r862:58c330ad0b5c
Sun, 04 Oct 2009 10:15:32
[Not Reviewed]
0 comments (0 inline)
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382
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| ... | ... |
@@ -44,768 +44,768 @@ |
| 44 | 44 |
template <typename Graph> |
| 45 | 45 |
struct PlanarityVisitor : DfsVisitor<Graph> {
|
| 46 | 46 |
|
| 47 | 47 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 48 | 48 |
|
| 49 | 49 |
typedef typename Graph::template NodeMap<Arc> PredMap; |
| 50 | 50 |
|
| 51 | 51 |
typedef typename Graph::template EdgeMap<bool> TreeMap; |
| 52 | 52 |
|
| 53 | 53 |
typedef typename Graph::template NodeMap<int> OrderMap; |
| 54 | 54 |
typedef std::vector<Node> OrderList; |
| 55 | 55 |
|
| 56 | 56 |
typedef typename Graph::template NodeMap<int> LowMap; |
| 57 | 57 |
typedef typename Graph::template NodeMap<int> AncestorMap; |
| 58 | 58 |
|
| 59 | 59 |
PlanarityVisitor(const Graph& graph, |
| 60 | 60 |
PredMap& pred_map, TreeMap& tree_map, |
| 61 | 61 |
OrderMap& order_map, OrderList& order_list, |
| 62 | 62 |
AncestorMap& ancestor_map, LowMap& low_map) |
| 63 | 63 |
: _graph(graph), _pred_map(pred_map), _tree_map(tree_map), |
| 64 | 64 |
_order_map(order_map), _order_list(order_list), |
| 65 | 65 |
_ancestor_map(ancestor_map), _low_map(low_map) {}
|
| 66 | 66 |
|
| 67 | 67 |
void reach(const Node& node) {
|
| 68 | 68 |
_order_map[node] = _order_list.size(); |
| 69 | 69 |
_low_map[node] = _order_list.size(); |
| 70 | 70 |
_ancestor_map[node] = _order_list.size(); |
| 71 | 71 |
_order_list.push_back(node); |
| 72 | 72 |
} |
| 73 | 73 |
|
| 74 | 74 |
void discover(const Arc& arc) {
|
| 75 | 75 |
Node source = _graph.source(arc); |
| 76 | 76 |
Node target = _graph.target(arc); |
| 77 | 77 |
|
| 78 | 78 |
_tree_map[arc] = true; |
| 79 | 79 |
_pred_map[target] = arc; |
| 80 | 80 |
} |
| 81 | 81 |
|
| 82 | 82 |
void examine(const Arc& arc) {
|
| 83 | 83 |
Node source = _graph.source(arc); |
| 84 | 84 |
Node target = _graph.target(arc); |
| 85 | 85 |
|
| 86 | 86 |
if (_order_map[target] < _order_map[source] && !_tree_map[arc]) {
|
| 87 | 87 |
if (_low_map[source] > _order_map[target]) {
|
| 88 | 88 |
_low_map[source] = _order_map[target]; |
| 89 | 89 |
} |
| 90 | 90 |
if (_ancestor_map[source] > _order_map[target]) {
|
| 91 | 91 |
_ancestor_map[source] = _order_map[target]; |
| 92 | 92 |
} |
| 93 | 93 |
} |
| 94 | 94 |
} |
| 95 | 95 |
|
| 96 | 96 |
void backtrack(const Arc& arc) {
|
| 97 | 97 |
Node source = _graph.source(arc); |
| 98 | 98 |
Node target = _graph.target(arc); |
| 99 | 99 |
|
| 100 | 100 |
if (_low_map[source] > _low_map[target]) {
|
| 101 | 101 |
_low_map[source] = _low_map[target]; |
| 102 | 102 |
} |
| 103 | 103 |
} |
| 104 | 104 |
|
| 105 | 105 |
const Graph& _graph; |
| 106 | 106 |
PredMap& _pred_map; |
| 107 | 107 |
TreeMap& _tree_map; |
| 108 | 108 |
OrderMap& _order_map; |
| 109 | 109 |
OrderList& _order_list; |
| 110 | 110 |
AncestorMap& _ancestor_map; |
| 111 | 111 |
LowMap& _low_map; |
| 112 | 112 |
}; |
| 113 | 113 |
|
| 114 | 114 |
template <typename Graph, bool embedding = true> |
| 115 | 115 |
struct NodeDataNode {
|
| 116 | 116 |
int prev, next; |
| 117 | 117 |
int visited; |
| 118 | 118 |
typename Graph::Arc first; |
| 119 | 119 |
bool inverted; |
| 120 | 120 |
}; |
| 121 | 121 |
|
| 122 | 122 |
template <typename Graph> |
| 123 | 123 |
struct NodeDataNode<Graph, false> {
|
| 124 | 124 |
int prev, next; |
| 125 | 125 |
int visited; |
| 126 | 126 |
}; |
| 127 | 127 |
|
| 128 | 128 |
template <typename Graph> |
| 129 | 129 |
struct ChildListNode {
|
| 130 | 130 |
typedef typename Graph::Node Node; |
| 131 | 131 |
Node first; |
| 132 | 132 |
Node prev, next; |
| 133 | 133 |
}; |
| 134 | 134 |
|
| 135 | 135 |
template <typename Graph> |
| 136 | 136 |
struct ArcListNode {
|
| 137 | 137 |
typename Graph::Arc prev, next; |
| 138 | 138 |
}; |
| 139 | 139 |
|
| 140 |
template <typename Graph> |
|
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class PlanarityChecking {
|
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private: |
|
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|
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TEMPLATE_GRAPH_TYPEDEFS(Graph); |
|
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|
|
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const Graph& _graph; |
|
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|
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private: |
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|
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typedef typename Graph::template NodeMap<Arc> PredMap; |
|
| 151 |
|
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typedef typename Graph::template EdgeMap<bool> TreeMap; |
|
| 153 |
|
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typedef typename Graph::template NodeMap<int> OrderMap; |
|
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typedef std::vector<Node> OrderList; |
|
| 156 |
|
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typedef typename Graph::template NodeMap<int> LowMap; |
|
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typedef typename Graph::template NodeMap<int> AncestorMap; |
|
| 159 |
|
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typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
|
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typedef std::vector<NodeDataNode> NodeData; |
|
| 162 |
|
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typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
|
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typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
|
| 165 |
|
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typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
|
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|
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typedef typename Graph::template NodeMap<bool> EmbedArc; |
|
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public: |
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|
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PlanarityChecking(const Graph& graph) : _graph(graph) {}
|
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|
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bool run() {
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typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
|
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|
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PredMap pred_map(_graph, INVALID); |
|
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TreeMap tree_map(_graph, false); |
|
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|
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OrderMap order_map(_graph, -1); |
|
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OrderList order_list; |
|
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|
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AncestorMap ancestor_map(_graph, -1); |
|
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LowMap low_map(_graph, -1); |
|
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|
