/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library.

  *

  * Copyright (C) 2003-2009

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 /// \ingroup tools

 /// \file

 /// \brief Special plane graph generator.

 ///

 /// Graph generator application for various types of plane graphs.

 ///

 /// See

 /// \code

 ///   lgf-gen --help

 /// \endcode

 /// for more information on the usage.

 #include <algorithm>

 #include <set>

 #include <ctime>

 #include <lemon/list_graph.h>

 #include <lemon/random.h>

 #include <lemon/dim2.h>

 #include <lemon/bfs.h>

 #include <lemon/counter.h>

 #include <lemon/suurballe.h>

 #include <lemon/graph_to_eps.h>

 #include <lemon/lgf_writer.h>

 #include <lemon/arg_parser.h>

 #include <lemon/euler.h>

 #include <lemon/math.h>

 #include <lemon/kruskal.h>

 #include <lemon/time_measure.h>

 using namespace lemon;

 typedef dim2::Point<double> Point;

 GRAPH_TYPEDEFS(ListGraph);

 bool progress=true;

 int N;

 // int girth;

 ListGraph g;

 std::vector<Node> nodes;

 ListGraph::NodeMap<Point> coords(g);

 double totalLen(){

   double tlen=0;

   for(EdgeIt e(g);e!=INVALID;++e)

     tlen+=std::sqrt((coords[g.v(e)]-coords[g.u(e)]).normSquare());

   return tlen;

 }

 int tsp_impr_num=0;

 const double EPSILON=1e-8;

 bool tsp_improve(Node u, Node v)

 {

   double luv=std::sqrt((coords[v]-coords[u]).normSquare());

   Node u2=u;

   Node v2=v;

   do {

     Node n;

     for(IncEdgeIt e(g,v2);(n=g.runningNode(e))==u2;++e) { }

     u2=v2;

     v2=n;

     if(luv+std::sqrt((coords[v2]-coords[u2]).normSquare())-EPSILON>

        std::sqrt((coords[u]-coords[u2]).normSquare())+

        std::sqrt((coords[v]-coords[v2]).normSquare()))

       {

          g.erase(findEdge(g,u,v));

          g.erase(findEdge(g,u2,v2));

         g.addEdge(u2,u);

         g.addEdge(v,v2);

         tsp_impr_num++;

         return true;

       }

   } while(v2!=u);

   return false;

 }

 bool tsp_improve(Node u)

 {

   for(IncEdgeIt e(g,u);e!=INVALID;++e)

     if(tsp_improve(u,g.runningNode(e))) return true;

   return false;

 }

 void tsp_improve()

 {

   bool b;

   do {

     b=false;

     for(NodeIt n(g);n!=INVALID;++n)

       if(tsp_improve(n)) b=true;

   } while(b);

 }

 void tsp()

 {

   for(int i=0;i<N;i++) g.addEdge(nodes[i],nodes[(i+1)%N]);

   tsp_improve();

 }

 class Line

 {

 public:

   Point a;

   Point b;

   Line(Point _a,Point _b) :a(_a),b(_b) {}

   Line(Node _a,Node _b) : a(coords[_a]),b(coords[_b]) {}

   Line(const Arc &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {}

   Line(const Edge &e) : a(coords[g.u(e)]),b(coords[g.v(e)]) {}

 };

 inline std::ostream& operator<<(std::ostream &os, const Line &l)

 {

   os << l.a << "->" << l.b;

   return os;

 }

 bool cross(Line a, Line b)

 {

   Point ao=rot90(a.b-a.a);

   Point bo=rot90(b.b-b.a);

   return (ao*(b.a-a.a))*(ao*(b.b-a.a))<0 &&

     (bo*(a.a-b.a))*(bo*(a.b-b.a))<0;

 }

 struct Parc

 {

   Node a;

   Node b;

   double len;

 };

 bool pedgeLess(Parc a,Parc b)

 {

   return a.len<b.len;

 }

 std::vector<Edge> arcs;

 namespace _delaunay_bits {

   struct Part {

     int prev, curr, next;

     Part(int p, int c, int n) : prev(p), curr(c), next(n) {}

   };

   inline std::ostream& operator<<(std::ostream& os, const Part& part) {

     os << '(' << part.prev << ',' << part.curr << ',' << part.next << ')';

     return os;

