1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/planarity.h Sun Sep 30 19:14:33 2007 +0000
1.3 @@ -0,0 +1,1815 @@
1.4 +/* -*- C++ -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library
1.7 + *
1.8 + * Copyright (C) 2003-2007
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +#ifndef LEMON_PLANARITY_H
1.22 +#define LEMON_PLANARITY_H
1.23 +
1.24 +/// \ingroup graph_prop
1.25 +/// \file
1.26 +/// \brief Planarity checking, embedding
1.27 +
1.28 +#include <vector>
1.29 +#include <list>
1.30 +
1.31 +#include <lemon/dfs.h>
1.32 +#include <lemon/radix_sort.h>
1.33 +#include <lemon/maps.h>
1.34 +#include <lemon/path.h>
1.35 +
1.36 +
1.37 +namespace lemon {
1.38 +
1.39 + namespace _planarity_bits {
1.40 +
1.41 + template <typename UGraph>
1.42 + struct PlanarityVisitor : DfsVisitor<UGraph> {
1.43 +
1.44 + typedef typename UGraph::Node Node;
1.45 + typedef typename UGraph::Edge Edge;
1.46 +
1.47 + typedef typename UGraph::template NodeMap<Edge> PredMap;
1.48 +
1.49 + typedef typename UGraph::template UEdgeMap<bool> TreeMap;
1.50 +
1.51 + typedef typename UGraph::template NodeMap<int> OrderMap;
1.52 + typedef std::vector<Node> OrderList;
1.53 +
1.54 + typedef typename UGraph::template NodeMap<int> LowMap;
1.55 + typedef typename UGraph::template NodeMap<int> AncestorMap;
1.56 +
1.57 + PlanarityVisitor(const UGraph& ugraph,
1.58 + PredMap& pred_map, TreeMap& tree_map,
1.59 + OrderMap& order_map, OrderList& order_list,
1.60 + AncestorMap& ancestor_map, LowMap& low_map)
1.61 + : _ugraph(ugraph), _pred_map(pred_map), _tree_map(tree_map),
1.62 + _order_map(order_map), _order_list(order_list),
1.63 + _ancestor_map(ancestor_map), _low_map(low_map) {}
1.64 +
1.65 + void reach(const Node& node) {
1.66 + _order_map[node] = _order_list.size();
1.67 + _low_map[node] = _order_list.size();
1.68 + _ancestor_map[node] = _order_list.size();
1.69 + _order_list.push_back(node);
1.70 + }
1.71 +
1.72 + void discover(const Edge& edge) {
1.73 + Node source = _ugraph.source(edge);
1.74 + Node target = _ugraph.target(edge);
1.75 +
1.76 + _tree_map[edge] = true;
1.77 + _pred_map[target] = edge;
1.78 + }
1.79 +
1.80 + void examine(const Edge& edge) {
1.81 + Node source = _ugraph.source(edge);
1.82 + Node target = _ugraph.target(edge);
1.83 +
1.84 + if (_order_map[target] < _order_map[source] && !_tree_map[edge]) {
1.85 + if (_low_map[source] > _order_map[target]) {
1.86 + _low_map[source] = _order_map[target];
1.87 + }
1.88 + if (_ancestor_map[source] > _order_map[target]) {
1.89 + _ancestor_map[source] = _order_map[target];
1.90 + }
1.91 + }
1.92 + }
1.93 +
1.94 + void backtrack(const Edge& edge) {
1.95 + Node source = _ugraph.source(edge);
1.96 + Node target = _ugraph.target(edge);
1.97 +
1.98 + if (_low_map[source] > _low_map[target]) {
1.99 + _low_map[source] = _low_map[target];
1.100 + }
1.101 + }
1.102 +
1.103 + const UGraph& _ugraph;
1.104 + PredMap& _pred_map;
1.105 + TreeMap& _tree_map;
1.106 + OrderMap& _order_map;
1.107 + OrderList& _order_list;
1.108 + AncestorMap& _ancestor_map;
1.109 + LowMap& _low_map;
1.110 + };
1.111 +
1.112 + template <typename UGraph, bool embedding = true>
1.113 + struct NodeDataNode {
1.114 + int prev, next;
1.115 + int visited;
1.116 + typename UGraph::Edge first;
1.117 + bool inverted;
1.118 + };
1.119 +
1.120 + template <typename UGraph>
1.121 + struct NodeDataNode<UGraph, false> {
1.122 + int prev, next;
1.123 + int visited;
1.124 + };
1.125 +
1.126 + template <typename UGraph>
1.127 + struct ChildListNode {
1.128 + typedef typename UGraph::Node Node;
1.129 + Node first;
1.130 + Node prev, next;
1.131 + };
1.132 +
1.133 + template <typename UGraph>
1.134 + struct EdgeListNode {
1.135 + typename UGraph::Edge prev, next;
1.136 + };
1.137 +
1.138 + }
1.139 +
1.140 + /// \ingroup graph_prop
1.141 + ///
1.142 + /// \brief Planarity checking of an undirected simple graph
1.143 + ///
1.144 + /// This class implements the Boyer-Myrvold algorithm for planar
1.145 + /// checking of an undirected graph. This class is a simplified
1.146 + /// version of the PlanarEmbedding algorithm class, and it does
1.147 + /// provide neither embedding nor kuratowski subdivisons.
1.148 + template <typename UGraph>
1.149 + class PlanarityChecking {
1.150 + private:
1.151 +
1.152 + UGRAPH_TYPEDEFS(typename UGraph)
1.153 +
1.154 + const UGraph& _ugraph;
1.155 +
1.156 + private:
1.157 +
1.158 + typedef typename UGraph::template NodeMap<Edge> PredMap;
1.159 +
1.160 + typedef typename UGraph::template UEdgeMap<bool> TreeMap;
1.161 +
1.162 + typedef typename UGraph::template NodeMap<int> OrderMap;
1.163 + typedef std::vector<Node> OrderList;
1.164 +
1.165 + typedef typename UGraph::template NodeMap<int> LowMap;
1.166 + typedef typename UGraph::template NodeMap<int> AncestorMap;
1.167 +
1.168 + typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode;
1.169 + typedef std::vector<NodeDataNode> NodeData;
1.170 +
1.171 + typedef _planarity_bits::ChildListNode<UGraph> ChildListNode;
1.172 + typedef typename UGraph::template NodeMap<ChildListNode> ChildLists;
1.173 +
1.174 + typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots;
1.175 +
1.176 + typedef typename UGraph::template NodeMap<bool> EmbedEdge;
1.177 +
1.178 + public:
1.179 +
1.180 + /// \brief Constructor
1.181 + ///
1.182 + /// \warining The graph should be simple, i.e. parallel and loop edge
1.183 + /// free.
1.184 + PlanarityChecking(const UGraph& ugraph) : _ugraph(ugraph) {}
1.185 +
1.186 + /// \brief Runs the algorithm.
1.187 + ///
1.188 + /// Runs the algorithm.
1.189 + /// \param kuratowski If the parameter is false, then the
1.190 + /// algorithm does not calculate the isolate Kuratowski
1.191 + /// subdivisions.
1.192 + /// \return %True when the graph is planar.