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Visitor visitor(_graph, pred_map, tree_map, |
|
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order_map, order_list, ancestor_map, low_map); |
|
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DfsVisit<Graph, Visitor> visit(_graph, visitor); |
|
| 189 |
visit.run(); |
|
| 190 |
|
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ChildLists child_lists(_graph); |
|
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createChildLists(tree_map, order_map, low_map, child_lists); |
|
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|
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NodeData node_data(2 * order_list.size()); |
|
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|
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EmbedArc embed_arc(_graph, false); |
|
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|
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MergeRoots merge_roots(_graph); |
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|
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for (int i = order_list.size() - 1; i >= 0; --i) {
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|
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Node node = order_list[i]; |
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| 203 |
|
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Node source = node; |
|
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e); |
|
| 207 |
|
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if (order_map[source] < order_map[target] && tree_map[e]) {
|
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initFace(target, node_data, order_map, order_list); |
|
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} |
|
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} |
|
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|
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e); |
|
| 215 |
|
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if (order_map[source] < order_map[target] && !tree_map[e]) {
|
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embed_arc[target] = true; |
|
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walkUp(target, source, i, pred_map, low_map, |
|
| 219 |
order_map, order_list, node_data, merge_roots); |
|
| 220 |
} |
|
| 221 |
} |
|
| 222 |
|
|
| 223 |
for (typename MergeRoots::Value::iterator it = |
|
| 224 |
merge_roots[node].begin(); |
|
| 225 |
it != merge_roots[node].end(); ++it) {
|
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int rn = *it; |
|
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walkDown(rn, i, node_data, order_list, child_lists, |
|
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ancestor_map, low_map, embed_arc, merge_roots); |
|
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} |
|
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merge_roots[node].clear(); |
|
| 231 |
|
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e); |
|
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|
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if (order_map[source] < order_map[target] && !tree_map[e]) {
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if (embed_arc[target]) {
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return false; |
|
| 238 |
} |
|
| 239 |
} |
|
| 240 |
} |
|
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} |
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| 242 |
|
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return true; |
|
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} |
|
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|
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private: |
|
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|
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| 248 |
void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
|
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const LowMap& low_map, ChildLists& child_lists) {
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| 250 |
|
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for (NodeIt n(_graph); n != INVALID; ++n) {
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Node source = n; |
|
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|
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| 254 |
std::vector<Node> targets; |
|
| 255 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
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Node target = _graph.target(e); |
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| 258 |
if (order_map[source] < order_map[target] && tree_map[e]) {
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targets.push_back(target); |
|
| 260 |
} |
|
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} |
|
| 262 |
|
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| 263 |
if (targets.size() == 0) {
|
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child_lists[source].first = INVALID; |
|
| 265 |
} else if (targets.size() == 1) {
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child_lists[source].first = targets[0]; |
|
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child_lists[targets[0]].prev = INVALID; |
|
| 268 |
child_lists[targets[0]].next = INVALID; |
|
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} else {
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radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
|
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for (int i = 1; i < int(targets.size()); ++i) {
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child_lists[targets[i]].prev = targets[i - 1]; |
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child_lists[targets[i - 1]].next = targets[i]; |
|
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} |
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child_lists[targets.back()].next = INVALID; |
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child_lists[targets.front()].prev = INVALID; |
|
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child_lists[source].first = targets.front(); |
|
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} |
|
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} |
|
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} |
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|
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void walkUp(const Node& node, Node root, int rorder, |
|
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const PredMap& pred_map, const LowMap& low_map, |
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const OrderMap& order_map, const OrderList& order_list, |
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NodeData& node_data, MergeRoots& merge_roots) {
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int na, nb; |
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bool da, db; |
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na = nb = order_map[node]; |
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da = true; db = false; |
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while (true) {