   }

   inline double circle_point(const Point& p, const Point& q, const Point& r) {

     double a = p.x * (q.y - r.y) + q.x * (r.y - p.y) + r.x * (p.y - q.y);

     if (a == 0) return std::numeric_limits<double>::quiet_NaN();

     double d = (p.x * p.x + p.y * p.y) * (q.y - r.y) +

       (q.x * q.x + q.y * q.y) * (r.y - p.y) +

       (r.x * r.x + r.y * r.y) * (p.y - q.y);

     double e = (p.x * p.x + p.y * p.y) * (q.x - r.x) +

       (q.x * q.x + q.y * q.y) * (r.x - p.x) +

       (r.x * r.x + r.y * r.y) * (p.x - q.x);

     double f = (p.x * p.x + p.y * p.y) * (q.x * r.y - r.x * q.y) +

       (q.x * q.x + q.y * q.y) * (r.x * p.y - p.x * r.y) +

       (r.x * r.x + r.y * r.y) * (p.x * q.y - q.x * p.y);

     return d / (2 * a) + std::sqrt((d * d + e * e) / (4 * a * a) + f / a);

   }

   inline bool circle_form(const Point& p, const Point& q, const Point& r) {

     return rot90(q - p) * (r - q) < 0.0;

   }

   inline double intersection(const Point& p, const Point& q, double sx) {

     const double epsilon = 1e-8;

     if (p.x == q.x) return (p.y + q.y) / 2.0;

     if (sx < p.x + epsilon) return p.y;

     if (sx < q.x + epsilon) return q.y;

     double a = q.x - p.x;

     double b = (q.x - sx) * p.y - (p.x - sx) * q.y;

     double d = (q.x - sx) * (p.x - sx) * (p - q).normSquare();

     return (b - std::sqrt(d)) / a;

   }

   struct YLess {

     YLess(const std::vector<Point>& points, double& sweep)

       : _points(points), _sweep(sweep) {}

     bool operator()(const Part& l, const Part& r) const {

       const double epsilon = 1e-8;

       //      std::cerr << l << " vs " << r << std::endl;

       double lbx = l.prev != -1 ?

         intersection(_points[l.prev], _points[l.curr], _sweep) :

         - std::numeric_limits<double>::infinity();

       double rbx = r.prev != -1 ?

         intersection(_points[r.prev], _points[r.curr], _sweep) :

         - std::numeric_limits<double>::infinity();

       double lex = l.next != -1 ?

         intersection(_points[l.curr], _points[l.next], _sweep) :

         std::numeric_limits<double>::infinity();

       double rex = r.next != -1 ?

         intersection(_points[r.curr], _points[r.next], _sweep) :

         std::numeric_limits<double>::infinity();

       if (lbx > lex) std::swap(lbx, lex);

       if (rbx > rex) std::swap(rbx, rex);

       if (lex < epsilon + rex && lbx + epsilon < rex) return true;

       if (rex < epsilon + lex && rbx + epsilon < lex) return false;

       return lex < rex;

     }

     const std::vector<Point>& _points;

     double& _sweep;

   };

   struct BeachIt;

   typedef std::multimap<double, BeachIt> SpikeHeap;

   typedef std::multimap<Part, SpikeHeap::iterator, YLess> Beach;

   struct BeachIt {

     Beach::iterator it;

     BeachIt(Beach::iterator iter) : it(iter) {}

   };

 }

 inline void delaunay() {

   Counter cnt("Number of arcs added: ");

   using namespace _delaunay_bits;

   typedef _delaunay_bits::Part Part;

   typedef std::vector<std::pair<double, int> > SiteHeap;

   std::vector<Point> points;

   std::vector<Node> nodes;

   for (NodeIt it(g); it != INVALID; ++it) {

     nodes.push_back(it);

     points.push_back(coords[it]);

   }

   SiteHeap siteheap(points.size());

   double sweep;

   for (int i = 0; i < int(siteheap.size()); ++i) {

     siteheap[i] = std::make_pair(points[i].x, i);

   }

   std::sort(siteheap.begin(), siteheap.end());

   sweep = siteheap.front().first;

   YLess yless(points, sweep);

   Beach beach(yless);

   SpikeHeap spikeheap;

   std::set<std::pair<int, int> > arcs;

   int siteindex = 0;

   {

     SiteHeap front;

     while (siteindex < int(siteheap.size()) &&

            siteheap[0].first == siteheap[siteindex].first) {

       front.push_back(std::make_pair(points[siteheap[siteindex].second].y,

                                      siteheap[siteindex].second));

       ++siteindex;

     }

     std::sort(front.begin(), front.end());

     for (int i = 0; i < int(front.size()); ++i) {

       int prev = (i == 0 ? -1 : front[i - 1].second);

       int curr = front[i].second;

       int next = (i + 1 == int(front.size()) ? -1 : front[i + 1].second);

       beach.insert(std::make_pair(Part(prev, curr, next),

                                   spikeheap.end()));