1.193 + bool run(bool kuratowski = true) {
1.194 + typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor;
1.195 +
1.196 + PredMap pred_map(_ugraph, INVALID);
1.197 + TreeMap tree_map(_ugraph, false);
1.198 +
1.199 + OrderMap order_map(_ugraph, -1);
1.200 + OrderList order_list;
1.201 +
1.202 + AncestorMap ancestor_map(_ugraph, -1);
1.203 + LowMap low_map(_ugraph, -1);
1.204 +
1.205 + Visitor visitor(_ugraph, pred_map, tree_map,
1.206 + order_map, order_list, ancestor_map, low_map);
1.207 + DfsVisit<UGraph, Visitor> visit(_ugraph, visitor);
1.208 + visit.run();
1.209 +
1.210 + ChildLists child_lists(_ugraph);
1.211 + createChildLists(tree_map, order_map, low_map, child_lists);
1.212 +
1.213 + NodeData node_data(2 * order_list.size());
1.214 +
1.215 + EmbedEdge embed_edge(_ugraph, false);
1.216 +
1.217 + MergeRoots merge_roots(_ugraph);
1.218 +
1.219 + for (int i = order_list.size() - 1; i >= 0; --i) {
1.220 +
1.221 + Node node = order_list[i];
1.222 +
1.223 + Node source = node;
1.224 + for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) {
1.225 + Node target = _ugraph.target(e);
1.226 +
1.227 + if (order_map[source] < order_map[target] && tree_map[e]) {
1.228 + initFace(target, node_data, pred_map, order_map, order_list);
1.229 + }
1.230 + }
1.231 +
1.232 + for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) {
1.233 + Node target = _ugraph.target(e);
1.234 +
1.235 + if (order_map[source] < order_map[target] && !tree_map[e]) {
1.236 + embed_edge[target] = true;
1.237 + walkUp(target, source, i, pred_map, low_map,
1.238 + order_map, order_list, node_data, merge_roots);
1.239 + }
1.240 + }
1.241 +
1.242 + for (typename MergeRoots::Value::iterator it =
1.243 + merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
1.244 + int rn = *it;
1.245 + walkDown(rn, i, node_data, order_list, child_lists,
1.246 + ancestor_map, low_map, embed_edge, merge_roots);
1.247 + }
1.248 + merge_roots[node].clear();
1.249 +
1.250 + for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) {
1.251 + Node target = _ugraph.target(e);
1.252 +
1.253 + if (order_map[source] < order_map[target] && !tree_map[e]) {
1.254 + if (embed_edge[target]) {
1.255 + return false;
1.256 + }
1.257 + }
1.258 + }
1.259 + }
1.260 +
1.261 + return true;
1.262 + }
1.263 +
1.264 + private:
1.265 +
1.266 + void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
1.267 + const LowMap& low_map, ChildLists& child_lists) {
1.268 +
1.269 + for (NodeIt n(_ugraph); n != INVALID; ++n) {
1.270 + Node source = n;
1.271 +
1.272 + std::vector<Node> targets;
1.273 + for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) {
1.274 + Node target = _ugraph.target(e);
1.275 +
1.276 + if (order_map[source] < order_map[target] && tree_map[e]) {
1.277 + targets.push_back(target);
1.278 + }
1.279 + }
1.280 +
1.281 + if (targets.size() == 0) {
1.282 + child_lists[source].first = INVALID;
1.283 + } else if (targets.size() == 1) {
1.284 + child_lists[source].first = targets[0];
1.285 + child_lists[targets[0]].prev = INVALID;
1.286 + child_lists[targets[0]].next = INVALID;
1.287 + } else {
1.288 + radixSort(targets.begin(), targets.end(), mapFunctor(low_map));
1.289 + for (int i = 1; i < int(targets.size()); ++i) {
1.290 + child_lists[targets[i]].prev = targets[i - 1];
1.291 + child_lists[targets[i - 1]].next = targets[i];
1.292 + }
1.293 + child_lists[targets.back()].next = INVALID;
1.294 + child_lists[targets.front()].prev = INVALID;
1.295 + child_lists[source].first = targets.front();
1.296 + }
1.297 + }
1.298 + }
1.299 +
1.300 + void walkUp(const Node& node, Node root, int rorder,
1.301 + const PredMap& pred_map, const LowMap& low_map,
1.302 + const OrderMap& order_map, const OrderList& order_list,
1.303 + NodeData& node_data, MergeRoots& merge_roots) {
1.304 +
1.305 + int na, nb;
1.306 + bool da, db;
1.307 +
1.308 + na = nb = order_map[node];
1.309 + da = true; db = false;
1.310 +
1.311 + while (true) {
1.312 +
1.313 + if (node_data[na].visited == rorder) break;
1.314 + if (node_data[nb].visited == rorder) break;
1.315 +
1.316 + node_data[na].visited = rorder;
1.317 + node_data[nb].visited = rorder;
1.318 +
1.319 + int rn = -1;
1.320 +
1.321 + if (na >= int(order_list.size())) {
1.322 + rn = na;
1.323 + } else if (nb >= int(order_list.size())) {
1.324 + rn = nb;
1.325 + }
1.326 +
1.327 + if (rn == -1) {
1.328 + int nn;
1.329 +
1.330 + nn = da ? node_data[na].prev : node_data[na].next;
1.331 + da = node_data[nn].prev != na;
1.332 + na = nn;
1.333 +
1.334 + nn = db ? node_data[nb].prev : node_data[nb].next;
1.335 + db = node_data[nn].prev != nb;
1.336 + nb = nn;
1.337 +
1.338 + } else {
1.339 +
1.340 + Node rep = order_list[rn - order_list.size()];
1.341 + Node parent = _ugraph.source(pred_map[rep]);
1.342 +
1.343 + if (low_map[rep] < rorder) {
1.344 + merge_roots[parent].push_back(rn);
1.345 + } else {
1.346 + merge_roots[parent].push_front(rn);
1.347 + }
1.348 +
1.349 + if (parent != root) {
1.350 + na = nb = order_map[parent];
1.351 + da = true; db = false;
1.352 + } else {
1.353 + break;
1.354 + }
1.355 + }
1.356 + }
1.357 + }
1.358 +
1.359 + void walkDown(int rn, int rorder, NodeData& node_data,
1.360 + OrderList& order_list, ChildLists& child_lists,
1.361 + AncestorMap& ancestor_map, LowMap& low_map,
1.362 + EmbedEdge& embed_edge, MergeRoots& merge_roots) {
1.363 +
1.364 + std::vector<std::pair<int, bool> > merge_stack;
1.365 +
1.366 + for (int di = 0; di < 2; ++di) {
1.367 + bool rd = di == 0;
1.368 + int pn = rn;
1.369 + int n = rd ? node_data[rn].next : node_data[rn].prev;
1.370 +
1.371 + while (n != rn) {
1.372 +
1.373 + Node node = order_list[n];
1.374 +
1.375 + if (embed_edge[node]) {
1.376 +
1.377 + // Merging components on the critical path
1.378 + while (!merge_stack.empty()) {
1.379 +
1.380 + // Component root
1.381 + int cn = merge_stack.back().first;
1.382 + bool cd = merge_stack.back().second;
1.383 + merge_stack.pop_back();
1.384 +
1.385 + // Parent of component
1.386 + int dn = merge_stack.back().first;
1.387 + bool dd = merge_stack.back().second;
1.388 + merge_stack.pop_back();
1.389 +
1.390 + Node parent = order_list[dn];
1.391 +
1.392 + // Erasing from merge_roots
1.393 + merge_roots[parent].pop_front();
1.394 +
1.395 + Node child = order_list[cn - order_list.size()];
1.396 +
1.397 + // Erasing from child_lists
1.398 + if (child_lists[child].prev != INVALID) {
1.399 + child_lists[child_lists[child].prev].next =
1.400 + child_lists[child].next;
1.401 + } else {
1.402 + child_lists[parent].first = child_lists[child].next;
1.403 + }
1.404 +
1.405 + if (child_lists[child].next != INVALID) {
1.406 + child_lists[child_lists[child].next].prev =
1.407 + child_lists[child].prev;
1.408 + }
1.409 +
1.410 + // Merging external faces
1.411 + {
1.412 + int en = cn;
1.413 + cn = cd ? node_data[cn].prev : node_data[cn].next;
1.414 + cd = node_data[cn].next == en;
1.415 +
1.416 + }
1.417 +
1.418 + if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
1.419 + if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
1.420 +
1.421 + }
1.422 +
1.423 + bool d = pn == node_data[n].prev;
1.424 +
1.425 + if (node_data[n].prev == node_data[n].next &&
1.426 + node_data[n].inverted) {
1.427 + d = !d;
1.428 + }
1.429 +
1.430 + // Embedding edge into external face
1.431 + if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
1.432 + if (d) node_data[n].prev = rn; else node_data[n].next = rn;
1.433 + pn = rn;
1.434 +
1.435 + embed_edge[order_list[n]] = false;
1.436 + }
1.437 +
1.438 + if (!merge_roots[node].empty()) {
1.439 +
1.440 + bool d = pn == node_data[n].prev;
1.441 +
1.442 + merge_stack.push_back(std::make_pair(n, d));
1.443 +
1.444 + int rn = merge_roots[node].front();
1.445 +
1.446 + int xn = node_data[rn].next;
1.447 + Node xnode = order_list[xn];
1.448 +
1.449 + int yn = node_data[rn].prev;
1.450 + Node ynode = order_list[yn];
1.451 +
1.452 + bool rd;
1.453 + if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) {
1.454 + rd = true;
1.455 + } else if (!external(ynode, rorder, child_lists,
1.456 + ancestor_map, low_map)) {
1.457 + rd = false;
1.458 + } else if (pertinent(xnode, embed_edge, merge_roots)) {
1.459 + rd = true;
1.460 + } else {
1.461 + rd = false;
1.462 + }
1.463 +
1.464 + merge_stack.push_back(std::make_pair(rn, rd));
1.465 +
1.466 + pn = rn;
1.467 + n = rd ? xn : yn;
1.468 +
1.469 + } else if (!external(node, rorder, child_lists,
1.470 + ancestor_map, low_map)) {
1.471 + int nn = (node_data[n].next != pn ?