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if (node_data[na].visited == rorder) break; |
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if (node_data[nb].visited == rorder) break; |
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node_data[na].visited = rorder; |
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node_data[nb].visited = rorder; |
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int rn = -1; |
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if (na >= int(order_list.size())) {
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rn = na; |
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} else if (nb >= int(order_list.size())) {
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rn = nb; |
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} |
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if (rn == -1) {
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int nn; |
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nn = da ? node_data[na].prev : node_data[na].next; |
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da = node_data[nn].prev != na; |
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na = nn; |
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nn = db ? node_data[nb].prev : node_data[nb].next; |
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db = node_data[nn].prev != nb; |
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nb = nn; |
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} else {
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Node rep = order_list[rn - order_list.size()]; |
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Node parent = _graph.source(pred_map[rep]); |
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if (low_map[rep] < rorder) {
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merge_roots[parent].push_back(rn); |
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} else {
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merge_roots[parent].push_front(rn); |
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} |
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|
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if (parent != root) {
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na = nb = order_map[parent]; |
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da = true; db = false; |
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} else {
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break; |
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} |
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} |
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} |
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} |
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| 340 |
|
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void walkDown(int rn, int rorder, NodeData& node_data, |
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OrderList& order_list, ChildLists& child_lists, |
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AncestorMap& ancestor_map, LowMap& low_map, |
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EmbedArc& embed_arc, MergeRoots& merge_roots) {
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std::vector<std::pair<int, bool> > merge_stack; |
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| 348 |
for (int di = 0; di < 2; ++di) {
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bool rd = di == 0; |
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int pn = rn; |
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int n = rd ? node_data[rn].next : node_data[rn].prev; |
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while (n != rn) {
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Node node = order_list[n]; |
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| 357 |
if (embed_arc[node]) {
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| 358 |
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| 359 |
// Merging components on the critical path |
|
| 360 |
while (!merge_stack.empty()) {
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| 361 |
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| 362 |
// Component root |
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int cn = merge_stack.back().first; |
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| 364 |
bool cd = merge_stack.back().second; |
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| 365 |
merge_stack.pop_back(); |
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| 366 |
|
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| 367 |
// Parent of component |
|
| 368 |
int dn = merge_stack.back().first; |
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| 369 |
bool dd = merge_stack.back().second; |
|
| 370 |
merge_stack.pop_back(); |
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| 371 |
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| 372 |
Node parent = order_list[dn]; |
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| 373 |
|
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| 374 |
// Erasing from merge_roots |
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| 375 |
merge_roots[parent].pop_front(); |
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| 376 |
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| 377 |
Node child = order_list[cn - order_list.size()]; |
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| 378 |
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| 379 |
// Erasing from child_lists |
|
| 380 |
if (child_lists[child].prev != INVALID) {
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| 381 |
child_lists[child_lists[child].prev].next = |
|
| 382 |
child_lists[child].next; |
|
| 383 |
} else {
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| 384 |
child_lists[parent].first = child_lists[child].next; |
|
| 385 |
} |
|
| 386 |
|
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| 387 |
if (child_lists[child].next != INVALID) {
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| 388 |
child_lists[child_lists[child].next].prev = |
|
| 389 |
child_lists[child].prev; |
|
| 390 |
} |
|
| 391 |
|
|
| 392 |
// Merging external faces |
|
| 393 |
{
|
|
| 394 |
int en = cn; |
|
| 395 |
cn = cd ? node_data[cn].prev : node_data[cn].next; |
|
| 396 |
cd = node_data[cn].next == en; |
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| 397 |
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| 398 |
} |
|
| 399 |
|
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| 400 |
if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
|
| 401 |
if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
|
| 402 |
|
|
| 403 |
} |
|
| 404 |
|
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| 405 |
bool d = pn == node_data[n].prev; |
|
| 406 |
|
|
| 407 |
if (node_data[n].prev == node_data[n].next && |
|
| 408 |
node_data[n].inverted) {
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|
| 409 |
d = !d; |
|
| 410 |
} |
|
| 411 |
|
|
| 412 |
// Embedding arc into external face |
|
| 413 |
if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
