1 | #include <lemon/list_graph.h> |
---|
2 | #include <lemon/graph_utils.h> |
---|
3 | #include <lemon/random.h> |
---|
4 | #include <lemon/dim2.h> |
---|
5 | #include <lemon/bfs.h> |
---|
6 | #include <lemon/counter.h> |
---|
7 | #include <lemon/suurballe.h> |
---|
8 | #include <lemon/graph_to_eps.h> |
---|
9 | #include <lemon/graph_writer.h> |
---|
10 | #include <lemon/arg_parser.h> |
---|
11 | #include <cmath> |
---|
12 | #include <algorithm> |
---|
13 | #include <lemon/unionfind.h> |
---|
14 | |
---|
15 | using namespace lemon; |
---|
16 | |
---|
17 | typedef dim2::Point<double> Point; |
---|
18 | |
---|
19 | UGRAPH_TYPEDEFS(ListUGraph); |
---|
20 | |
---|
21 | int N; |
---|
22 | int girth; |
---|
23 | |
---|
24 | ListUGraph g; |
---|
25 | |
---|
26 | std::vector<Node> nodes; |
---|
27 | ListUGraph::NodeMap<Point> coords(g); |
---|
28 | |
---|
29 | int tsp_impr_num=0; |
---|
30 | |
---|
31 | const double EPSILON=1e-8; |
---|
32 | bool tsp_improve(Node u, Node v) |
---|
33 | { |
---|
34 | double luv=std::sqrt((coords[v]-coords[u]).normSquare()); |
---|
35 | Node u2=u; |
---|
36 | Node v2=v; |
---|
37 | do { |
---|
38 | Node n; |
---|
39 | for(IncEdgeIt e(g,v2);(n=g.runningNode(e))==u2;++e); |
---|
40 | u2=v2; |
---|
41 | v2=n; |
---|
42 | if(luv+std::sqrt((coords[v2]-coords[u2]).normSquare())-EPSILON> |
---|
43 | std::sqrt((coords[u]-coords[u2]).normSquare())+ |
---|
44 | std::sqrt((coords[v]-coords[v2]).normSquare())) |
---|
45 | { |
---|
46 | g.erase(findUEdge(g,u,v)); |
---|
47 | g.erase(findUEdge(g,u2,v2)); |
---|
48 | g.addEdge(u2,u); |
---|
49 | g.addEdge(v,v2); |
---|
50 | tsp_impr_num++; |
---|
51 | return true; |
---|
52 | } |
---|
53 | } while(v2!=u); |
---|
54 | return false; |
---|
55 | } |
---|
56 | |
---|
57 | bool tsp_improve(Node u) |
---|
58 | { |
---|
59 | for(IncEdgeIt e(g,u);e!=INVALID;++e) |
---|
60 | if(tsp_improve(u,g.runningNode(e))) return true; |
---|
61 | return false; |
---|
62 | } |
---|
63 | |
---|
64 | void tsp_improve() |
---|
65 | { |
---|
66 | bool b; |
---|
67 | do { |
---|
68 | b=false; |
---|
69 | for(NodeIt n(g);n!=INVALID;++n) |
---|
70 | if(tsp_improve(n)) b=true; |
---|
71 | } while(b); |
---|
72 | } |
---|
73 | |
---|
74 | void tsp() |
---|
75 | { |
---|
76 | for(int i=0;i<N;i++) g.addEdge(nodes[i],nodes[(i+1)%N]); |
---|
77 | tsp_improve(); |
---|
78 | } |
---|
79 | |
---|
80 | class Line |
---|
81 | { |
---|
82 | public: |
---|
83 | Point a; |
---|
84 | Point b; |
---|
85 | Line(Point _a,Point _b) :a(_a),b(_b) {} |
---|
86 | Line(Node _a,Node _b) : a(coords[_a]),b(coords[_b]) {} |
---|
87 | Line(const Edge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {} |
---|
88 | Line(const UEdge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {} |
---|
89 | }; |
---|
90 | |
---|
91 | inline std::ostream& operator<<(std::ostream &os, const Line &l) |
---|
92 | { |
---|
93 | os << l.a << "->" << l.b; |
---|
94 | return os; |
---|
95 | } |
---|
96 | |
---|
97 | bool cross(Line a, Line b) |
---|
98 | { |
---|
99 | Point ao=rot90(a.b-a.a); |
---|
100 | Point bo=rot90(b.b-b.a); |
---|
101 | return (ao*(b.a-a.a))*(ao*(b.b-a.a))<0 && |