1.472 + node_data[n].next : node_data[n].prev);
1.473 +
1.474 + bool nd = n == node_data[nn].prev;
1.475 +
1.476 + if (nd) node_data[nn].prev = pn;
1.477 + else node_data[nn].next = pn;
1.478 +
1.479 + if (n == node_data[pn].prev) node_data[pn].prev = nn;
1.480 + else node_data[pn].next = nn;
1.481 +
1.482 + node_data[nn].inverted =
1.483 + (node_data[nn].prev == node_data[nn].next && nd != rd);
1.484 +
1.485 + n = nn;
1.486 + }
1.487 + else break;
1.488 +
1.489 + }
1.490 +
1.491 + if (!merge_stack.empty() || n == rn) {
1.492 + break;
1.493 + }
1.494 + }
1.495 + }
1.496 +
1.497 + void initFace(const Node& node, NodeData& node_data,
1.498 + const PredMap& pred_map, const OrderMap& order_map,
1.499 + const OrderList& order_list) {
1.500 + int n = order_map[node];
1.501 + int rn = n + order_list.size();
1.502 +
1.503 + node_data[n].next = node_data[n].prev = rn;
1.504 + node_data[rn].next = node_data[rn].prev = n;
1.505 +
1.506 + node_data[n].visited = order_list.size();
1.507 + node_data[rn].visited = order_list.size();
1.508 +
1.509 + }
1.510 +
1.511 + bool external(const Node& node, int rorder,
1.512 + ChildLists& child_lists, AncestorMap& ancestor_map,
1.513 + LowMap& low_map) {
1.514 + Node child = child_lists[node].first;
1.515 +
1.516 + if (child != INVALID) {
1.517 + if (low_map[child] < rorder) return true;
1.518 + }
1.519 +
1.520 + if (ancestor_map[node] < rorder) return true;
1.521 +
1.522 + return false;
1.523 + }
1.524 +
1.525 + bool pertinent(const Node& node, const EmbedEdge& embed_edge,
1.526 + const MergeRoots& merge_roots) {
1.527 + return !merge_roots[node].empty() || embed_edge[node];
1.528 + }
1.529 +
1.530 + };
1.531 +
1.532 + /// \ingroup graph_prop
1.533 + ///
1.534 + /// \brief Planar embedding of an undirected simple graph
1.535 + ///
1.536 + /// This class implements the Boyer-Myrvold algorithm for planar
1.537 + /// embedding of an undirected graph. The planar embeding is an
1.538 + /// ordering of the outgoing edges in each node, which is a possible
1.539 + /// configuration to draw the graph in the plane. If there is not
1.540 + /// such ordering then the graph contains a \f$ K_5 \f$ (full graph
1.541 + /// with 5 nodes) or an \f$ K_{3,3} \f$ (complete bipartite graph on
1.542 + /// 3 ANode and 3 BNode) subdivision.
1.543 + ///
1.544 + /// The current implementation calculates an embedding or an
1.545 + /// Kuratowski subdivision if the graph is not planar. The running
1.546 + /// time of the algorithm is \f$ O(n) \f$.
1.547 + template <typename UGraph>
1.548 + class PlanarEmbedding {
1.549 + private:
1.550 +
1.551 + UGRAPH_TYPEDEFS(typename UGraph)
1.552 +
1.553 + const UGraph& _ugraph;
1.554 + typename UGraph::template EdgeMap<Edge> _embedding;
1.555 +
1.556 + typename UGraph::template UEdgeMap<bool> _kuratowski;
1.557 +
1.558 + private:
1.559 +
1.560 + typedef typename UGraph::template NodeMap<Edge> PredMap;
1.561 +
1.562 + typedef typename UGraph::template UEdgeMap<bool> TreeMap;
1.563 +
1.564 + typedef typename UGraph::template NodeMap<int> OrderMap;
1.565 + typedef std::vector<Node> OrderList;
1.566 +
1.567 + typedef typename UGraph::template NodeMap<int> LowMap;
1.568 + typedef typename UGraph::template NodeMap<int> AncestorMap;
1.569 +
1.570 + typedef _planarity_bits::NodeDataNode<UGraph> NodeDataNode;
1.571 + typedef std::vector<NodeDataNode> NodeData;
1.572 +
1.573 + typedef _planarity_bits::ChildListNode<UGraph> ChildListNode;
1.574 + typedef typename UGraph::template NodeMap<ChildListNode> ChildLists;
1.575 +
1.576 + typedef typename UGraph::template NodeMap<std::list<int> > MergeRoots;
1.577 +
1.578 + typedef typename UGraph::template NodeMap<Edge> EmbedEdge;
1.579 +
1.580 + typedef _planarity_bits::EdgeListNode<UGraph> EdgeListNode;
1.581 + typedef typename UGraph::template EdgeMap<EdgeListNode> EdgeLists;
1.582 +
1.583 + typedef typename UGraph::template NodeMap<bool> FlipMap;
1.584 +
1.585 + typedef typename UGraph::template NodeMap<int> TypeMap;
1.586 +
1.587 + enum IsolatorNodeType {
1.588 + HIGHX = 6, LOWX = 7,
1.589 + HIGHY = 8, LOWY = 9,
1.590 + ROOT = 10, PERTINENT = 11,
1.591 + INTERNAL = 12
1.592 + };
1.593 +
1.594 + public:
1.595 +
1.596 + /// \brief Constructor
1.597 + ///
1.598 + /// \warining The graph should be simple, i.e. parallel and loop edge
1.599 + /// free.
1.600 + PlanarEmbedding(const UGraph& ugraph)
1.601 + : _ugraph(ugraph), _embedding(_ugraph), _kuratowski(ugraph, false) {}
1.602 +
1.603 + /// \brief Runs the algorithm.
1.604 + ///
1.605 + /// Runs the algorithm.
1.606 + /// \param kuratowski If the parameter is false, then the
1.607 + /// algorithm does not calculate the isolate Kuratowski
1.608 + /// subdivisions.
1.609 + ///\return %True when the graph is planar.
1.610 + bool run(bool kuratowski = true) {
1.611 + typedef _planarity_bits::PlanarityVisitor<UGraph> Visitor;
1.612 +
1.613 + PredMap pred_map(_ugraph, INVALID);
1.614 + TreeMap tree_map(_ugraph, false);
1.615 +
1.616 + OrderMap order_map(_ugraph, -1);
1.617 + OrderList order_list;
1.618 +
1.619 + AncestorMap ancestor_map(_ugraph, -1);
1.620 + LowMap low_map(_ugraph, -1);
1.621 +
1.622 + Visitor visitor(_ugraph, pred_map, tree_map,
1.623 + order_map, order_list, ancestor_map, low_map);
1.624 + DfsVisit<UGraph, Visitor> visit(_ugraph, visitor);
1.625 + visit.run();
1.626 +
1.627 + ChildLists child_lists(_ugraph);
1.628 + createChildLists(tree_map, order_map, low_map, child_lists);
1.629 +
1.630 + NodeData node_data(2 * order_list.size());
1.631 +
1.632 + EmbedEdge embed_edge(_ugraph, INVALID);
1.633 +
1.634 + MergeRoots merge_roots(_ugraph);
1.635 +
1.636 + EdgeLists edge_lists(_ugraph);
1.637 +
1.638 + FlipMap flip_map(_ugraph, false);
1.639 +
1.640 + for (int i = order_list.size() - 1; i >= 0; --i) {
1.641 +
1.642 + Node node = order_list[i];
1.643 +
1.644 + node_data[i].first = INVALID;
1.645 +
1.646 + Node source = node;
1.647 + for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) {
1.648 + Node target = _ugraph.target(e);
1.649 +
1.650 + if (order_map[source] < order_map[target] && tree_map[e]) {
1.651 + initFace(target, edge_lists, node_data,
1.652 + pred_map, order_map, order_list);
1.653 + }
1.654 + }
1.655 +
1.656 + for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) {
1.657 + Node target = _ugraph.target(e);
1.658 +
1.659 + if (order_map[source] < order_map[target] && !tree_map[e]) {
1.660 + embed_edge[target] = e;
1.661 + walkUp(target, source, i, pred_map, low_map,
1.662 + order_map, order_list, node_data, merge_roots);
1.663 + }
1.664 + }
1.665 +
1.666 + for (typename MergeRoots::Value::iterator it =
1.667 + merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
1.668 + int rn = *it;
1.669 + walkDown(rn, i, node_data, edge_lists, flip_map, order_list,
1.670 + child_lists, ancestor_map, low_map, embed_edge, merge_roots);
1.671 + }
1.672 + merge_roots[node].clear();
1.673 +
1.674 + for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) {
1.675 + Node target = _ugraph.target(e);
1.676 +
1.677 + if (order_map[source] < order_map[target] && !tree_map[e]) {
1.678 + if (embed_edge[target] != INVALID) {
1.679 + if (kuratowski) {
1.680 + isolateKuratowski(e, node_data, edge_lists, flip_map,
1.681 + order_map, order_list, pred_map, child_lists,
1.682 + ancestor_map, low_map,
1.683 + embed_edge, merge_roots);
1.684 + }
1.685 + return false;
1.686 + }
1.687 + }
1.688 + }
1.689 + }
1.690 +
1.691 + for (int i = 0; i < int(order_list.size()); ++i) {
1.692 +
1.693 + mergeRemainingFaces(order_list[i], node_data, order_list, order_map,
1.694 + child_lists, edge_lists);
1.695 + storeEmbedding(order_list[i], node_data, order_map, pred_map,
1.696 + edge_lists, flip_map);
1.697 + }
1.698 +
1.699 + return true;
1.700 + }
1.701 +
1.702 + /// \brief Gives back the successor of an edge
1.703 + ///
1.704 + /// Gives back the successor of an edge. This function makes
1.705 + /// possible to query the cyclic order of the outgoing edges from
1.706 + /// a node.