|
| 414 |
if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
|
| 415 |
pn = rn; |
|
| 416 |
|
|
| 417 |
embed_arc[order_list[n]] = false; |
|
| 418 |
} |
|
| 419 |
|
|
| 420 |
if (!merge_roots[node].empty()) {
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|
| 421 |
|
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| 422 |
bool d = pn == node_data[n].prev; |
|
| 423 |
|
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| 424 |
merge_stack.push_back(std::make_pair(n, d)); |
|
| 425 |
|
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| 426 |
int rn = merge_roots[node].front(); |
|
| 427 |
|
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| 428 |
int xn = node_data[rn].next; |
|
| 429 |
Node xnode = order_list[xn]; |
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| 430 |
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| 431 |
int yn = node_data[rn].prev; |
|
| 432 |
Node ynode = order_list[yn]; |
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| 433 |
|
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| 434 |
bool rd; |
|
| 435 |
if (!external(xnode, rorder, child_lists, |
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| 436 |
ancestor_map, low_map)) {
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| 437 |
rd = true; |
|
| 438 |
} else if (!external(ynode, rorder, child_lists, |
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| 439 |
ancestor_map, low_map)) {
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| 440 |
rd = false; |
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| 441 |
} else if (pertinent(xnode, embed_arc, merge_roots)) {
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| 442 |
rd = true; |
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| 443 |
} else {
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| 444 |
rd = false; |
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| 445 |
} |
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| 446 |
|
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| 447 |
merge_stack.push_back(std::make_pair(rn, rd)); |
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| 448 |
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| 449 |
pn = rn; |
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| 450 |
n = rd ? xn : yn; |
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| 451 |
|
|
| 452 |
} else if (!external(node, rorder, child_lists, |
|
| 453 |
ancestor_map, low_map)) {
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| 454 |
int nn = (node_data[n].next != pn ? |
|
| 455 |
node_data[n].next : node_data[n].prev); |
|
| 456 |
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| 457 |
bool nd = n == node_data[nn].prev; |
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| 458 |
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| 459 |
if (nd) node_data[nn].prev = pn; |
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| 460 |
else node_data[nn].next = pn; |
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| 461 |
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| 462 |
if (n == node_data[pn].prev) node_data[pn].prev = nn; |
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| 463 |
else node_data[pn].next = nn; |
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| 464 |
|
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| 465 |
node_data[nn].inverted = |
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| 466 |
(node_data[nn].prev == node_data[nn].next && nd != rd); |
|
| 467 |
|
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| 468 |
n = nn; |
|
| 469 |
} |
|
| 470 |
else break; |
|
| 471 |
|
|
| 472 |
} |
|
| 473 |
|
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| 474 |
if (!merge_stack.empty() || n == rn) {
|
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| 475 |
break; |
|
| 476 |
} |
|
| 477 |
} |
|
| 478 |
} |
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| 479 |
|
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| 480 |
void initFace(const Node& node, NodeData& node_data, |
|
| 481 |
const OrderMap& order_map, const OrderList& order_list) {
|
|
| 482 |
int n = order_map[node]; |
|
| 483 |
int rn = n + order_list.size(); |
|
| 484 |
|
|
| 485 |
node_data[n].next = node_data[n].prev = rn; |
|
| 486 |
node_data[rn].next = node_data[rn].prev = n; |
|
| 487 |
|
|
| 488 |
node_data[n].visited = order_list.size(); |
|
| 489 |
node_data[rn].visited = order_list.size(); |
|
| 490 |
|
|
| 491 |
} |
|
| 492 |
|
|
| 493 |
bool external(const Node& node, int rorder, |
|
| 494 |
ChildLists& child_lists, AncestorMap& ancestor_map, |
|
| 495 |
LowMap& low_map) {
|
|
| 496 |
Node child = child_lists[node].first; |
|
| 497 |
|
|
| 498 |
if (child != INVALID) {
|
|
| 499 |
if (low_map[child] < rorder) return true; |
|
| 500 |
} |
|
| 501 |
|
|
| 502 |
if (ancestor_map[node] < rorder) return true; |
|
| 503 |
|
|
| 504 |
return false; |
|
| 505 |
} |
|
| 506 |
|
|
| 507 |
bool pertinent(const Node& node, const EmbedArc& embed_arc, |
|
| 508 |
const MergeRoots& merge_roots) {
|
|
| 509 |
return !merge_roots[node].empty() || embed_arc[node]; |
|
| 510 |
} |
|
| 511 |
|
|
| 512 |
}; |
|
| 513 |
|
|
| 140 | 514 |
} |
| 141 | 515 |
|
| 142 | 516 |
/// \ingroup planar |
| 143 | 517 |
/// |
| 144 | 518 |
/// \brief Planarity checking of an undirected simple graph |
| 145 | 519 |
/// |
| 146 |
/// This class implements the Boyer-Myrvold algorithm for planarity |
|
| 147 |
/// checking of an undirected graph. This class is a simplified |
|
| 520 |
/// This function implements the Boyer-Myrvold algorithm for |
|
| 521 |
/// planarity checking of an undirected graph. It is a simplified |
|
| 148 | 522 |
/// version of the PlanarEmbedding algorithm class because neither |
| 149 | 523 |
/// the embedding nor the kuratowski subdivisons are not computed. |
| 150 |
template <typename Graph> |
|
| 151 |
class PlanarityChecking {
|
|
| 152 |
private: |
|
| 153 |
|
|
| 154 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
|
| 155 |
|
|
| 156 |
const Graph& _graph; |
|
| 157 |
|
|
| 158 |
private: |
|
| 159 |
|
|
| 160 |
typedef typename Graph::template NodeMap<Arc> PredMap; |
|
| 161 |
|
|
| 162 |
typedef typename Graph::template EdgeMap<bool> TreeMap; |
|
| 163 |
|
|
| 164 |
typedef typename Graph::template NodeMap<int> OrderMap; |
|
| 165 |
typedef std::vector<Node> OrderList; |
|
| 166 |
|
|
| 167 |
typedef typename Graph::template NodeMap<int> LowMap; |
|
| 168 |
typedef typename Graph::template NodeMap<int> AncestorMap; |
|
| 169 |
|
|
| 170 |
typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
|
| 171 |
typedef std::vector<NodeDataNode> NodeData; |
|
| 172 |
|
|
| 173 |
typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
|
| 174 |
typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
|
| 175 |
|
|
| 176 |
typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
|
| 177 |
|
|
| 178 |
typedef typename Graph::template NodeMap<bool> EmbedArc; |
|
| 179 |
|
|
| 180 |
public: |
|
| 181 |
|
|
| 182 |
/// \brief Constructor |
|
| 183 |
/// |
|
| 184 |
/// \note The graph should be simple, i.e. parallel and loop arc |
|
| 185 |
/// free. |
