This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub maspypy/library
#include "graph/st_numbering.hpp"
#include "graph/base.hpp" // https://en.wikipedia.org/wiki/Bipolar_orientation // 順列 p を求める. s=p[0], ..., p[n-1]=t. // この順で向き付けると任意の v に対して svt パスが存在. // 存在条件:BCT で全部の成分を通る st パスがある 不可能ならば empty をかえす. template <typename GT> vc<int> st_numbering(GT &G, int s, int t) { static_assert(!GT::is_directed); assert(G.is_prepared()); int N = G.N; if (N == 1) return {0}; if (s == t) return {}; vc<int> par(N, -1), pre(N, -1), low(N, -1); vc<int> V; auto dfs = [&](auto &dfs, int v) -> void { pre[v] = len(V), V.eb(v); low[v] = v; for (auto &e: G[v]) { int w = e.to; if (v == w) continue; if (pre[w] == -1) { dfs(dfs, w); par[w] = v; if (pre[low[w]] < pre[low[v]]) { low[v] = low[w]; } } elif (pre[w] < pre[low[v]]) { low[v] = w; } } }; pre[s] = 0, V.eb(s); dfs(dfs, t); if (len(V) != N) return {}; vc<int> nxt(N, -1), prev(N); nxt[s] = t, prev[t] = s; vc<int> sgn(N); sgn[s] = -1; FOR(i, 2, len(V)) { int v = V[i]; int p = par[v]; if (sgn[low[v]] == -1) { int q = prev[p]; if (q == -1) return {}; nxt[q] = v, nxt[v] = p; prev[v] = q, prev[p] = v; sgn[p] = 1; } else { int q = nxt[p]; if (q == -1) return {}; nxt[p] = v, nxt[v] = q; prev[v] = p, prev[q] = v; sgn[p] = -1; } } vc<int> A = {s}; while (A.back() != t) { A.eb(nxt[A.back()]); } // 作れているか判定 if (len(A) < N) return {}; assert(A[0] == s && A.back() == t); vc<int> rk(N, -1); FOR(i, N) rk[A[i]] = i; assert(MIN(rk) != -1); FOR(i, N) { bool l = 0, r = 0; int v = A[i]; for (auto &e: G[v]) { if (rk[e.to] < rk[v]) l = 1; if (rk[v] < rk[e.to]) r = 1; } if (i > 0 && !l) return {}; if (i < N - 1 && !r) return {}; } return A; }
#line 1 "graph/st_numbering.hpp" #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 3 "graph/st_numbering.hpp" // https://en.wikipedia.org/wiki/Bipolar_orientation // 順列 p を求める. s=p[0], ..., p[n-1]=t. // この順で向き付けると任意の v に対して svt パスが存在. // 存在条件:BCT で全部の成分を通る st パスがある 不可能ならば empty をかえす. template <typename GT> vc<int> st_numbering(GT &G, int s, int t) { static_assert(!GT::is_directed); assert(G.is_prepared()); int N = G.N; if (N == 1) return {0}; if (s == t) return {}; vc<int> par(N, -1), pre(N, -1), low(N, -1); vc<int> V; auto dfs = [&](auto &dfs, int v) -> void { pre[v] = len(V), V.eb(v); low[v] = v; for (auto &e: G[v]) { int w = e.to; if (v == w) continue; if (pre[w] == -1) { dfs(dfs, w); par[w] = v; if (pre[low[w]] < pre[low[v]]) { low[v] = low[w]; } } elif (pre[w] < pre[low[v]]) { low[v] = w; } } }; pre[s] = 0, V.eb(s); dfs(dfs, t); if (len(V) != N) return {}; vc<int> nxt(N, -1), prev(N); nxt[s] = t, prev[t] = s; vc<int> sgn(N); sgn[s] = -1; FOR(i, 2, len(V)) { int v = V[i]; int p = par[v]; if (sgn[low[v]] == -1) { int q = prev[p]; if (q == -1) return {}; nxt[q] = v, nxt[v] = p; prev[v] = q, prev[p] = v; sgn[p] = 1; } else { int q = nxt[p]; if (q == -1) return {}; nxt[p] = v, nxt[v] = q; prev[v] = p, prev[q] = v; sgn[p] = -1; } } vc<int> A = {s}; while (A.back() != t) { A.eb(nxt[A.back()]); } // 作れているか判定 if (len(A) < N) return {}; assert(A[0] == s && A.back() == t); vc<int> rk(N, -1); FOR(i, N) rk[A[i]] = i; assert(MIN(rk) != -1); FOR(i, N) { bool l = 0, r = 0; int v = A[i]; for (auto &e: G[v]) { if (rk[e.to] < rk[v]) l = 1; if (rk[v] < rk[e.to]) r = 1; } if (i > 0 && !l) return {}; if (i < N - 1 && !r) return {}; } return A; }