } const int idx = std::distance(std::upper_bound(msb.rbegin(), msb.rend(), m), msb.rend()); v.emplace(std::next(v.begin(), idx), val); msb.emplace(std::next(msb.begin(), idx), m); for (int i = idx + 1; i <= n; ++i) { if (v[idx][msb[i]]) v[idx] ^= v[i]; } for (int i = idx - 1; i >= 0; --i) { if (v[i][m]) v[i] ^= v[idx]; } return true; } int rank() const { return v.size(); } inline bool operator<(const Basis& x) const { const int n = v.size(); if (n != x.rank()) return n < x.rank(); if (n == D) return false; for (int i = 0; i < n; ++i) { if (msb[i] != x.msb[i]) return msb[i] < x.msb[i]; } for (int i = 0; i < n; ++i) { for (int j = msb[i] - 1; ; --j) { if (v[i][j] != x.v[i][j]) return x.v[i][j]; } } return false; } }; } // namespace emthrm #line 13 "test/math/basis.test.cpp" int main() { constexpr int D = 60; int n, m, q; std::cin >> n >> m >> q; std::vector<std::vector<emthrm::Edge<long long>>> graph(n); while (m--) { int f, t; long long p; std::cin >> f >> t >> p; graph[f].emplace_back(f, t, p); graph[t].emplace_back(t, f, p); } std::vector<long long> x(n, -1); x[0] = 0; emthrm::Basis<D> basis; const auto dfs = [&graph, &x, &basis](auto dfs, const int par, const int ver) -> void { for (const emthrm::Edge<long long>& e : graph[ver]) { if (e.dst != par) { if (x[e.dst] == -1) { x[e.dst] = x[ver] ^ e.cost; dfs(dfs, ver, e.dst); } else { basis.add(x[ver] ^ x[e.dst] ^ e.cost); } } } }; dfs(dfs, -1, 0); while (q--) { int a, b; std::cin >> a >> b; std::bitset<D> ans(x[a] ^ x[b]); for (int i = 0; i < basis.rank(); ++i) { if (!ans[basis.msb[i]]) ans ^= basis.v[i]; } std::cout << ans.to_ulong() << '\n'; } return 0; }