|
| 186 |
PlanarityChecking(const Graph& graph) : _graph(graph) {}
|
|
| 187 |
|
|
| 188 |
/// \brief Runs the algorithm. |
|
| 189 |
/// |
|
| 190 |
/// Runs the algorithm. |
|
| 191 |
/// \return %True when the graph is planar. |
|
| 192 |
bool run() {
|
|
| 193 |
typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
|
| 194 |
|
|
| 195 |
PredMap pred_map(_graph, INVALID); |
|
| 196 |
TreeMap tree_map(_graph, false); |
|
| 197 |
|
|
| 198 |
OrderMap order_map(_graph, -1); |
|
| 199 |
OrderList order_list; |
|
| 200 |
|
|
| 201 |
AncestorMap ancestor_map(_graph, -1); |
|
| 202 |
LowMap low_map(_graph, -1); |
|
| 203 |
|
|
| 204 |
Visitor visitor(_graph, pred_map, tree_map, |
|
| 205 |
order_map, order_list, ancestor_map, low_map); |
|
| 206 |
DfsVisit<Graph, Visitor> visit(_graph, visitor); |
|
| 207 |
visit.run(); |
|
| 208 |
|
|
| 209 |
ChildLists child_lists(_graph); |
|
| 210 |
createChildLists(tree_map, order_map, low_map, child_lists); |
|
| 211 |
|
|
| 212 |
NodeData node_data(2 * order_list.size()); |
|
| 213 |
|
|
| 214 |
EmbedArc embed_arc(_graph, false); |
|
| 215 |
|
|
| 216 |
MergeRoots merge_roots(_graph); |
|
| 217 |
|
|
| 218 |
for (int i = order_list.size() - 1; i >= 0; --i) {
|
|
| 219 |
|
|
| 220 |
Node node = order_list[i]; |
|
| 221 |
|
|
| 222 |
Node source = node; |
|
| 223 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
|
| 224 |
Node target = _graph.target(e); |
|
| 225 |
|
|
| 226 |
if (order_map[source] < order_map[target] && tree_map[e]) {
|
|
| 227 |
initFace(target, node_data, order_map, order_list); |
|
| 228 |
} |
|
| 229 |
} |
|
| 230 |
|
|
| 231 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
|
| 232 |
Node target = _graph.target(e); |
|
| 233 |
|
|
| 234 |
if (order_map[source] < order_map[target] && !tree_map[e]) {
|
|
| 235 |
embed_arc[target] = true; |
|
| 236 |
walkUp(target, source, i, pred_map, low_map, |
|
| 237 |
order_map, order_list, node_data, merge_roots); |
|
| 238 |
} |
|
| 239 |
} |
|
| 240 |
|
|
| 241 |
for (typename MergeRoots::Value::iterator it = |
|
| 242 |
merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
|
|
| 243 |
int rn = *it; |
|
| 244 |
walkDown(rn, i, node_data, order_list, child_lists, |
|
| 245 |
ancestor_map, low_map, embed_arc, merge_roots); |
|
| 246 |
} |
|
| 247 |
merge_roots[node].clear(); |
|
| 248 |
|
|
| 249 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
|
| 250 |
Node target = _graph.target(e); |
|
| 251 |
|
|
| 252 |
if (order_map[source] < order_map[target] && !tree_map[e]) {
|
|
| 253 |
if (embed_arc[target]) {
|
|
| 254 |
return false; |
|
| 255 |
} |
|
| 256 |
} |
|
| 257 |
} |
|
| 258 |
} |
|
| 259 |
|
|
| 260 |
return true; |
|
| 261 |
} |
|
| 262 |
|
|
| 263 |
private: |
|
| 264 |
|
|
| 265 |
void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
|
| 266 |
const LowMap& low_map, ChildLists& child_lists) {
|
|
| 267 |
|
|
| 268 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
| 269 |
Node source = n; |
|
| 270 |
|
|
| 271 |
std::vector<Node> targets; |
|
| 272 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
|
| 273 |
Node target = _graph.target(e); |
|
| 274 |
|
|
| 275 |
if (order_map[source] < order_map[target] && tree_map[e]) {
|
|
| 276 |
targets.push_back(target); |
|
| 277 |
} |
|
| 278 |
} |
|
| 279 |
|
|
| 280 |
if (targets.size() == 0) {
|
|
| 281 |
child_lists[source].first = INVALID; |
|
| 282 |
} else if (targets.size() == 1) {
|
|
| 283 |
child_lists[source].first = targets[0]; |
|
| 284 |
child_lists[targets[0]].prev = INVALID; |
|
| 285 |
child_lists[targets[0]].next = INVALID; |
|
| 286 |
} else {
|
|
| 287 |
radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
|
| 288 |
for (int i = 1; i < int(targets.size()); ++i) {
|
|
| 289 |
child_lists[targets[i]].prev = targets[i - 1]; |
|
| 290 |
child_lists[targets[i - 1]].next = targets[i]; |
|
| 291 |
} |
|
| 292 |
child_lists[targets.back()].next = INVALID; |
|
| 293 |
child_lists[targets.front()].prev = INVALID; |
|
| 294 |
child_lists[source].first = targets.front(); |
|
| 295 |
} |
|
| 296 |
} |
|
| 297 |
} |
|
| 298 |
|
|
| 299 |
void walkUp(const Node& node, Node root, int rorder, |
|
| 300 |
const PredMap& pred_map, const LowMap& low_map, |
|
| 301 |
const OrderMap& order_map, const OrderList& order_list, |
|
| 302 |
NodeData& node_data, MergeRoots& merge_roots) {
|
|
| 303 |
|
|
| 304 |
int na, nb; |
|
| 305 |
bool da, db; |
|
| 306 |
|
|
| 307 |
na = nb = order_map[node]; |
|
| 308 |
da = true; db = false; |
|
| 309 |
|
|
| 310 |
while (true) {
|
|
| 311 |
|
|
| 312 |
if (node_data[na].visited == rorder) break; |
|
| 313 |
if (node_data[nb].visited == rorder) break; |
|
| 314 |
|
|
| 315 |
node_data[na].visited = rorder; |
|
| 316 |
node_data[nb].visited = rorder; |
|
| 317 |
|
|
| 318 |
int rn = -1; |
|
| 319 |
|
|
| 320 |
if (na >= int(order_list.size())) {
|
|
| 321 |
rn = na; |
|
| 322 |
} else if (nb >= int(order_list.size())) {
|
|
| 323 |
rn = nb; |
|
| 324 |
} |
|
| 325 |
|
|
| 326 |
if (rn == -1) {
|
|
| 327 |
int nn; |
|
| 328 |
|
|
| 329 |
nn = da ? node_data[na].prev : node_data[na].next; |
|
| 330 |
da = node_data[nn].prev != na; |
|
| 331 |
na = nn; |
|
| 332 |
|
|
| 333 |
nn = db ? node_data[nb].prev : node_data[nb].next; |
|
| 334 |
db = node_data[nn].prev != nb; |
|
| 335 |
nb = nn; |
|
| 336 |
|
|
| 337 |
} else {
|
|
| 338 |
|
|
| 339 |
Node rep = order_list[rn - order_list.size()]; |
|
| 340 |
Node parent = _graph.source(pred_map[rep]); |
|
| 341 |
|
|
| 342 |
if (low_map[rep] < rorder) {
|
|
| 343 |
merge_roots[parent].push_back(rn); |
|
| 344 |
} else {
|
|
| 345 |
merge_roots[parent].push_front(rn); |
|
| 346 |
} |
|
| 347 |
|
|
| 348 |
if (parent != root) {
|
|
| 349 |
na = nb = order_map[parent]; |
|
| 350 |
da = true; db = false; |
|
| 351 |
} else {
|
|
| 352 |
break; |
|
| 353 |
} |
|
| 354 |
} |
|
| 355 |
} |
|
| 356 |
} |
|
| 357 |
|
|
| 358 |
void walkDown(int rn, int rorder, NodeData& node_data, |
|
| 359 |
OrderList& order_list, ChildLists& child_lists, |
|
| 360 |
AncestorMap& ancestor_map, LowMap& low_map, |
|
| 361 |
EmbedArc& embed_arc, MergeRoots& merge_roots) {
|
|
| 362 |
|
|
| 363 |
std::vector<std::pair<int, bool> > merge_stack; |
|
| 364 |
|
|
| 365 |
for (int di = 0; di < 2; ++di) {
|
|
| 366 |
bool rd = di == 0; |
|
| 367 |
int pn = rn; |
|
| 368 |
int n = rd ? node_data[rn].next : node_data[rn].prev; |
|
| 369 |
|
|
| 370 |
while (n != rn) {
|
|
| 371 |
|
|
| 372 |
Node node = order_list[n]; |
|
| 373 |
|
|
| 374 |
if (embed_arc[node]) {
|
|
| 375 |
|
|
| 376 |
// Merging components on the critical path |
|
| 377 |
while (!merge_stack.empty()) {
|
|
| 378 |
|
|
| 379 |
// Component root |
|
| 380 |
int cn = merge_stack.back().first; |
|
| 381 |
bool cd = merge_stack.back().second; |
|
| 382 |
merge_stack.pop_back(); |
|
| 383 |
|
|
| 384 |
// Parent of component |
|
| 385 |
int dn = merge_stack.back().first; |
|
| 386 |
bool dd = merge_stack.back().second; |
|
| 387 |
merge_stack.pop_back(); |
|
| 388 |
|
|
| 389 |
Node parent = order_list[dn]; |
|
| 390 |
|
|
| 391 |
// Erasing from merge_roots |
|
| 392 |
merge_roots[parent].pop_front(); |
|
| 393 |
|
|
| 394 |
Node child = order_list[cn - order_list.size()]; |