1.707 + Edge next(const Edge& edge) const {
1.708 + return _embedding[edge];
1.709 + }
1.710 +
1.711 + /// \brief Gives back true when the undirected edge is in the
1.712 + /// kuratowski subdivision
1.713 + ///
1.714 + /// Gives back true when the undirected edge is in the kuratowski
1.715 + /// subdivision
1.716 + bool kuratowski(const UEdge& uedge) {
1.717 + return _kuratowski[uedge];
1.718 + }
1.719 +
1.720 + private:
1.721 +
1.722 + void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
1.723 + const LowMap& low_map, ChildLists& child_lists) {
1.724 +
1.725 + for (NodeIt n(_ugraph); n != INVALID; ++n) {
1.726 + Node source = n;
1.727 +
1.728 + std::vector<Node> targets;
1.729 + for (OutEdgeIt e(_ugraph, n); e != INVALID; ++e) {
1.730 + Node target = _ugraph.target(e);
1.731 +
1.732 + if (order_map[source] < order_map[target] && tree_map[e]) {
1.733 + targets.push_back(target);
1.734 + }
1.735 + }
1.736 +
1.737 + if (targets.size() == 0) {
1.738 + child_lists[source].first = INVALID;
1.739 + } else if (targets.size() == 1) {
1.740 + child_lists[source].first = targets[0];
1.741 + child_lists[targets[0]].prev = INVALID;
1.742 + child_lists[targets[0]].next = INVALID;
1.743 + } else {
1.744 + radixSort(targets.begin(), targets.end(), mapFunctor(low_map));
1.745 + for (int i = 1; i < int(targets.size()); ++i) {
1.746 + child_lists[targets[i]].prev = targets[i - 1];
1.747 + child_lists[targets[i - 1]].next = targets[i];
1.748 + }
1.749 + child_lists[targets.back()].next = INVALID;
1.750 + child_lists[targets.front()].prev = INVALID;
1.751 + child_lists[source].first = targets.front();
1.752 + }
1.753 + }
1.754 + }
1.755 +
1.756 + void walkUp(const Node& node, Node root, int rorder,
1.757 + const PredMap& pred_map, const LowMap& low_map,
1.758 + const OrderMap& order_map, const OrderList& order_list,
1.759 + NodeData& node_data, MergeRoots& merge_roots) {
1.760 +
1.761 + int na, nb;
1.762 + bool da, db;
1.763 +
1.764 + na = nb = order_map[node];
1.765 + da = true; db = false;
1.766 +
1.767 + while (true) {
1.768 +
1.769 + if (node_data[na].visited == rorder) break;
1.770 + if (node_data[nb].visited == rorder) break;
1.771 +
1.772 + node_data[na].visited = rorder;
1.773 + node_data[nb].visited = rorder;
1.774 +
1.775 + int rn = -1;
1.776 +
1.777 + if (na >= int(order_list.size())) {
1.778 + rn = na;
1.779 + } else if (nb >= int(order_list.size())) {
1.780 + rn = nb;
1.781 + }
1.782 +
1.783 + if (rn == -1) {
1.784 + int nn;
1.785 +
1.786 + nn = da ? node_data[na].prev : node_data[na].next;
1.787 + da = node_data[nn].prev != na;
1.788 + na = nn;
1.789 +
1.790 + nn = db ? node_data[nb].prev : node_data[nb].next;
1.791 + db = node_data[nn].prev != nb;
1.792 + nb = nn;
1.793 +
1.794 + } else {
1.795 +
1.796 + Node rep = order_list[rn - order_list.size()];
1.797 + Node parent = _ugraph.source(pred_map[rep]);
1.798 +
1.799 + if (low_map[rep] < rorder) {
1.800 + merge_roots[parent].push_back(rn);
1.801 + } else {
1.802 + merge_roots[parent].push_front(rn);
1.803 + }
1.804 +
1.805 + if (parent != root) {
1.806 + na = nb = order_map[parent];
1.807 + da = true; db = false;
1.808 + } else {
1.809 + break;
1.810 + }
1.811 + }
1.812 + }
1.813 + }
1.814 +
1.815 + void walkDown(int rn, int rorder, NodeData& node_data,
1.816 + EdgeLists& edge_lists, FlipMap& flip_map,
1.817 + OrderList& order_list, ChildLists& child_lists,
1.818 + AncestorMap& ancestor_map, LowMap& low_map,
1.819 + EmbedEdge& embed_edge, MergeRoots& merge_roots) {
1.820 +
1.821 + std::vector<std::pair<int, bool> > merge_stack;
1.822 +
1.823 + for (int di = 0; di < 2; ++di) {
1.824 + bool rd = di == 0;
1.825 + int pn = rn;
1.826 + int n = rd ? node_data[rn].next : node_data[rn].prev;
1.827 +
1.828 + while (n != rn) {
1.829 +
1.830 + Node node = order_list[n];
1.831 +
1.832 + if (embed_edge[node] != INVALID) {
1.833 +
1.834 + // Merging components on the critical path
1.835 + while (!merge_stack.empty()) {
1.836 +
1.837 + // Component root
1.838 + int cn = merge_stack.back().first;
1.839 + bool cd = merge_stack.back().second;
1.840 + merge_stack.pop_back();
1.841 +
1.842 + // Parent of component
1.843 + int dn = merge_stack.back().first;
1.844 + bool dd = merge_stack.back().second;
1.845 + merge_stack.pop_back();
1.846 +
1.847 + Node parent = order_list[dn];
1.848 +
1.849 + // Erasing from merge_roots
1.850 + merge_roots[parent].pop_front();
1.851 +
1.852 + Node child = order_list[cn - order_list.size()];
1.853 +
1.854 + // Erasing from child_lists
1.855 + if (child_lists[child].prev != INVALID) {
1.856 + child_lists[child_lists[child].prev].next =
1.857 + child_lists[child].next;
1.858 + } else {
1.859 + child_lists[parent].first = child_lists[child].next;
1.860 + }
1.861 +
1.862 + if (child_lists[child].next != INVALID) {
1.863 + child_lists[child_lists[child].next].prev =
1.864 + child_lists[child].prev;
1.865 + }
1.866 +
1.867 + // Merging edges + flipping
1.868 + Edge de = node_data[dn].first;
1.869 + Edge ce = node_data[cn].first;
1.870 +
1.871 + flip_map[order_list[cn - order_list.size()]] = cd != dd;
1.872 + if (cd != dd) {
1.873 + std::swap(edge_lists[ce].prev, edge_lists[ce].next);
1.874 + ce = edge_lists[ce].prev;
1.875 + std::swap(edge_lists[ce].prev, edge_lists[ce].next);
1.876 + }
1.877 +
1.878 + {
1.879 + Edge dne = edge_lists[de].next;
1.880 + Edge cne = edge_lists[ce].next;
1.881 +
1.882 + edge_lists[de].next = cne;
1.883 + edge_lists[ce].next = dne;
1.884 +
1.885 + edge_lists[dne].prev = ce;
1.886 + edge_lists[cne].prev = de;
1.887 + }
1.888 +
1.889 + if (dd) {
1.890 + node_data[dn].first = ce;
1.891 + }
1.892 +
1.893 + // Merging external faces
1.894 + {
1.895 + int en = cn;
1.896 + cn = cd ? node_data[cn].prev : node_data[cn].next;
1.897 + cd = node_data[cn].next == en;
1.898 +
1.899 + if (node_data[cn].prev == node_data[cn].next &&
1.900 + node_data[cn].inverted) {
1.901 + cd = !cd;
1.902 + }
1.903 + }
1.904 +
1.905 + if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
1.906 + if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
1.907 +
1.908 + }
1.909 +
1.910 + bool d = pn == node_data[n].prev;
1.911 +
1.912 + if (node_data[n].prev == node_data[n].next &&
1.913 + node_data[n].inverted) {
1.914 + d = !d;
1.915 + }
1.916 +
1.917 + // Add new edge
1.918 + {
1.919 + Edge edge = embed_edge[node];
1.920 + Edge re = node_data[rn].first;
1.921 +
1.922 + edge_lists[edge_lists[re].next].prev = edge;
1.923 + edge_lists[edge].next = edge_lists[re].next;
1.924 + edge_lists[edge].prev = re;
1.925 + edge_lists[re].next = edge;
1.926 +
1.927 + if (!rd) {
1.928 + node_data[rn].first = edge;
1.929 + }
1.930 +
1.931 + Edge rev = _ugraph.oppositeEdge(edge);
1.932 + Edge e = node_data[n].first;
1.933 +
1.934 + edge_lists[edge_lists[e].next].prev = rev;
1.935 + edge_lists[rev].next = edge_lists[e].next;
1.936 + edge_lists[rev].prev = e;
1.937 + edge_lists[e].next = rev;
1.938 +
1.939 + if (d) {
1.940 + node_data[n].first = rev;
1.941 + }
1.942 +
1.943 + }
1.944 +
1.945 + // Embedding edge into external face
1.946 + if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
1.947 + if (d) node_data[n].prev = rn; else node_data[n].next = rn;
1.948 + pn = rn;
1.949 +
1.950 + embed_edge[order_list[n]] = INVALID;
1.951 + }
1.952 +
1.953 + if (!merge_roots[node].empty()) {
1.954 +
1.955 + bool d = pn == node_data[n].prev;
1.956 + if (node_data[n].prev == node_data[n].next &&
1.957 + node_data[n].inverted) {
1.958 + d = !d;
1.959 + }
1.960 +
1.961 + merge_stack.push_back(std::make_pair(n, d));
1.962 +
1.963 + int rn = merge_roots[node].front();
1.964 +
1.965 + int xn = node_data[rn].next;
1.966 + Node xnode = order_list[xn];
1.967 +
1.968 + int yn = node_data[rn].prev;
1.969 + Node ynode = order_list[yn];
1.970 +
1.971 + bool rd;
1.972 + if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) {
1.973 + rd = true;
1.974 + } else if (!external(ynode, rorder, child_lists,
1.975 + ancestor_map, low_map)) {
1.976 + rd = false;
1.977 + } else if (pertinent(xnode, embed_edge, merge_roots)) {
1.978 + rd = true;
1.979 + } else {
1.980 + rd = false;
1.981 + }
1.982 +
1.983 + merge_stack.push_back(std::make_pair(rn, rd));
1.984 +
1.985 + pn = rn;
1.986 + n = rd ? xn : yn;
1.987 +
1.988 + } else if (!external(node, rorder, child_lists,
1.989 + ancestor_map, low_map)) {
1.990 + int nn = (node_data[n].next != pn ?
