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#include "random/random_graph.hpp"

#include "graph/base.hpp" #include "random/base.hpp" #include "random/shuffle.hpp" #include "ds/unionfind/unionfind.hpp" void random_relabel(int N, vc<pair<int, int>>& G) { shuffle(G); vc<int> A(N); FOR(i, N) A[i] = i; shuffle(A); for (auto& [a, b]: G) a = A[a], b = A[b]; } template <int DIRECTED> vc<pair<int, int>> random_graph(int n, bool simple) { vc<pair<int, int>> G, cand; FOR(a, n) FOR(b, n) { if (simple && a == b) continue; if (!DIRECTED && a > b) continue; cand.eb(a, b); } int m = RNG(0, len(cand) + 1); set<int> ss; FOR(m) { while (1) { int i = RNG(0, len(cand)); if (simple && ss.count(i)) continue; ss.insert(i); auto [a, b] = cand[i]; G.eb(a, b); break; } } random_relabel(n, G); return G; } vc<pair<int, int>> random_tree(int n) { vc<pair<int, int>> G; FOR(i, 1, n) { G.eb(RNG(0, i), i); } random_relabel(n, G); return G; } // EDGE = true: 各辺が唯一のサイクル（関節点でサイクルまたは辺） // EDGE = false： 各頂点が唯一のサイクル（橋でサイクルまたは辺） vc<pair<int, int>> random_cactus(int N, bool EDGE) { if (!EDGE) { // n 頂点を 1 または 3 以上に分割 vvc<int> A; int n = RNG(1, N + 1); vc<int> S(n, 1); int rest = N - n; while (rest > 0) { int k = RNG(0, n); if (S[k] == 1) { if (rest == 1) { S.eb(1), rest = 0; } else { S[k] += 2, rest -= 2; } } else { S[k]++, rest--; } } n = len(S); int p = 0; FOR(i, n) { vc<int> C; FOR(v, p, p + S[i]) C.eb(v); A.eb(C); p += S[i]; } int m = len(A); auto H = random_tree(m); vc<pair<int, int>> G; FOR(i, m) { vc<int>& V = A[i]; if (len(V) == 1) continue; FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); } } for (auto& [c1, c2]: H) { int a = A[c1][RNG(0, len(A[c1]))]; int b = A[c2][RNG(0, len(A[c2]))]; G.eb(a, b); } random_relabel(N, G); return G; } assert(EDGE); if (N == 1) return {}; int n = RNG(1, N); vc<int> S(n, 2); int rest = N - 1 - n; while (rest > 0) { int k = RNG(0, n); S[k]++, --rest; } vvc<int> A; int p = 0; FOR(i, n) { vc<int> C; FOR(v, p, p + S[i]) C.eb(v); A.eb(C); p += S[i]; } assert(p == N + n - 1); UnionFind uf(p); auto H = random_tree(n); for (auto& [c1, c2]: H) { int a = A[c1][RNG(0, len(A[c1]))]; int b = A[c2][RNG(0, len(A[c2]))]; uf.merge(a, b); } vc<int> new_idx(p); int x = 0; FOR(i, p) if (uf[i] == i) new_idx[i] = x++; assert(x == N); FOR(i, p) new_idx[i] = new_idx[uf[i]]; vc<pair<int, int>> G; FOR(i, n) { vc<int>& V = A[i]; for (auto& v: V) v = new_idx[v]; if (len(V) == 2) { G.eb(V[0], V[1]); } else { FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); } } } random_relabel(N, G); return G; }

#line 2 "graph/base.hpp" template <typename T> struct Edge { int frm, to; T cost; int id; }; template <typename T = int, bool directed = false> struct Graph { static constexpr bool is_directed = directed; int N, M; using cost_type = T; using edge_type = Edge<T>; vector<edge_type> edges; vector<int> indptr; vector<edge_type> csr_edges; vc<int> vc_deg, vc_indeg, vc_outdeg; bool prepared; class OutgoingEdges { public: OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {} const edge_type* begin() const { if (l == r) { return 0; } return &G->csr_edges[l]; } const edge_type* end() const { if (l == r) { return 0; } return &G->csr_edges[r]; } private: const Graph* G; int