|
| 395 |
|
|
| 396 |
// Erasing from child_lists |
|
| 397 |
if (child_lists[child].prev != INVALID) {
|
|
| 398 |
child_lists[child_lists[child].prev].next = |
|
| 399 |
child_lists[child].next; |
|
| 400 |
} else {
|
|
| 401 |
child_lists[parent].first = child_lists[child].next; |
|
| 402 |
} |
|
| 403 |
|
|
| 404 |
if (child_lists[child].next != INVALID) {
|
|
| 405 |
child_lists[child_lists[child].next].prev = |
|
| 406 |
child_lists[child].prev; |
|
| 407 |
} |
|
| 408 |
|
|
| 409 |
// Merging external faces |
|
| 410 |
{
|
|
| 411 |
int en = cn; |
|
| 412 |
cn = cd ? node_data[cn].prev : node_data[cn].next; |
|
| 413 |
cd = node_data[cn].next == en; |
|
| 414 |
|
|
| 415 |
} |
|
| 416 |
|
|
| 417 |
if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
|
| 418 |
if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
|
| 419 |
|
|
| 420 |
} |
|
| 421 |
|
|
| 422 |
bool d = pn == node_data[n].prev; |
|
| 423 |
|
|
| 424 |
if (node_data[n].prev == node_data[n].next && |
|
| 425 |
node_data[n].inverted) {
|
|
| 426 |
d = !d; |
|
| 427 |
} |
|
| 428 |
|
|
| 429 |
// Embedding arc into external face |
|
| 430 |
if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
|
| 431 |
if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
|
| 432 |
pn = rn; |
|
| 433 |
|
|
| 434 |
embed_arc[order_list[n]] = false; |
|
| 435 |
} |
|
| 436 |
|
|
| 437 |
if (!merge_roots[node].empty()) {
|
|
| 438 |
|
|
| 439 |
bool d = pn == node_data[n].prev; |
|
| 440 |
|
|
| 441 |
merge_stack.push_back(std::make_pair(n, d)); |
|
| 442 |
|
|
| 443 |
int rn = merge_roots[node].front(); |
|
| 444 |
|
|
| 445 |
int xn = node_data[rn].next; |
|
| 446 |
Node xnode = order_list[xn]; |
|
| 447 |
|
|
| 448 |
int yn = node_data[rn].prev; |
|
| 449 |
Node ynode = order_list[yn]; |
|
| 450 |
|
|
| 451 |
bool rd; |
|
| 452 |
if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) {
|
|
| 453 |
rd = true; |
|
| 454 |
} else if (!external(ynode, rorder, child_lists, |
|
| 455 |
ancestor_map, low_map)) {
|
|
| 456 |
rd = false; |
|
| 457 |
} else if (pertinent(xnode, embed_arc, merge_roots)) {
|
|
| 458 |
rd = true; |
|
| 459 |
} else {
|
|
| 460 |
rd = false; |
|
| 461 |
} |
|
| 462 |
|
|
| 463 |
merge_stack.push_back(std::make_pair(rn, rd)); |
|
| 464 |
|
|
| 465 |
pn = rn; |
|
| 466 |
n = rd ? xn : yn; |
|
| 467 |
|
|
| 468 |
} else if (!external(node, rorder, child_lists, |
|
| 469 |
ancestor_map, low_map)) {
|
|
| 470 |
int nn = (node_data[n].next != pn ? |
|
| 471 |
node_data[n].next : node_data[n].prev); |
|
| 472 |
|
|
| 473 |
bool nd = n == node_data[nn].prev; |
|
| 474 |
|
|
| 475 |
if (nd) node_data[nn].prev = pn; |
|
| 476 |
else node_data[nn].next = pn; |
|
| 477 |
|
|
| 478 |
if (n == node_data[pn].prev) node_data[pn].prev = nn; |
|
| 479 |
else node_data[pn].next = nn; |
|
| 480 |
|
|
| 481 |
node_data[nn].inverted = |
|
| 482 |
(node_data[nn].prev == node_data[nn].next && nd != rd); |
|
| 483 |
|
|
| 484 |
n = nn; |
|
| 485 |
} |
|
| 486 |
else break; |
|
| 487 |
|
|
| 488 |
} |
|
| 489 |
|
|
| 490 |
if (!merge_stack.empty() || n == rn) {
|
|
| 491 |
break; |
|
| 492 |
} |
|
| 493 |
} |
|
| 494 |
} |
|
| 495 |
|
|
| 496 |
void initFace(const Node& node, NodeData& node_data, |
|
| 497 |
const OrderMap& order_map, const OrderList& order_list) {
|
|
| 498 |
int n = order_map[node]; |
|
| 499 |
int rn = n + order_list.size(); |
|
| 500 |
|
|
| 501 |
node_data[n].next = node_data[n].prev = rn; |
|
| 502 |
node_data[rn].next = node_data[rn].prev = n; |
|
| 503 |
|
|
| 504 |
node_data[n].visited = order_list.size(); |
|
| 505 |
node_data[rn].visited = order_list.size(); |
|
| 506 |
|
|
| 507 |
} |
|
| 508 |
|
|
| 509 |
bool external(const Node& node, int rorder, |
|
| 510 |
ChildLists& child_lists, AncestorMap& ancestor_map, |
|
| 511 |
LowMap& low_map) {
|
|
| 512 |
Node child = child_lists[node].first; |
|
| 513 |
|
|
| 514 |
if (child != INVALID) {
|
|
| 515 |
if (low_map[child] < rorder) return true; |
|
| 516 |
} |
|
| 517 |
|
|
| 518 |
if (ancestor_map[node] < rorder) return true; |
|
| 519 |
|
|
| 520 |
return false; |
|
| 521 |
} |
|
| 522 |
|
|
| 523 |
bool pertinent(const Node& node, const EmbedArc& embed_arc, |
|
| 524 |
const MergeRoots& merge_roots) {
|
|
| 525 |
return !merge_roots[node].empty() || embed_arc[node]; |
|
| 526 |
} |
|
| 527 |
|
|
| 528 |
|
|
| 524 |
template <typename GR> |
|
| 525 |
bool checkPlanarity(const GR& graph) {
|
|
| 526 |
_planarity_bits::PlanarityChecking<GR> pc(graph); |
|
| 527 |
return pc.run(); |
|
| 528 |
} |
|
| 529 | 529 |
|
| 530 | 530 |
/// \ingroup planar |
| 531 | 531 |
/// |
| 532 | 532 |
/// \brief Planar embedding of an undirected simple graph |
| 533 | 533 |
/// |
| 534 | 534 |
/// This class implements the Boyer-Myrvold algorithm for planar |
| 535 | 535 |
/// embedding of an undirected graph. The planar embedding is an |
| 536 | 536 |
/// ordering of the outgoing edges of the nodes, which is a possible |
| 537 | 537 |
/// configuration to draw the graph in the plane. If there is not |
| 538 | 538 |
/// such ordering then the graph contains a \f$ K_5 \f$ (full graph |
| 539 | 539 |
/// with 5 nodes) or a \f$ K_{3,3} \f$ (complete bipartite graph on
|
| 540 | 540 |
/// 3 ANode and 3 BNode) subdivision. |
| 541 | 541 |
/// |
| 542 | 542 |
/// The current implementation calculates either an embedding or a |
| 543 | 543 |
/// Kuratowski subdivision. The running time of the algorithm is |
| 544 | 544 |
/// \f$ O(n) \f$. |
| 545 | 545 |
template <typename Graph> |
| 546 | 546 |
class PlanarEmbedding {
|
| 547 | 547 |
private: |
| 548 | 548 |
|
| 549 | 549 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 550 | 550 |
|
| 551 | 551 |
const Graph& _graph; |
| 552 | 552 |
typename Graph::template ArcMap<Arc> _embedding; |
| 553 | 553 |
|
| 554 | 554 |
typename Graph::template EdgeMap<bool> _kuratowski; |
| 555 | 555 |
|
| 556 | 556 |
private: |
| 557 | 557 |
|
| 558 | 558 |
typedef typename Graph::template NodeMap<Arc> PredMap; |
| 559 | 559 |
|
| 560 | 560 |
typedef typename Graph::template EdgeMap<bool> TreeMap; |
| 561 | 561 |
|
| 562 | 562 |
typedef typename Graph::template NodeMap<int> OrderMap; |
| 563 | 563 |
typedef std::vector<Node> OrderList; |
| 564 | 564 |
|
| 565 | 565 |
typedef typename Graph::template NodeMap<int> LowMap; |
| 566 | 566 |
typedef typename Graph::template NodeMap<int> AncestorMap; |
| 567 | 567 |
|
| 568 | 568 |
typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
| 569 | 569 |
typedef std::vector<NodeDataNode> NodeData; |
| 570 | 570 |
|
| 571 | 571 |
typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
| 572 | 572 |
typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
| 573 | 573 |
|
| 574 | 574 |
typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
| 575 | 575 |
|
| 576 | 576 |
typedef typename Graph::template NodeMap<Arc> EmbedArc; |
| 577 | 577 |
|
| 578 | 578 |
typedef _planarity_bits::ArcListNode<Graph> ArcListNode; |
| 579 | 579 |
typedef typename Graph::template ArcMap<ArcListNode> ArcLists; |
| 580 | 580 |
|
| 581 | 581 |
typedef typename Graph::template NodeMap<bool> FlipMap; |
| 582 | 582 |
|
| 583 | 583 |