1.991 + node_data[n].next : node_data[n].prev);
1.992 +
1.993 + bool nd = n == node_data[nn].prev;
1.994 +
1.995 + if (nd) node_data[nn].prev = pn;
1.996 + else node_data[nn].next = pn;
1.997 +
1.998 + if (n == node_data[pn].prev) node_data[pn].prev = nn;
1.999 + else node_data[pn].next = nn;
1.1000 +
1.1001 + node_data[nn].inverted =
1.1002 + (node_data[nn].prev == node_data[nn].next && nd != rd);
1.1003 +
1.1004 + n = nn;
1.1005 + }
1.1006 + else break;
1.1007 +
1.1008 + }
1.1009 +
1.1010 + if (!merge_stack.empty() || n == rn) {
1.1011 + break;
1.1012 + }
1.1013 + }
1.1014 + }
1.1015 +
1.1016 + void initFace(const Node& node, EdgeLists& edge_lists,
1.1017 + NodeData& node_data, const PredMap& pred_map,
1.1018 + const OrderMap& order_map, const OrderList& order_list) {
1.1019 + int n = order_map[node];
1.1020 + int rn = n + order_list.size();
1.1021 +
1.1022 + node_data[n].next = node_data[n].prev = rn;
1.1023 + node_data[rn].next = node_data[rn].prev = n;
1.1024 +
1.1025 + node_data[n].visited = order_list.size();
1.1026 + node_data[rn].visited = order_list.size();
1.1027 +
1.1028 + node_data[n].inverted = false;
1.1029 + node_data[rn].inverted = false;
1.1030 +
1.1031 + Edge edge = pred_map[node];
1.1032 + Edge rev = _ugraph.oppositeEdge(edge);
1.1033 +
1.1034 + node_data[rn].first = edge;
1.1035 + node_data[n].first = rev;
1.1036 +
1.1037 + edge_lists[edge].prev = edge;
1.1038 + edge_lists[edge].next = edge;
1.1039 +
1.1040 + edge_lists[rev].prev = rev;
1.1041 + edge_lists[rev].next = rev;
1.1042 +
1.1043 + }
1.1044 +
1.1045 + void mergeRemainingFaces(const Node& node, NodeData& node_data,
1.1046 + OrderList& order_list, OrderMap& order_map,
1.1047 + ChildLists& child_lists, EdgeLists& edge_lists) {
1.1048 + while (child_lists[node].first != INVALID) {
1.1049 + int dd = order_map[node];
1.1050 + Node child = child_lists[node].first;
1.1051 + int cd = order_map[child] + order_list.size();
1.1052 + child_lists[node].first = child_lists[child].next;
1.1053 +
1.1054 + Edge de = node_data[dd].first;
1.1055 + Edge ce = node_data[cd].first;
1.1056 +
1.1057 + if (de != INVALID) {
1.1058 + Edge dne = edge_lists[de].next;
1.1059 + Edge cne = edge_lists[ce].next;
1.1060 +
1.1061 + edge_lists[de].next = cne;
1.1062 + edge_lists[ce].next = dne;
1.1063 +
1.1064 + edge_lists[dne].prev = ce;
1.1065 + edge_lists[cne].prev = de;
1.1066 + }
1.1067 +
1.1068 + node_data[dd].first = ce;
1.1069 +
1.1070 + }
1.1071 + }
1.1072 +
1.1073 + void storeEmbedding(const Node& node, NodeData& node_data,
1.1074 + OrderMap& order_map, PredMap& pred_map,
1.1075 + EdgeLists& edge_lists, FlipMap& flip_map) {
1.1076 +
1.1077 + if (node_data[order_map[node]].first == INVALID) return;
1.1078 +
1.1079 + if (pred_map[node] != INVALID) {
1.1080 + Node source = _ugraph.source(pred_map[node]);
1.1081 + flip_map[node] = flip_map[node] != flip_map[source];
1.1082 + }
1.1083 +
1.1084 + Edge first = node_data[order_map[node]].first;
1.1085 + Edge prev = first;
1.1086 +
1.1087 + Edge edge = flip_map[node] ?
1.1088 + edge_lists[prev].prev : edge_lists[prev].next;
1.1089 +
1.1090 + _embedding[prev] = edge;
1.1091 +
1.1092 + while (edge != first) {
1.1093 + Edge next = edge_lists[edge].prev == prev ?
1.1094 + edge_lists[edge].next : edge_lists[edge].prev;
1.1095 + prev = edge; edge = next;
1.1096 + _embedding[prev] = edge;
1.1097 + }
1.1098 + }
1.1099 +
1.1100 +
1.1101 + bool external(const Node& node, int rorder,
1.1102 + ChildLists& child_lists, AncestorMap& ancestor_map,
1.1103 + LowMap& low_map) {
1.1104 + Node child = child_lists[node].first;
1.1105 +
1.1106 + if (child != INVALID) {
1.1107 + if (low_map[child] < rorder) return true;
1.1108 + }
1.1109 +
1.1110 + if (ancestor_map[node] < rorder) return true;
1.1111 +
1.1112 + return false;
1.1113 + }
1.1114 +
1.1115 + bool pertinent(const Node& node, const EmbedEdge& embed_edge,
1.1116 + const MergeRoots& merge_roots) {
1.1117 + return !merge_roots[node].empty() || embed_edge[node] != INVALID;
1.1118 + }
1.1119 +
1.1120 + int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists,
1.1121 + AncestorMap& ancestor_map, LowMap& low_map) {
1.1122 + int low_point;
1.1123 +
1.1124 + Node child = child_lists[node].first;
1.1125 +
1.1126 + if (child != INVALID) {
1.1127 + low_point = low_map[child];
1.1128 + } else {
1.1129 + low_point = order_map[node];
1.1130 + }
1.1131 +
1.1132 + if (low_point > ancestor_map[node]) {
1.1133 + low_point = ancestor_map[node];
1.1134 + }
1.1135 +
1.1136 + return low_point;
1.1137 + }
1.1138 +
1.1139 + int findComponentRoot(Node root, Node node, ChildLists& child_lists,
1.1140 + OrderMap& order_map, OrderList& order_list) {
1.1141 +
1.1142 + int order = order_map[root];
1.1143 + int norder = order_map[node];
1.1144 +
1.1145 + Node child = child_lists[root].first;
1.1146 + while (child != INVALID) {
1.1147 + int corder = order_map[child];
1.1148 + if (corder > order && corder < norder) {
1.1149 + order = corder;
1.1150 + }
1.1151 + child = child_lists[child].next;
1.1152 + }
1.1153 + return order + order_list.size();
1.1154 + }
1.1155 +
1.1156 + Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data,
1.1157 + EmbedEdge& embed_edge, MergeRoots& merge_roots) {
1.1158 + Node wnode =_ugraph.target(node_data[order_map[node]].first);
1.1159 + while (!pertinent(wnode, embed_edge, merge_roots)) {
1.1160 + wnode = _ugraph.target(node_data[order_map[wnode]].first);
1.1161 + }
1.1162 + return wnode;
1.1163 + }
1.1164 +
1.1165 +
1.1166 + Node findExternal(Node node, int rorder, OrderMap& order_map,
1.1167 + ChildLists& child_lists, AncestorMap& ancestor_map,
1.1168 + LowMap& low_map, NodeData& node_data) {
1.1169 + Node wnode =_ugraph.target(node_data[order_map[node]].first);
1.1170 + while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
1.1171 + wnode = _ugraph.target(node_data[order_map[wnode]].first);
1.1172 + }
1.1173 + return wnode;
1.1174 + }
1.1175 +
1.1176 + void markCommonPath(Node node, int rorder, Node& wnode, Node& znode,
1.1177 + OrderList& order_list, OrderMap& order_map,
1.1178 + NodeData& node_data, EdgeLists& edge_lists,
1.1179 + EmbedEdge& embed_edge, MergeRoots& merge_roots,
1.1180 + ChildLists& child_lists, AncestorMap& ancestor_map,
1.1181 + LowMap& low_map) {
1.1182 +
1.1183 + Node cnode = node;
1.1184 + Node pred = INVALID;
1.1185 +
1.1186 + while (true) {
1.1187 +
1.1188 + bool pert = pertinent(cnode, embed_edge, merge_roots);
1.1189 + bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map);
1.1190 +
1.1191 + if (pert && ext) {
1.1192 + if (!merge_roots[cnode].empty()) {
1.1193 + int cn = merge_roots[cnode].back();
1.1194 +
1.1195 + if (low_map[order_list[cn - order_list.size()]] < rorder) {
1.1196 + Edge edge = node_data[cn].first;
1.1197 + _kuratowski.set(edge, true);
1.1198 +
1.1199 + pred = cnode;
1.1200 + cnode = _ugraph.target(edge);