l, r; }; bool is_prepared() { return prepared; } Graph() : N(0), M(0), prepared(0) {} Graph(int N) : N(N), M(0), prepared(0) {} void build(int n) { N = n, M = 0; prepared = 0; edges.clear(); indptr.clear(); csr_edges.clear(); vc_deg.clear(); vc_indeg.clear(); vc_outdeg.clear(); } void add(int frm, int to, T cost = 1, int i = -1) { assert(!prepared); assert(0 <= frm && 0 <= to && to < N); if (i == -1) i = M; auto e = edge_type({frm, to, cost, i}); edges.eb(e); ++M; } #ifdef FASTIO // wt, off void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); } void read_graph(int M, bool wt = false, int off = 1) { for (int m = 0; m < M; ++m) { INT(a, b); a -= off, b -= off; if (!wt) { add(a, b); } else { T c; read(c); add(a, b, c); } } build(); } #endif void build() { assert(!prepared); prepared = true; indptr.assign(N + 1, 0); for (auto&& e: edges) { indptr[e.frm + 1]++; if (!directed) indptr[e.to + 1]++; } for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; } auto counter = indptr; csr_edges.resize(indptr.back() + 1); for (auto&& e: edges) { csr_edges[counter[e.frm]++] = e; if (!directed) csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id}); } } OutgoingEdges operator[](int v) const { assert(prepared); return {this, indptr[v], indptr[v + 1]}; } vc<int> deg_array() { if (vc_deg.empty()) calc_deg(); return vc_deg; } pair<vc<int>, vc<int>> deg_array_inout() { if (vc_indeg.empty()) calc_deg_inout(); return {vc_indeg, vc_outdeg}; } int deg(int v) { if (vc_deg.empty()) calc_deg(); return vc_deg[v]; } int in_deg(int v) { if (vc_indeg.empty()) calc_deg_inout(); return vc_indeg[v]; } int out_deg(int v) { if (vc_outdeg.empty()) calc_deg_inout(); return vc_outdeg[v]; } #ifdef FASTIO void debug() { print("Graph"); if (!prepared) { print("frm to cost id"); for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id); } else { print("indptr", indptr); print("frm to cost id"); FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id); } } #endif vc<int> new_idx; vc<bool> used_e; // G における頂点 V[i] が、新しいグラフで i になるようにする // {G, es} Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) { if (len(new_idx) != N) new_idx.assign(N, -1); int n = len(V); FOR(i, n) new_idx[V[i]] = i; Graph<T, directed> G(n); vc<int> history; FOR(i, n) { for (auto&& e: (*this)[V[i]]) { if (len(used_e) <= e.id) used_e.resize(e.id + 1); if (used_e[e.id]) continue; int a = e.frm, b = e.to; if (new_idx[a] != -1 && new_idx[b] != -1) { history.eb(e.id); used_e[e.id] = 1; int eid = (keep_eid ? e.id : -1); G.add(new_idx[a], new_idx[b], e.cost, eid); } } } FOR(i, n) new_idx[V[i]] = -1; for (auto&& eid: history) used_e[eid] = 0; G.build(); return G; } private: void calc_deg() { assert(vc_deg.empty()); vc_deg.resize(N); for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++; } void calc_deg_inout() { assert(vc_indeg.empty()); vc_indeg.resize(N); vc_outdeg.resize(N); for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; } } }; #line 2 "random/base.hpp" u64 RNG_64() { static uint64_t x_ = uint64_t(chrono::duration_cast<chrono::nanoseconds>( chrono::high_resolution_clock::now().time_since_epoch()) .count()) * 10150724397891781847ULL; x_ ^= x_ << 7; return x_ ^= x_ >> 9; } u64 RNG(u64 lim) { return