---|
102 | (bo*(a.a-b.a))*(bo*(a.b-b.a))<0; |
---|
103 | } |
---|
104 | |
---|
105 | struct Pedge |
---|
106 | { |
---|
107 | Node a; |
---|
108 | Node b; |
---|
109 | double len; |
---|
110 | }; |
---|
111 | |
---|
112 | bool pedgeLess(Pedge a,Pedge b) |
---|
113 | { |
---|
114 | return a.len<b.len; |
---|
115 | } |
---|
116 | |
---|
117 | std::vector<UEdge> edges; |
---|
118 | |
---|
119 | void triangle() |
---|
120 | { |
---|
121 | Counter cnt("Number of edges added: "); |
---|
122 | std::vector<Pedge> pedges; |
---|
123 | for(NodeIt n(g);n!=INVALID;++n) |
---|
124 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
---|
125 | { |
---|
126 | Pedge p; |
---|
127 | p.a=n; |
---|
128 | p.b=m; |
---|
129 | p.len=(coords[m]-coords[n]).normSquare(); |
---|
130 | pedges.push_back(p); |
---|
131 | } |
---|
132 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
---|
133 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
---|
134 | { |
---|
135 | Line li(pi->a,pi->b); |
---|
136 | UEdgeIt e(g); |
---|
137 | for(;e!=INVALID && !cross(e,li);++e) ; |
---|
138 | UEdge ne; |
---|
139 | if(e==INVALID) { |
---|
140 | ne=g.addEdge(pi->a,pi->b); |
---|
141 | edges.push_back(ne); |
---|
142 | cnt++; |
---|
143 | } |
---|
144 | } |
---|
145 | } |
---|
146 | |
---|
147 | void sparse(int d) |
---|
148 | { |
---|
149 | Counter cnt("Number of edges removed: "); |
---|
150 | Bfs<ListUGraph> bfs(g); |
---|
151 | for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin(); |
---|
152 | ei!=edges.rend();++ei) |
---|
153 | { |
---|
154 | Node a=g.source(*ei); |
---|
155 | Node b=g.target(*ei); |
---|
156 | g.erase(*ei); |
---|
157 | bfs.run(a,b); |
---|
158 | if(bfs.predEdge(b)==INVALID || bfs.dist(b)>d) |
---|
159 | g.addEdge(a,b); |
---|
160 | else cnt++; |
---|
161 | } |
---|
162 | } |
---|
163 | |
---|
164 | void sparse2(int d) |
---|
165 | { |
---|
166 | Counter cnt("Number of edges removed: "); |
---|
167 | for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin(); |
---|
168 | ei!=edges.rend();++ei) |
---|
169 | { |
---|
170 | Node a=g.source(*ei); |
---|
171 | Node b=g.target(*ei); |
---|
172 | g.erase(*ei); |
---|
173 | ConstMap<Edge,int> cegy(1); |
---|
174 | Suurballe<ListUGraph,ConstMap<Edge,int> > sur(g,cegy,a,b); |
---|
175 | int k=sur.run(2); |
---|
176 | if(k<2 || sur.totalLength()>d) |
---|
177 | g.addEdge(a,b); |
---|
178 | else cnt++; |
---|
179 | // else std::cout << "Remove edge " << g.id(a) << "-" << g.id(b) << '\n'; |
---|
180 | } |
---|
181 | } |
---|
182 | |
---|
183 | void sparseTriangle(int d) |
---|
184 | { |
---|
185 | Counter cnt("Number of edges added: "); |
---|
186 | std::vector<Pedge> pedges; |
---|
187 | for(NodeIt n(g);n!=INVALID;++n) |
---|
188 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
---|
189 | { |
---|
190 | Pedge p; |
---|
191 | p.a=n; |
---|
192 | p.b=m; |
---|
193 | p.len=(coords[m]-coords[n]).normSquare(); |
---|
194 | pedges.push_back(p); |
---|
195 | } |
---|
196 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
---|
197 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
---|
198 | { |
---|