1.1201 +
1.1202 + continue;
1.1203 + }
1.1204 + }
1.1205 + wnode = znode = cnode;
1.1206 + return;
1.1207 +
1.1208 + } else if (pert) {
1.1209 + wnode = cnode;
1.1210 +
1.1211 + while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) {
1.1212 + Edge edge = node_data[order_map[cnode]].first;
1.1213 +
1.1214 + if (_ugraph.target(edge) == pred) {
1.1215 + edge = edge_lists[edge].next;
1.1216 + }
1.1217 + _kuratowski.set(edge, true);
1.1218 +
1.1219 + Node next = _ugraph.target(edge);
1.1220 + pred = cnode; cnode = next;
1.1221 + }
1.1222 +
1.1223 + znode = cnode;
1.1224 + return;
1.1225 +
1.1226 + } else if (ext) {
1.1227 + znode = cnode;
1.1228 +
1.1229 + while (!pertinent(cnode, embed_edge, merge_roots)) {
1.1230 + Edge edge = node_data[order_map[cnode]].first;
1.1231 +
1.1232 + if (_ugraph.target(edge) == pred) {
1.1233 + edge = edge_lists[edge].next;
1.1234 + }
1.1235 + _kuratowski.set(edge, true);
1.1236 +
1.1237 + Node next = _ugraph.target(edge);
1.1238 + pred = cnode; cnode = next;
1.1239 + }
1.1240 +
1.1241 + wnode = cnode;
1.1242 + return;
1.1243 +
1.1244 + } else {
1.1245 + Edge edge = node_data[order_map[cnode]].first;
1.1246 +
1.1247 + if (_ugraph.target(edge) == pred) {
1.1248 + edge = edge_lists[edge].next;
1.1249 + }
1.1250 + _kuratowski.set(edge, true);
1.1251 +
1.1252 + Node next = _ugraph.target(edge);
1.1253 + pred = cnode; cnode = next;
1.1254 + }
1.1255 +
1.1256 + }
1.1257 +
1.1258 + }
1.1259 +
1.1260 + void orientComponent(Node root, int rn, OrderMap& order_map,
1.1261 + PredMap& pred_map, NodeData& node_data,
1.1262 + EdgeLists& edge_lists, FlipMap& flip_map,
1.1263 + TypeMap& type_map) {
1.1264 + node_data[order_map[root]].first = node_data[rn].first;
1.1265 + type_map[root] = 1;
1.1266 +
1.1267 + std::vector<Node> st, qu;
1.1268 +
1.1269 + st.push_back(root);
1.1270 + while (!st.empty()) {
1.1271 + Node node = st.back();
1.1272 + st.pop_back();
1.1273 + qu.push_back(node);
1.1274 +
1.1275 + Edge edge = node_data[order_map[node]].first;
1.1276 +
1.1277 + if (type_map[_ugraph.target(edge)] == 0) {
1.1278 + st.push_back(_ugraph.target(edge));
1.1279 + type_map[_ugraph.target(edge)] = 1;
1.1280 + }
1.1281 +
1.1282 + Edge last = edge, pred = edge;
1.1283 + edge = edge_lists[edge].next;
1.1284 + while (edge != last) {
1.1285 +
1.1286 + if (type_map[_ugraph.target(edge)] == 0) {
1.1287 + st.push_back(_ugraph.target(edge));
1.1288 + type_map[_ugraph.target(edge)] = 1;
1.1289 + }
1.1290 +
1.1291 + Edge next = edge_lists[edge].next != pred ?
1.1292 + edge_lists[edge].next : edge_lists[edge].prev;
1.1293 + pred = edge; edge = next;
1.1294 + }
1.1295 +
1.1296 + }
1.1297 +
1.1298 + type_map[root] = 2;
1.1299 + flip_map[root] = false;
1.1300 +
1.1301 + for (int i = 1; i < int(qu.size()); ++i) {
1.1302 +
1.1303 + Node node = qu[i];
1.1304 +
1.1305 + while (type_map[node] != 2) {
1.1306 + st.push_back(node);
1.1307 + type_map[node] = 2;
1.1308 + node = _ugraph.source(pred_map[node]);
1.1309 + }
1.1310 +
1.1311 + bool flip = flip_map[node];
1.1312 +
1.1313 + while (!st.empty()) {
1.1314 + node = st.back();
1.1315 + st.pop_back();
1.1316 +
1.1317 + flip_map[node] = flip != flip_map[node];
1.1318 + flip = flip_map[node];
1.1319 +
1.1320 + if (flip) {
1.1321 + Edge edge = node_data[order_map[node]].first;
1.1322 + std::swap(edge_lists[edge].prev, edge_lists[edge].next);
1.1323 + edge = edge_lists[edge].prev;
1.1324 + std::swap(edge_lists[edge].prev, edge_lists[edge].next);
1.1325 + node_data[order_map[node]].first = edge;
1.1326 + }
1.1327 + }
1.1328 + }
1.1329 +
1.1330 + for (int i = 0; i < int(qu.size()); ++i) {
1.1331 +
1.1332 + Edge edge = node_data[order_map[qu[i]]].first;
1.1333 + Edge last = edge, pred = edge;
1.1334 +
1.1335 + edge = edge_lists[edge].next;
1.1336 + while (edge != last) {
1.1337 +
1.1338 + if (edge_lists[edge].next == pred) {
1.1339 + std::swap(edge_lists[edge].next, edge_lists[edge].prev);
1.1340 + }
1.1341 + pred = edge; edge = edge_lists[edge].next;
1.1342 + }
1.1343 +
1.1344 + }
1.1345 + }
1.1346 +
1.1347 + void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode,
1.1348 + OrderMap& order_map, NodeData& node_data,
1.1349 + TypeMap& type_map) {
1.1350 + Node node = _ugraph.target(node_data[order_map[root]].first);
1.1351 +
1.1352 + while (node != ynode) {
1.1353 + type_map[node] = HIGHY;
1.1354 + node = _ugraph.target(node_data[order_map[node]].first);
1.1355 + }
1.1356 +
1.1357 + while (node != wnode) {
1.1358 + type_map[node] = LOWY;
1.1359 + node = _ugraph.target(node_data[order_map[node]].first);
1.1360 + }
1.1361 +
1.1362 + node = _ugraph.target(node_data[order_map[wnode]].first);
1.1363 +
1.1364 + while (node != xnode) {
1.1365 + type_map[node] = LOWX;
1.1366 + node = _ugraph.target(node_data[order_map[node]].first);
1.1367 + }
1.1368 + type_map[node] = LOWX;
1.1369 +
1.1370 + node = _ugraph.target(node_data[order_map[xnode]].first);
1.1371 + while (node != root) {
1.1372 + type_map[node] = HIGHX;
1.1373 + node = _ugraph.target(node_data[order_map[node]].first);
1.1374 + }
1.1375 +
1.1376 + type_map[wnode] = PERTINENT;
1.1377 + type_map[root] = ROOT;
1.1378 + }
1.1379 +
1.1380 + void findInternalPath(std::vector<Edge>& ipath,
1.1381 + Node wnode, Node root, TypeMap& type_map,
1.1382 + OrderMap& order_map, NodeData& node_data,
1.1383 + EdgeLists& edge_lists) {
1.1384 + std::vector<Edge> st;
1.1385 +
1.1386 + Node node = wnode;
1.1387 +
1.1388 + while (node != root) {
1.1389 + Edge edge = edge_lists[node_data[order_map[node]].first].next;
1.1390 + st.push_back(edge);
1.1391 + node = _ugraph.target(edge);
1.1392 + }
1.1393 +
1.1394 + while (true) {
1.1395 + Edge edge = st.back();
1.1396 + if (type_map[_ugraph.target(edge)] == LOWX ||
1.1397 + type_map[_ugraph.target(edge)] == HIGHX) {
1.1398 + break;
1.1399 + }
1.1400 + if (type_map[_ugraph.target(edge)] == 2) {
1.1401 + type_map[_ugraph.target(edge)] = 3;
1.1402 +
1.1403 + edge = edge_lists[_ugraph.oppositeEdge(edge)].next;
1.1404 + st.push_back(edge);
1.1405 + } else {
1.1406 + st.pop_back();
1.1407 + edge = edge_lists[edge].next;
1.1408 +
1.1409 + while (_ugraph.oppositeEdge(edge) == st.back()) {
1.1410 + edge = st.back();
1.1411 + st.pop_back();
1.1412 + edge = edge_lists[edge].next;
1.1413 + }
1.1414 + st.push_back(edge);
1.1415 + }
1.1416 + }
1.1417 +
1.1418 + for (int i = 0; i < int(st.size()); ++i) {
1.1419 + if (type_map[_ugraph.target(st[i])] != LOWY &&
1.1420 + type_map[_ugraph.target(st[i])] != HIGHY) {
1.1421 + for (; i < int(st.size()); ++i) {
1.1422 + ipath.push_back(st[i]);
1.1423 + }
1.1424 + }
1.1425 + }
1.1426 + }
1.1427 +
1.1428 + void setInternalFlags(std::vector<Edge>& ipath, TypeMap& type_map) {
1.1429 + for (int i = 1; i < int(ipath.size()); ++i) {
1.1430 + type_map[_ugraph.source(ipath[i])] = INTERNAL;
1.1431 + }
1.1432 + }
1.1433 +