typedef typename Graph::template NodeMap<int> TypeMap; |
| 584 | 584 |
|
| 585 | 585 |
enum IsolatorNodeType {
|
| 586 | 586 |
HIGHX = 6, LOWX = 7, |
| 587 | 587 |
HIGHY = 8, LOWY = 9, |
| 588 | 588 |
ROOT = 10, PERTINENT = 11, |
| 589 | 589 |
INTERNAL = 12 |
| 590 | 590 |
}; |
| 591 | 591 |
|
| 592 | 592 |
public: |
| 593 | 593 |
|
| 594 | 594 |
/// \brief The map for store of embedding |
| 595 | 595 |
typedef typename Graph::template ArcMap<Arc> EmbeddingMap; |
| 596 | 596 |
|
| 597 | 597 |
/// \brief Constructor |
| 598 | 598 |
/// |
| 599 | 599 |
/// \note The graph should be simple, i.e. parallel and loop arc |
| 600 | 600 |
/// free. |
| 601 | 601 |
PlanarEmbedding(const Graph& graph) |
| 602 | 602 |
: _graph(graph), _embedding(_graph), _kuratowski(graph, false) {}
|
| 603 | 603 |
|
| 604 | 604 |
/// \brief Runs the algorithm. |
| 605 | 605 |
/// |
| 606 | 606 |
/// Runs the algorithm. |
| 607 | 607 |
/// \param kuratowski If the parameter is false, then the |
| 608 | 608 |
/// algorithm does not compute a Kuratowski subdivision. |
| 609 | 609 |
///\return %True when the graph is planar. |
| 610 | 610 |
bool run(bool kuratowski = true) {
|
| 611 | 611 |
typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
| 612 | 612 |
|
| 613 | 613 |
PredMap pred_map(_graph, INVALID); |
| 614 | 614 |
TreeMap tree_map(_graph, false); |
| 615 | 615 |
|
| 616 | 616 |
OrderMap order_map(_graph, -1); |
| 617 | 617 |
OrderList order_list; |
| 618 | 618 |
|
| 619 | 619 |
AncestorMap ancestor_map(_graph, -1); |
| 620 | 620 |
LowMap low_map(_graph, -1); |
| 621 | 621 |
|
| 622 | 622 |
Visitor visitor(_graph, pred_map, tree_map, |
| 623 | 623 |
order_map, order_list, ancestor_map, low_map); |
| 624 | 624 |
DfsVisit<Graph, Visitor> visit(_graph, visitor); |
| 625 | 625 |
visit.run(); |
| 626 | 626 |
|
| 627 | 627 |
ChildLists child_lists(_graph); |
| 628 | 628 |
createChildLists(tree_map, order_map, low_map, child_lists); |
| 629 | 629 |
|
| 630 | 630 |
NodeData node_data(2 * order_list.size()); |
| 631 | 631 |
|
| 632 | 632 |
EmbedArc embed_arc(_graph, INVALID); |
| 633 | 633 |
|
| 634 | 634 |
MergeRoots merge_roots(_graph); |
| 635 | 635 |
|
| 636 | 636 |
ArcLists arc_lists(_graph); |
| 637 | 637 |
|
| 638 | 638 |
FlipMap flip_map(_graph, false); |
| 639 | 639 |
|
| 640 | 640 |
for (int i = order_list.size() - 1; i >= 0; --i) {
|
| 641 | 641 |
|
| 642 | 642 |
Node node = order_list[i]; |
| 643 | 643 |
|
| 644 | 644 |
node_data[i].first = INVALID; |
| 645 | 645 |
|
| 646 | 646 |
Node source = node; |
| 647 | 647 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
| 648 | 648 |
Node target = _graph.target(e); |
| 649 | 649 |
|
| 650 | 650 |
if (order_map[source] < order_map[target] && tree_map[e]) {
|
| 651 | 651 |
initFace(target, arc_lists, node_data, |
| 652 | 652 |
pred_map, order_map, order_list); |
| 653 | 653 |
} |
| 654 | 654 |
} |
| 655 | 655 |
|
| 656 | 656 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
| 657 | 657 |
Node target = _graph.target(e); |
| 658 | 658 |
|
| 659 | 659 |
if (order_map[source] < order_map[target] && !tree_map[e]) {
|
| 660 | 660 |
embed_arc[target] = e; |
| 661 | 661 |
walkUp(target, source, i, pred_map, low_map, |
| 662 | 662 |
order_map, order_list, node_data, merge_roots); |
| 663 | 663 |
} |
| 664 | 664 |
} |
| 665 | 665 |
|
| 666 | 666 |
for (typename MergeRoots::Value::iterator it = |
| 667 | 667 |
merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
|
| 668 | 668 |
int rn = *it; |
| 669 | 669 |
walkDown(rn, i, node_data, arc_lists, flip_map, order_list, |
| 670 | 670 |
child_lists, ancestor_map, low_map, embed_arc, merge_roots); |
| 671 | 671 |
} |
| 672 | 672 |
merge_roots[node].clear(); |
| 673 | 673 |
|
| 674 | 674 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
| 675 | 675 |
Node target = _graph.target(e); |
| 676 | 676 |
|
| 677 | 677 |
if (order_map[source] < order_map[target] && !tree_map[e]) {
|
| 678 | 678 |
if (embed_arc[target] != INVALID) {
|
| 679 | 679 |
if (kuratowski) {
|
| 680 | 680 |
isolateKuratowski(e, node_data, arc_lists, flip_map, |
| 681 | 681 |
order_map, order_list, pred_map, child_lists, |
| 682 | 682 |
ancestor_map, low_map, |
| 683 | 683 |
embed_arc, merge_roots); |
| 684 | 684 |
} |
| 685 | 685 |
return false; |
| 686 | 686 |
} |
| 687 | 687 |
} |
| 688 | 688 |
} |
| 689 | 689 |
} |
| 690 | 690 |
|
| 691 | 691 |
for (int i = 0; i < int(order_list.size()); ++i) {
|
| 692 | 692 |
|
| 693 | 693 |
mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
| 694 | 694 |
child_lists, arc_lists); |
| 695 | 695 |
storeEmbedding(order_list[i], node_data, order_map, pred_map, |
| 696 | 696 |
arc_lists, flip_map); |
| 697 | 697 |
} |
| 698 | 698 |
|
| 699 | 699 |
return true; |
| 700 | 700 |
} |
| 701 | 701 |
|
| 702 | 702 |
/// \brief Gives back the successor of an arc |
| 703 | 703 |
/// |
| 704 | 704 |
/// Gives back the successor of an arc. This function makes |
| 705 | 705 |
/// possible to query the cyclic order of the outgoing arcs from |
| 706 | 706 |
/// a node. |
| 707 | 707 |
Arc next(const Arc& arc) const {
|
| 708 | 708 |
return _embedding[arc]; |
| 709 | 709 |
} |
| 710 | 710 |
|
| 711 | 711 |
/// \brief Gives back the calculated embedding map |
| 712 | 712 |
/// |
| 713 | 713 |
/// The returned map contains the successor of each arc in the |
| 714 | 714 |
/// graph. |
| 715 |
const EmbeddingMap& |
|
| 715 |
const EmbeddingMap& embeddingMap() const {
|
|
| 716 | 716 |
return _embedding; |
| 717 | 717 |
} |
| 718 | 718 |
|
| 719 | 719 |
/// \brief Gives back true if the undirected arc is in the |
| 720 | 720 |
/// kuratowski subdivision |
| 721 | 721 |
/// |
| 722 | 722 |
/// Gives back true if the undirected arc is in the kuratowski |
| 723 | 723 |
/// subdivision |
| 724 | 724 |
/// \note The \c run() had to be called with true value. |
| 725 | 725 |
bool kuratowski(const Edge& edge) {
|
| 726 | 726 |
return _kuratowski[edge]; |
| 727 | 727 |
} |
| 728 | 728 |
|
| 729 | 729 |
private: |
| 730 | 730 |
|
| 731 | 731 |
void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
| 732 | 732 |
const LowMap& low_map, ChildLists& child_lists) {
|
| 733 | 733 |
|
| 734 | 734 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
| 735 | 735 |
Node source = n; |
| 736 | 736 |
|
| 737 | 737 |
std::vector<Node> targets; |
| 738 | 738 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
| 739 | 739 |
Node target = _graph.target(e); |
| 740 | 740 |
|
| 741 | 741 |
if (order_map[source] < order_map[target] && tree_map[e]) {
|
| 742 | 742 |
targets.push_back(target); |
| 743 | 743 |
} |
| 744 | 744 |
} |
| 745 | 745 |
|
| 746 | 746 |
if (targets.size() == 0) {
|
| 747 | 747 |
child_lists[source].first = INVALID; |
| 748 | 748 |
} else if (targets.size() == 1) {
|
| 749 | 749 |
child_lists[source].first = targets[0]; |
| 750 | 750 |
child_lists[targets[0]].prev = INVALID; |
| 751 | 751 |
child_lists[targets[0]].next = INVALID; |
| 752 | 752 |
} else {
|
| 753 | 753 |
radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
| 754 | 754 |
for (int i = 1; i < int(targets.size()); ++i) {
|
| 755 | 755 |
child_lists[targets[i]].prev = targets[i - 1]; |
| 756 | 756 |
child_lists[targets[i - 1]].next = targets[i]; |