199 | Line li(pi->a,pi->b); |
---|
200 | UEdgeIt e(g); |
---|
201 | for(;e!=INVALID && !cross(e,li);++e) ; |
---|
202 | UEdge ne; |
---|
203 | if(e==INVALID) { |
---|
204 | ConstMap<Edge,int> cegy(1); |
---|
205 | Suurballe<ListUGraph,ConstMap<Edge,int> > |
---|
206 | sur(g,cegy,pi->a,pi->b); |
---|
207 | int k=sur.run(2); |
---|
208 | if(k<2 || sur.totalLength()>d) |
---|
209 | { |
---|
210 | ne=g.addEdge(pi->a,pi->b); |
---|
211 | edges.push_back(ne); |
---|
212 | cnt++; |
---|
213 | } |
---|
214 | } |
---|
215 | } |
---|
216 | } |
---|
217 | |
---|
218 | void minTree() { |
---|
219 | std::vector<Pedge> pedges; |
---|
220 | for(NodeIt n(g);n!=INVALID;++n) |
---|
221 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
---|
222 | { |
---|
223 | Pedge p; |
---|
224 | p.a=n; |
---|
225 | p.b=m; |
---|
226 | p.len=(coords[m]-coords[n]).normSquare(); |
---|
227 | pedges.push_back(p); |
---|
228 | } |
---|
229 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
---|
230 | ListUGraph::NodeMap<int> comp(g); |
---|
231 | UnionFind<ListUGraph::NodeMap<int> > uf(comp); |
---|
232 | for (NodeIt it(g); it != INVALID; ++it) |
---|
233 | uf.insert(it); |
---|
234 | |
---|
235 | int en=0; |
---|
236 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
---|
237 | { |
---|
238 | if ( uf.join(pi->a,pi->b) ) { |
---|
239 | g.addEdge(pi->a,pi->b); |
---|
240 | en++; |
---|
241 | if(en>=N-1) return; |
---|
242 | } |
---|
243 | } |
---|
244 | } |
---|
245 | |
---|
246 | |
---|
247 | |
---|
248 | int main(int argc,char **argv) |
---|
249 | { |
---|
250 | ArgParser ap(argc,argv); |
---|
251 | |
---|
252 | bool eps; |
---|
253 | bool disc_d, square_d, gauss_d; |
---|
254 | bool tsp_a,two_a,tree_a; |
---|
255 | int num_of_cities=1; |
---|
256 | double area=1; |
---|
257 | N=100; |
---|
258 | girth=10; |
---|
259 | std::string ndist("disc"); |
---|
260 | ap.option("n", "Number of nodes (default is 100)", N) |
---|
261 | .option("g", "Girth parameter (default is 10)", girth) |
---|
262 | .option("cities", "Number of cities (default is 1)", num_of_cities) |
---|
263 | .option("area", "Full relative area of the cities (default is 1)", area) |
---|
264 | .option("disc", "Nodes are evenly distributed on a unit disc (default)",disc_d) |
---|
265 | .optionGroup("dist", "disc") |
---|
266 | .option("square", "Nodes are evenly distributed on a unit square", square_d) |
---|
267 | .optionGroup("dist", "square") |
---|
268 | .option("gauss", |
---|
269 | "Nodes are located according to a two-dim gauss distribution", |
---|
270 | gauss_d) |
---|
271 | .optionGroup("dist", "gauss") |
---|
272 | // .mandatoryGroup("dist") |
---|
273 | .onlyOneGroup("dist") |
---|
274 | .option("eps", "Also generate .eps output (prefix.eps)",eps) |
---|
275 | .option("2con", "Create a two connected planar graph",two_a) |
---|
276 | .optionGroup("alg","2con") |
---|
277 | .option("tree", "Create a min. cost spanning tree",tree_a) |
---|
278 | .optionGroup("alg","tree") |
---|
279 | .option("tsp", "Create a TSP tour",tsp_a) |
---|
280 | .optionGroup("alg","tsp") |
---|
281 | .onlyOneGroup("alg") |
---|