1.1434 + void findPilePath(std::vector<Edge>& ppath,
1.1435 + Node root, TypeMap& type_map, OrderMap& order_map,
1.1436 + NodeData& node_data, EdgeLists& edge_lists) {
1.1437 + std::vector<Edge> st;
1.1438 +
1.1439 + st.push_back(_ugraph.oppositeEdge(node_data[order_map[root]].first));
1.1440 + st.push_back(node_data[order_map[root]].first);
1.1441 +
1.1442 + while (st.size() > 1) {
1.1443 + Edge edge = st.back();
1.1444 + if (type_map[_ugraph.target(edge)] == INTERNAL) {
1.1445 + break;
1.1446 + }
1.1447 + if (type_map[_ugraph.target(edge)] == 3) {
1.1448 + type_map[_ugraph.target(edge)] = 4;
1.1449 +
1.1450 + edge = edge_lists[_ugraph.oppositeEdge(edge)].next;
1.1451 + st.push_back(edge);
1.1452 + } else {
1.1453 + st.pop_back();
1.1454 + edge = edge_lists[edge].next;
1.1455 +
1.1456 + while (!st.empty() && _ugraph.oppositeEdge(edge) == st.back()) {
1.1457 + edge = st.back();
1.1458 + st.pop_back();
1.1459 + edge = edge_lists[edge].next;
1.1460 + }
1.1461 + st.push_back(edge);
1.1462 + }
1.1463 + }
1.1464 +
1.1465 + for (int i = 1; i < int(st.size()); ++i) {
1.1466 + ppath.push_back(st[i]);
1.1467 + }
1.1468 + }
1.1469 +
1.1470 +
1.1471 + int markExternalPath(Node node, OrderMap& order_map,
1.1472 + ChildLists& child_lists, PredMap& pred_map,
1.1473 + AncestorMap& ancestor_map, LowMap& low_map) {
1.1474 + int lp = lowPoint(node, order_map, child_lists,
1.1475 + ancestor_map, low_map);
1.1476 +
1.1477 + if (ancestor_map[node] != lp) {
1.1478 + node = child_lists[node].first;
1.1479 + _kuratowski[pred_map[node]] = true;
1.1480 +
1.1481 + while (ancestor_map[node] != lp) {
1.1482 + for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) {
1.1483 + Node tnode = _ugraph.target(e);
1.1484 + if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) {
1.1485 + node = tnode;
1.1486 + _kuratowski[e] = true;
1.1487 + break;
1.1488 + }
1.1489 + }
1.1490 + }
1.1491 + }
1.1492 +
1.1493 + for (OutEdgeIt e(_ugraph, node); e != INVALID; ++e) {
1.1494 + if (order_map[_ugraph.target(e)] == lp) {
1.1495 + _kuratowski[e] = true;
1.1496 + break;
1.1497 + }
1.1498 + }
1.1499 +
1.1500 + return lp;
1.1501 + }
1.1502 +
1.1503 + void markPertinentPath(Node node, OrderMap& order_map,
1.1504 + NodeData& node_data, EdgeLists& edge_lists,
1.1505 + EmbedEdge& embed_edge, MergeRoots& merge_roots) {
1.1506 + while (embed_edge[node] == INVALID) {
1.1507 + int n = merge_roots[node].front();
1.1508 + Edge edge = node_data[n].first;
1.1509 +
1.1510 + _kuratowski.set(edge, true);
1.1511 +
1.1512 + Node pred = node;
1.1513 + node = _ugraph.target(edge);
1.1514 + while (!pertinent(node, embed_edge, merge_roots)) {
1.1515 + edge = node_data[order_map[node]].first;
1.1516 + if (_ugraph.target(edge) == pred) {
1.1517 + edge = edge_lists[edge].next;
1.1518 + }
1.1519 + _kuratowski.set(edge, true);
1.1520 + pred = node;
1.1521 + node = _ugraph.target(edge);
1.1522 + }
1.1523 + }
1.1524 + _kuratowski.set(embed_edge[node], true);
1.1525 + }
1.1526 +
1.1527 + void markPredPath(Node node, Node snode, PredMap& pred_map) {
1.1528 + while (node != snode) {
1.1529 + _kuratowski.set(pred_map[node], true);
1.1530 + node = _ugraph.source(pred_map[node]);
1.1531 + }
1.1532 + }
1.1533 +
1.1534 + void markFacePath(Node ynode, Node xnode,
1.1535 + OrderMap& order_map, NodeData& node_data) {
1.1536 + Edge edge = node_data[order_map[ynode]].first;
1.1537 + Node node = _ugraph.target(edge);
1.1538 + _kuratowski.set(edge, true);
1.1539 +
1.1540 + while (node != xnode) {
1.1541 + edge = node_data[order_map[node]].first;
1.1542 + _kuratowski.set(edge, true);
1.1543 + node = _ugraph.target(edge);
1.1544 + }
1.1545 + }
1.1546 +
1.1547 + void markInternalPath(std::vector<Edge>& path) {
1.1548 + for (int i = 0; i < int(path.size()); ++i) {
1.1549 + _kuratowski.set(path[i], true);
1.1550 + }
1.1551 + }
1.1552 +
1.1553 + void markPilePath(std::vector<Edge>& path) {
1.1554 + for (int i = 0; i < int(path.size()); ++i) {
1.1555 + _kuratowski.set(path[i], true);
1.1556 + }
1.1557 + }
1.1558 +
1.1559 + void isolateKuratowski(Edge edge, NodeData& node_data,
1.1560 + EdgeLists& edge_lists, FlipMap& flip_map,
1.1561 + OrderMap& order_map, OrderList& order_list,
1.1562 + PredMap& pred_map, ChildLists& child_lists,
1.1563 + AncestorMap& ancestor_map, LowMap& low_map,
1.1564 + EmbedEdge& embed_edge, MergeRoots& merge_roots) {
1.1565 +
1.1566 + Node root = _ugraph.source(edge);
1.1567 + Node enode = _ugraph.target(edge);
1.1568 +
1.1569 + int rorder = order_map[root];
1.1570 +
1.1571 + TypeMap type_map(_ugraph, 0);
1.1572 +
1.1573 + int rn = findComponentRoot(root, enode, child_lists,
1.1574 + order_map, order_list);
1.1575 +
1.1576 + Node xnode = order_list[node_data[rn].next];
1.1577 + Node ynode = order_list[node_data[rn].prev];
1.1578 +
1.1579 + // Minor-A
1.1580 + {
1.1581 + while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) {
1.1582 +
1.1583 + if (!merge_roots[xnode].empty()) {
1.1584 + root = xnode;
1.1585 + rn = merge_roots[xnode].front();
1.1586 + } else {
1.1587 + root = ynode;
1.1588 + rn = merge_roots[ynode].front();
1.1589 + }
1.1590 +
1.1591 + xnode = order_list[node_data[rn].next];
1.1592 + ynode = order_list[node_data[rn].prev];
1.1593 + }
1.1594 +
1.1595 + if (root != _ugraph.source(edge)) {
1.1596 + orientComponent(root, rn, order_map, pred_map,
1.1597 + node_data, edge_lists, flip_map, type_map);
1.1598 + markFacePath(root, root, order_map, node_data);
1.1599 + int xlp = markExternalPath(xnode, order_map, child_lists,
1.1600 + pred_map, ancestor_map, low_map);
1.1601 + int ylp = markExternalPath(ynode, order_map, child_lists,
1.1602 + pred_map, ancestor_map, low_map);
1.1603 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
1.1604 + Node lwnode = findPertinent(ynode, order_map, node_data,
1.1605 + embed_edge, merge_roots);
1.1606 +
1.1607 + markPertinentPath(lwnode, order_map, node_data, edge_lists,
1.1608 + embed_edge, merge_roots);
1.1609 +
1.1610 + return;
1.1611 + }
1.1612 + }
1.1613 +
1.1614 + orientComponent(root, rn, order_map, pred_map,
1.1615 + node_data, edge_lists, flip_map, type_map);
1.1616 +
1.1617 + Node wnode = findPertinent(ynode, order_map, node_data,
1.1618 + embed_edge, merge_roots);
1.1619 + setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map);
1.1620 +
1.1621 +
1.1622 + //Minor-B
1.1623 + if (!merge_roots[wnode].empty()) {
1.1624 + int cn = merge_roots[wnode].back();
1.1625 + Node rep = order_list[cn - order_list.size()];
1.1626 + if (low_map[rep] < rorder) {
1.1627 + markFacePath(root, root, order_map, node_data);
1.1628 + int xlp = markExternalPath(xnode, order_map, child_lists,
1.1629 + pred_map, ancestor_map, low_map);
1.1630 + int ylp = markExternalPath(ynode, order_map, child_lists,
1.1631 + pred_map, ancestor_map, low_map);
1.1632 +
1.1633 + Node lwnode, lznode;