RNG_64() % lim; } ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); } #line 2 "random/shuffle.hpp" template <typename T> void shuffle(vc<T>& A) { FOR(i, len(A)) swap(A[i], A[RNG(0, i + 1)]); } #line 2 "ds/unionfind/unionfind.hpp" struct UnionFind { int n, n_comp; vc<int> dat; // par or (-size) UnionFind(int n = 0) { build(n); } void build(int m) { n = m, n_comp = m; dat.assign(n, -1); } void reset() { build(n); } int operator[](int x) { while (dat[x] >= 0) { int pp = dat[dat[x]]; if (pp < 0) { return dat[x]; } x = dat[x] = pp; } return x; } ll size(int x) { x = (*this)[x]; return -dat[x]; } bool merge(int x, int y) { x = (*this)[x], y = (*this)[y]; if (x == y) return false; if (-dat[x] < -dat[y]) swap(x, y); dat[x] += dat[y], dat[y] = x, n_comp--; return true; } vc<int> get_all() { vc<int> A(n); FOR(i, n) A[i] = (*this)[i]; return A; } }; #line 5 "random/random_graph.hpp" void random_relabel(int N, vc<pair<int, int>>& G) { shuffle(G); vc<int> A(N); FOR(i, N) A[i] = i; shuffle(A); for (auto& [a, b]: G) a = A[a], b = A[b]; } template <int DIRECTED> vc<pair<int, int>> random_graph(int n, bool simple) { vc<pair<int, int>> G, cand; FOR(a, n) FOR(b, n) { if (simple && a == b) continue; if (!DIRECTED && a > b) continue; cand.eb(a, b); } int m = RNG(0, len(cand) + 1); set<int> ss; FOR(m) { while (1) { int i = RNG(0, len(cand)); if (simple && ss.count(i)) continue; ss.insert(i); auto [a, b] = cand[i]; G.eb(a, b); break; } } random_relabel(n, G); return G; } vc<pair<int, int>> random_tree(int n) { vc<pair<int, int>> G; FOR(i, 1, n) { G.eb(RNG(0, i), i); } random_relabel(n, G); return G; } // EDGE = true: 各辺が唯一のサイクル（関節点でサイクルまたは辺） // EDGE = false： 各頂点が唯一のサイクル（橋でサイクルまたは辺） vc<pair<int, int>> random_cactus(int N, bool EDGE) { if (!EDGE) { // n 頂点を 1 または 3 以上に分割 vvc<int> A; int n = RNG(1, N + 1); vc<int> S(n, 1); int rest = N - n; while (rest > 0) { int k = RNG(0, n); if (S[k] == 1) { if (rest == 1) { S.eb(1), rest = 0; } else { S[k] += 2, rest -= 2; } } else { S[k]++, rest--; } } n = len(S); int p = 0; FOR(i, n) { vc<int> C; FOR(v, p, p + S[i]) C.eb(v); A.eb(C); p += S[i]; } int m = len(A); auto H = random_tree(m); vc<pair<int, int>> G; FOR(i, m) { vc<int>& V = A[i]; if (len(V) == 1) continue; FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); } } for (auto& [c1, c2]: H) { int a = A[c1][RNG(0, len(A[c1]))]; int b = A[c2][RNG(0, len(A[c2]))]; G.eb(a, b); } random_relabel(N, G); return G; } assert(EDGE); if (N == 1) return {}; int n = RNG(1, N); vc<int> S(n, 2); int rest = N - 1 - n; while (rest > 0) { int k = RNG(0, n); S[k]++, --rest; } vvc<int> A; int p = 0; FOR(i, n) { vc<int> C; FOR(v, p, p + S[i]) C.eb(v); A.eb(C); p += S[i]; } assert(p == N + n - 1); UnionFind uf(p); auto H = random_tree(n); for (auto& [c1, c2]: H) { int a = A[c1][RNG(0, len(A[c1]))]; int b = A[c2][RNG(0, len(A[c2]))]; uf.merge(a, b); } vc<int> new_idx(p); int x = 0; FOR(i, p) if (uf[i] == i) new_idx[i] = x++; assert(x == N); FOR(i, p) new_idx[i] = new_idx[uf[i]]; vc<pair<int, int>> G; FOR(i, n) { vc<int>& V = A[i]; for (auto& v: V) v = new_idx[v]; if (len(V) == 2) { G.eb(V[0], V[1]); } else { FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); } } } random_relabel(N, G); return G; }