282 | .other("[prefix]","Prefix of the output files. Default is 'lgf-gen-out'") |
---|
283 | .run(); |
---|
284 | |
---|
285 | std::string prefix; |
---|
286 | switch(ap.files().size()) |
---|
287 | { |
---|
288 | case 0: |
---|
289 | prefix="lgf-gen-out"; |
---|
290 | break; |
---|
291 | case 1: |
---|
292 | prefix=ap.files()[0]; |
---|
293 | break; |
---|
294 | default: |
---|
295 | std::cerr << "\nAt most one prefix can be given\n\n"; |
---|
296 | exit(1); |
---|
297 | } |
---|
298 | |
---|
299 | double sum_sizes=0; |
---|
300 | std::vector<double> sizes; |
---|
301 | std::vector<double> cum_sizes; |
---|
302 | for(int s=0;s<num_of_cities;s++) |
---|
303 | { |
---|
304 | // sum_sizes+=rnd.exponential(); |
---|
305 | double d=rnd(); |
---|
306 | sum_sizes+=d; |
---|
307 | sizes.push_back(d); |
---|
308 | cum_sizes.push_back(sum_sizes); |
---|
309 | } |
---|
310 | int i=0; |
---|
311 | for(int s=0;s<num_of_cities;s++) |
---|
312 | { |
---|
313 | Point center=(num_of_cities==1?Point(0,0):rnd.disc()); |
---|
314 | if(gauss_d) |
---|
315 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
---|
316 | Node n=g.addNode(); |
---|
317 | nodes.push_back(n); |
---|
318 | coords[n]=center+rnd.gauss2()*area* |
---|
319 | std::sqrt(sizes[s]/sum_sizes); |
---|
320 | } |
---|
321 | else if(square_d) |
---|
322 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
---|
323 | Node n=g.addNode(); |
---|
324 | nodes.push_back(n); |
---|
325 | coords[n]=center+Point(rnd()*2-1,rnd()*2-1)*area* |
---|
326 | std::sqrt(sizes[s]/sum_sizes); |
---|
327 | } |
---|
328 | else if(disc_d || true) |
---|
329 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
---|
330 | Node n=g.addNode(); |
---|
331 | nodes.push_back(n); |
---|
332 | coords[n]=center+rnd.disc()*area* |
---|
333 | std::sqrt(sizes[s]/sum_sizes); |
---|
334 | } |
---|
335 | } |
---|
336 | |
---|
337 | if(tsp_a) { |
---|
338 | tsp(); |
---|
339 | std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl; |
---|
340 | } |
---|
341 | else if(two_a) { |
---|
342 | std::cout << "Make triangles\n"; |
---|
343 | // triangle(); |
---|
344 | sparseTriangle(girth); |
---|
345 | std::cout << "Make it sparser\n"; |
---|
346 | sparse2(girth); |
---|
347 | } |
---|
348 | else if(tree_a) { |
---|
349 | minTree(); |
---|
350 | } |
---|
351 | |
---|
352 | |
---|
353 | std::cout << "Number of nodes : " << countNodes(g) << std::endl; |
---|
354 | std::cout << "Number of edges : " << countUEdges(g) << std::endl; |
---|
355 | double tlen=0; |
---|
356 | for(UEdgeIt e(g);e!=INVALID;++e) |
---|
357 | tlen+=sqrt((coords[g.source(e)]-coords[g.target(e)]).normSquare()); |
---|
358 | std::cout << "Total edge length : " << tlen << std::endl; |
---|
359 | if(eps) |
---|
360 | graphToEps(g,prefix+".eps"). |
---|
361 | scale(600).nodeScale(.2).edgeWidthScale(.001).preScale(false). |
---|
362 | coords(coords).run(); |
---|
363 | |
---|
364 | UGraphWriter<ListUGraph>(prefix+".lgf",g). |
---|
365 | writeNodeMap("coordinates_x",scaleMap(xMap(coords),600)). |
---|
366 | writeNodeMap("coordinates_y",scaleMap(yMap(coords),600)). |
---|
367 | run(); |
---|
368 | } |
---|
369 | |
---|