1.1634 + markCommonPath(wnode, rorder, lwnode, lznode, order_list,
1.1635 + order_map, node_data, edge_lists, embed_edge,
1.1636 + merge_roots, child_lists, ancestor_map, low_map);
1.1637 +
1.1638 + markPertinentPath(lwnode, order_map, node_data, edge_lists,
1.1639 + embed_edge, merge_roots);
1.1640 + int zlp = markExternalPath(lznode, order_map, child_lists,
1.1641 + pred_map, ancestor_map, low_map);
1.1642 +
1.1643 + int minlp = xlp < ylp ? xlp : ylp;
1.1644 + if (zlp < minlp) minlp = zlp;
1.1645 +
1.1646 + int maxlp = xlp > ylp ? xlp : ylp;
1.1647 + if (zlp > maxlp) maxlp = zlp;
1.1648 +
1.1649 + markPredPath(order_list[maxlp], order_list[minlp], pred_map);
1.1650 +
1.1651 + return;
1.1652 + }
1.1653 + }
1.1654 +
1.1655 + Node pxnode, pynode;
1.1656 + std::vector<Edge> ipath;
1.1657 + findInternalPath(ipath, wnode, root, type_map, order_map,
1.1658 + node_data, edge_lists);
1.1659 + setInternalFlags(ipath, type_map);
1.1660 + pynode = _ugraph.source(ipath.front());
1.1661 + pxnode = _ugraph.target(ipath.back());
1.1662 +
1.1663 + wnode = findPertinent(pynode, order_map, node_data,
1.1664 + embed_edge, merge_roots);
1.1665 +
1.1666 + // Minor-C
1.1667 + {
1.1668 + if (type_map[_ugraph.source(ipath.front())] == HIGHY) {
1.1669 + if (type_map[_ugraph.target(ipath.back())] == HIGHX) {
1.1670 + markFacePath(xnode, pxnode, order_map, node_data);
1.1671 + }
1.1672 + markFacePath(root, xnode, order_map, node_data);
1.1673 + markPertinentPath(wnode, order_map, node_data, edge_lists,
1.1674 + embed_edge, merge_roots);
1.1675 + markInternalPath(ipath);
1.1676 + int xlp = markExternalPath(xnode, order_map, child_lists,
1.1677 + pred_map, ancestor_map, low_map);
1.1678 + int ylp = markExternalPath(ynode, order_map, child_lists,
1.1679 + pred_map, ancestor_map, low_map);
1.1680 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
1.1681 + return;
1.1682 + }
1.1683 +
1.1684 + if (type_map[_ugraph.target(ipath.back())] == HIGHX) {
1.1685 + markFacePath(ynode, root, order_map, node_data);
1.1686 + markPertinentPath(wnode, order_map, node_data, edge_lists,
1.1687 + embed_edge, merge_roots);
1.1688 + markInternalPath(ipath);
1.1689 + int xlp = markExternalPath(xnode, order_map, child_lists,
1.1690 + pred_map, ancestor_map, low_map);
1.1691 + int ylp = markExternalPath(ynode, order_map, child_lists,
1.1692 + pred_map, ancestor_map, low_map);
1.1693 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
1.1694 + return;
1.1695 + }
1.1696 + }
1.1697 +
1.1698 + std::vector<Edge> ppath;
1.1699 + findPilePath(ppath, root, type_map, order_map, node_data, edge_lists);
1.1700 +
1.1701 + // Minor-D
1.1702 + if (!ppath.empty()) {
1.1703 + markFacePath(ynode, xnode, order_map, node_data);
1.1704 + markPertinentPath(wnode, order_map, node_data, edge_lists,
1.1705 + embed_edge, merge_roots);
1.1706 + markPilePath(ppath);
1.1707 + markInternalPath(ipath);
1.1708 + int xlp = markExternalPath(xnode, order_map, child_lists,
1.1709 + pred_map, ancestor_map, low_map);
1.1710 + int ylp = markExternalPath(ynode, order_map, child_lists,
1.1711 + pred_map, ancestor_map, low_map);
1.1712 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
1.1713 + return;
1.1714 + }
1.1715 +
1.1716 + // Minor-E*
1.1717 + {
1.1718 +
1.1719 + if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
1.1720 + Node znode = findExternal(pynode, rorder, order_map,
1.1721 + child_lists, ancestor_map,
1.1722 + low_map, node_data);
1.1723 +
1.1724 + if (type_map[znode] == LOWY) {
1.1725 + markFacePath(root, xnode, order_map, node_data);
1.1726 + markPertinentPath(wnode, order_map, node_data, edge_lists,
1.1727 + embed_edge, merge_roots);
1.1728 + markInternalPath(ipath);
1.1729 + int xlp = markExternalPath(xnode, order_map, child_lists,
1.1730 + pred_map, ancestor_map, low_map);
1.1731 + int zlp = markExternalPath(znode, order_map, child_lists,
1.1732 + pred_map, ancestor_map, low_map);
1.1733 + markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map);
1.1734 + } else {
1.1735 + markFacePath(ynode, root, order_map, node_data);
1.1736 + markPertinentPath(wnode, order_map, node_data, edge_lists,
1.1737 + embed_edge, merge_roots);
1.1738 + markInternalPath(ipath);
1.1739 + int ylp = markExternalPath(ynode, order_map, child_lists,
1.1740 + pred_map, ancestor_map, low_map);
1.1741 + int zlp = markExternalPath(znode, order_map, child_lists,
1.1742 + pred_map, ancestor_map, low_map);
1.1743 + markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map);
1.1744 + }
1.1745 + return;
1.1746 + }
1.1747 +
1.1748 + int xlp = markExternalPath(xnode, order_map, child_lists,
1.1749 + pred_map, ancestor_map, low_map);
1.1750 + int ylp = markExternalPath(ynode, order_map, child_lists,
1.1751 + pred_map, ancestor_map, low_map);
1.1752 + int wlp = markExternalPath(wnode, order_map, child_lists,
1.1753 + pred_map, ancestor_map, low_map);
1.1754 +
1.1755 + if (wlp > xlp && wlp > ylp) {
1.1756 + markFacePath(root, root, order_map, node_data);
1.1757 + markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
1.1758 + return;
1.1759 + }
1.1760 +
1.1761 + markInternalPath(ipath);
1.1762 + markPertinentPath(wnode, order_map, node_data, edge_lists,
1.1763 + embed_edge, merge_roots);
1.1764 +
1.1765 + if (xlp > ylp && xlp > wlp) {
1.1766 + markFacePath(root, pynode, order_map, node_data);
1.1767 + markFacePath(wnode, xnode, order_map, node_data);
1.1768 + markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map);
1.1769 + return;
1.1770 + }
1.1771 +
1.1772 + if (ylp > xlp && ylp > wlp) {
1.1773 + markFacePath(pxnode, root, order_map, node_data);
1.1774 + markFacePath(ynode, wnode, order_map, node_data);
1.1775 + markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map);
1.1776 + return;
1.1777 + }
1.1778 +
1.1779 + if (pynode != ynode) {
1.1780 + markFacePath(pxnode, wnode, order_map, node_data);
1.1781 +
1.1782 + int minlp = xlp < ylp ? xlp : ylp;
1.1783 + if (wlp < minlp) minlp = wlp;
1.1784 +
1.1785 + int maxlp = xlp > ylp ? xlp : ylp;
1.1786 + if (wlp > maxlp) maxlp = wlp;
1.1787 +
1.1788 + markPredPath(order_list[maxlp], order_list[minlp], pred_map);
1.1789 + return;
1.1790 + }
1.1791 +
1.1792 + if (pxnode != xnode) {
1.1793 + markFacePath(wnode, pynode, order_map, node_data);
1.1794 +
1.1795 + int minlp = xlp < ylp ? xlp : ylp;
1.1796 + if (wlp < minlp) minlp = wlp;
1.1797 +
1.1798 + int maxlp = xlp > ylp ? xlp : ylp;
1.1799 + if (wlp > maxlp) maxlp = wlp;
1.1800 +
1.1801 + markPredPath(order_list[maxlp], order_list[minlp], pred_map);
1.1802 + return;
1.1803 + }
1.1804 +
1.1805 + markFacePath(root, root, order_map, node_data);
1.1806 + int minlp = xlp < ylp ? xlp : ylp;
1.1807 + if (wlp < minlp) minlp = wlp;
1.1808 + markPredPath(root, order_list[minlp], pred_map);
1.1809 + return;
1.1810 + }
1.1811 +
1.1812 + }
1.1813 +
1.1814 + };
1.1815 +
1.1816 +}
1.1817 +
1.1818 +#endif