| 757 | 757 |
} |
| 758 | 758 |
child_lists[targets.back()].next = INVALID; |
| 759 | 759 |
child_lists[targets.front()].prev = INVALID; |
| 760 | 760 |
child_lists[source].first = targets.front(); |
| 761 | 761 |
} |
| 762 | 762 |
} |
| 763 | 763 |
} |
| 764 | 764 |
|
| 765 | 765 |
void walkUp(const Node& node, Node root, int rorder, |
| 766 | 766 |
const PredMap& pred_map, const LowMap& low_map, |
| 767 | 767 |
const OrderMap& order_map, const OrderList& order_list, |
| 768 | 768 |
NodeData& node_data, MergeRoots& merge_roots) {
|
| 769 | 769 |
|
| 770 | 770 |
int na, nb; |
| 771 | 771 |
bool da, db; |
| 772 | 772 |
|
| 773 | 773 |
na = nb = order_map[node]; |
| 774 | 774 |
da = true; db = false; |
| 775 | 775 |
|
| 776 | 776 |
while (true) {
|
| 777 | 777 |
|
| 778 | 778 |
if (node_data[na].visited == rorder) break; |
| 779 | 779 |
if (node_data[nb].visited == rorder) break; |
| 780 | 780 |
|
| 781 | 781 |
node_data[na].visited = rorder; |
| 782 | 782 |
node_data[nb].visited = rorder; |
| 783 | 783 |
|
| 784 | 784 |
int rn = -1; |
| 785 | 785 |
|
| 786 | 786 |
if (na >= int(order_list.size())) {
|
| 787 | 787 |
rn = na; |
| 788 | 788 |
} else if (nb >= int(order_list.size())) {
|
| 789 | 789 |
rn = nb; |
| 790 | 790 |
} |
| 791 | 791 |
|
| 792 | 792 |
if (rn == -1) {
|
| 793 | 793 |
int nn; |
| 794 | 794 |
|
| 795 | 795 |
nn = da ? node_data[na].prev : node_data[na].next; |
| 796 | 796 |
da = node_data[nn].prev != na; |
| 797 | 797 |
na = nn; |
| 798 | 798 |
|
| 799 | 799 |
nn = db ? node_data[nb].prev : node_data[nb].next; |
| 800 | 800 |
db = node_data[nn].prev != nb; |
| 801 | 801 |
nb = nn; |
| 802 | 802 |
|
| 803 | 803 |
} else {
|
| 804 | 804 |
|
| 805 | 805 |
Node rep = order_list[rn - order_list.size()]; |
| 806 | 806 |
Node parent = _graph.source(pred_map[rep]); |
| 807 | 807 |
|
| 808 | 808 |
if (low_map[rep] < rorder) {
|
| 809 | 809 |
merge_roots[parent].push_back(rn); |
| 810 | 810 |
} else {
|
| 811 | 811 |
merge_roots[parent].push_front(rn); |
| ... | ... |
@@ -146,114 +146,117 @@ |
| 146 | 146 |
int deg = 0; |
| 147 | 147 |
for (IncEdgeIt e(graph, n); e != INVALID; ++e) {
|
| 148 | 148 |
if (pe.kuratowski(e)) {
|
| 149 | 149 |
++deg; |
| 150 | 150 |
} |
| 151 | 151 |
} |
| 152 | 152 |
++degs[deg]; |
| 153 | 153 |
} |
| 154 | 154 |
for (std::map<int, int>::iterator it = degs.begin(); it != degs.end(); ++it) {
|
| 155 | 155 |
check(it->first == 0 || it->first == 2 || |
| 156 | 156 |
(it->first == 3 && it->second == 6) || |
| 157 | 157 |
(it->first == 4 && it->second == 5), |
| 158 | 158 |
"Wrong degree in Kuratowski graph"); |
| 159 | 159 |
} |
| 160 | 160 |
|
| 161 | 161 |
// Not full test |
| 162 | 162 |
check((degs[3] == 0) != (degs[4] == 0), "Wrong Kuratowski graph"); |
| 163 | 163 |
} |
| 164 | 164 |
|
| 165 | 165 |
bool intersect(Point<int> e1, Point<int> e2, Point<int> f1, Point<int> f2) {
|
| 166 | 166 |
int l, r; |
| 167 | 167 |
if (std::min(e1.x, e2.x) > std::max(f1.x, f2.x)) return false; |
| 168 | 168 |
if (std::max(e1.x, e2.x) < std::min(f1.x, f2.x)) return false; |
| 169 | 169 |
if (std::min(e1.y, e2.y) > std::max(f1.y, f2.y)) return false; |
| 170 | 170 |
if (std::max(e1.y, e2.y) < std::min(f1.y, f2.y)) return false; |
| 171 | 171 |
|
| 172 | 172 |
l = (e2.x - e1.x) * (f1.y - e1.y) - (e2.y - e1.y) * (f1.x - e1.x); |
| 173 | 173 |
r = (e2.x - e1.x) * (f2.y - e1.y) - (e2.y - e1.y) * (f2.x - e1.x); |
| 174 | 174 |
if (!((l >= 0 && r <= 0) || (l <= 0 && r >= 0))) return false; |
| 175 | 175 |
l = (f2.x - f1.x) * (e1.y - f1.y) - (f2.y - f1.y) * (e1.x - f1.x); |
| 176 | 176 |
r = (f2.x - f1.x) * (e2.y - f1.y) - (f2.y - f1.y) * (e2.x - f1.x); |
| 177 | 177 |
if (!((l >= 0 && r <= 0) || (l <= 0 && r >= 0))) return false; |
| 178 | 178 |
return true; |
| 179 | 179 |
} |
| 180 | 180 |
|
| 181 | 181 |
bool collinear(Point<int> p, Point<int> q, Point<int> r) {
|
| 182 | 182 |
int v; |
| 183 | 183 |
v = (q.x - p.x) * (r.y - p.y) - (q.y - p.y) * (r.x - p.x); |
| 184 | 184 |
if (v != 0) return false; |
| 185 | 185 |
v = (q.x - p.x) * (r.x - p.x) + (q.y - p.y) * (r.y - p.y); |
| 186 | 186 |
if (v < 0) return false; |
| 187 | 187 |
return true; |
| 188 | 188 |
} |
| 189 | 189 |
|
| 190 | 190 |
void checkDrawing(const Graph& graph, PD& pd) {
|
| 191 | 191 |
for (Graph::NodeIt n(graph); n != INVALID; ++n) {
|
| 192 | 192 |
Graph::NodeIt m(n); |
| 193 | 193 |
for (++m; m != INVALID; ++m) {
|
| 194 | 194 |
check(pd[m] != pd[n], "Two nodes with identical coordinates"); |
| 195 | 195 |
} |
| 196 | 196 |
} |
| 197 | 197 |
|
| 198 | 198 |
for (Graph::EdgeIt e(graph); e != INVALID; ++e) {
|
| 199 | 199 |
for (Graph::EdgeIt f(e); f != e; ++f) {
|
| 200 | 200 |
Point<int> e1 = pd[graph.u(e)]; |
| 201 | 201 |
Point<int> e2 = pd[graph.v(e)]; |
| 202 | 202 |
Point<int> f1 = pd[graph.u(f)]; |
| 203 | 203 |
Point<int> f2 = pd[graph.v(f)]; |
| 204 | 204 |
|
| 205 | 205 |
if (graph.u(e) == graph.u(f)) {
|
| 206 | 206 |
check(!collinear(e1, e2, f2), "Wrong drawing"); |
| 207 | 207 |
} else if (graph.u(e) == graph.v(f)) {
|
| 208 | 208 |
check(!collinear(e1, e2, f1), "Wrong drawing"); |
| 209 | 209 |
} else if (graph.v(e) == graph.u(f)) {
|
| 210 | 210 |
check(!collinear(e2, e1, f2), "Wrong drawing"); |
| 211 | 211 |
} else if (graph.v(e) == graph.v(f)) {
|
| 212 | 212 |
check(!collinear(e2, e1, f1), "Wrong drawing"); |
| 213 | 213 |
} else {
|
| 214 | 214 |
check(!intersect(e1, e2, f1, f2), "Wrong drawing"); |
| 215 | 215 |
} |
| 216 | 216 |
} |
| 217 | 217 |
} |
| 218 | 218 |
} |
| 219 | 219 |
|
| 220 | 220 |
void checkColoring(const Graph& graph, PC& pc, int num) {
|
| 221 | 221 |
for (NodeIt n(graph); n != INVALID; ++n) {
|
| 222 | 222 |
check(pc.colorIndex(n) >= 0 && pc.colorIndex(n) < num, |
| 223 | 223 |
"Wrong coloring"); |
| 224 | 224 |
} |
| 225 | 225 |
for (EdgeIt e(graph); e != INVALID; ++e) {
|
| 226 | 226 |
check(pc.colorIndex(graph.u(e)) != pc.colorIndex(graph.v(e)), |
| 227 | 227 |
"Wrong coloring"); |
| 228 | 228 |
} |
| 229 | 229 |
} |
| 230 | 230 |
|
| 231 | 231 |
int main() {
|
| 232 | 232 |
|
| 233 | 233 |
for (int i = 0; i < lgfn; ++i) {
|
| 234 | 234 |
std::istringstream lgfs(lgf[i]); |
| 235 | 235 |
|
| 236 | 236 |
SmartGraph graph; |
| 237 | 237 |
graphReader(graph, lgfs).run(); |
| 238 | 238 |
|
| 239 | 239 |
check(simpleGraph(graph), "Test graphs must be simple"); |
| 240 | 240 |
|
| 241 | 241 |
PE pe(graph); |
| 242 |
|
|
| 242 |
bool planar = pe.run(); |
|
| 243 |
check(checkPlanarity(graph) == planar, "Planarity checking failed"); |
|
| 244 |
|
|
| 245 |
if (planar) {
|
|
| 243 | 246 |
checkEmbedding(graph, pe); |
| 244 | 247 |
|
| 245 | 248 |
PlanarDrawing<Graph> pd(graph); |
| 246 |
pd.run(pe. |
|
| 249 |
pd.run(pe.embeddingMap()); |
|
| 247 | 250 |
checkDrawing(graph, pd); |
| 248 | 251 |
|
| 249 | 252 |
PlanarColoring<Graph> pc(graph); |
| 250 |
pc.runFiveColoring(pe. |
|
| 253 |
pc.runFiveColoring(pe.embeddingMap()); |
|
| 251 | 254 |
checkColoring(graph, pc, 5); |
| 252 | 255 |
|
| 253 | 256 |
} else {
|
| 254 | 257 |
checkKuratowski(graph, pe); |
| 255 | 258 |
} |
| 256 | 259 |
} |
| 257 | 260 |
|
| 258 | 261 |
return 0; |
| 259 | 262 |
} |
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