     }

   }

   while (siteindex < int(points.size()) || !spikeheap.empty()) {

     SpikeHeap::iterator spit = spikeheap.begin();

     if (siteindex < int(points.size()) &&

         (spit == spikeheap.end() || siteheap[siteindex].first < spit->first)) {

       int site = siteheap[siteindex].second;

       sweep = siteheap[siteindex].first;

       Beach::iterator bit = beach.upper_bound(Part(site, site, site));

       if (bit->second != spikeheap.end()) {

         spikeheap.erase(bit->second);

       }

       int prev = bit->first.prev;

       int curr = bit->first.curr;

       int next = bit->first.next;

       beach.erase(bit);

       SpikeHeap::iterator pit = spikeheap.end();

       if (prev != -1 &&

           circle_form(points[prev], points[curr], points[site])) {

         double x = circle_point(points[prev], points[curr], points[site]);

         pit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));

         pit->second.it =

           beach.insert(std::make_pair(Part(prev, curr, site), pit));

       } else {

         beach.insert(std::make_pair(Part(prev, curr, site), pit));

       }

       beach.insert(std::make_pair(Part(curr, site, curr), spikeheap.end()));

       SpikeHeap::iterator nit = spikeheap.end();

       if (next != -1 &&

           circle_form(points[site], points[curr],points[next])) {

         double x = circle_point(points[site], points[curr], points[next]);

         nit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));

         nit->second.it =

           beach.insert(std::make_pair(Part(site, curr, next), nit));

       } else {

         beach.insert(std::make_pair(Part(site, curr, next), nit));

       }

       ++siteindex;

     } else {

       sweep = spit->first;

       Beach::iterator bit = spit->second.it;

       int prev = bit->first.prev;

       int curr = bit->first.curr;

       int next = bit->first.next;

       {

         std::pair<int, int> arc;

         arc = prev < curr ?

           std::make_pair(prev, curr) : std::make_pair(curr, prev);

         if (arcs.find(arc) == arcs.end()) {

           arcs.insert(arc);

           g.addEdge(nodes[prev], nodes[curr]);

           ++cnt;

         }

         arc = curr < next ?

           std::make_pair(curr, next) : std::make_pair(next, curr);

         if (arcs.find(arc) == arcs.end()) {

           arcs.insert(arc);

           g.addEdge(nodes[curr], nodes[next]);

           ++cnt;

         }

       }

       Beach::iterator pbit = bit; --pbit;

       int ppv = pbit->first.prev;

       Beach::iterator nbit = bit; ++nbit;

       int nnt = nbit->first.next;

       if (bit->second != spikeheap.end()) spikeheap.erase(bit->second);

       if (pbit->second != spikeheap.end()) spikeheap.erase(pbit->second);

       if (nbit->second != spikeheap.end()) spikeheap.erase(nbit->second);

       beach.erase(nbit);

       beach.erase(bit);

       beach.erase(pbit);

       SpikeHeap::iterator pit = spikeheap.end();

       if (ppv != -1 && ppv != next &&

           circle_form(points[ppv], points[prev], points[next])) {

         double x = circle_point(points[ppv], points[prev], points[next]);

         if (x < sweep) x = sweep;

         pit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));

         pit->second.it =

           beach.insert(std::make_pair(Part(ppv, prev, next), pit));

       } else {

         beach.insert(std::make_pair(Part(ppv, prev, next), pit));

       }

       SpikeHeap::iterator nit = spikeheap.end();

       if (nnt != -1 && prev != nnt &&

           circle_form(points[prev], points[next], points[nnt])) {

         double x = circle_point(points[prev], points[next], points[nnt]);

         if (x < sweep) x = sweep;

         nit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));

         nit->second.it =

           beach.insert(std::make_pair(Part(prev, next, nnt), nit));

       } else {

         beach.insert(std::make_pair(Part(prev, next, nnt), nit));

       }

     }

   }

   for (Beach::iterator it = beach.begin(); it != beach.end(); ++it) {

     int curr = it->first.curr;

     int next = it->first.next;

     if (next == -1) continue;

     std::pair<int, int> arc;

     arc = curr < next ?

       std::make_pair(curr, next) : std::make_pair(next, curr);

     if (arcs.find(arc) == arcs.end()) {

       arcs.insert(arc);

       g.addEdge(nodes[curr], nodes[next]);

       ++cnt;

     }

   }

 }

 void sparse(int d)

 {

   Counter cnt("Number of arcs removed: ");

   Bfs<ListGraph> bfs(g);

   for(std::vector<Edge>::reverse_iterator ei=arcs.rbegin();

       ei!=arcs.rend();++ei)

     {

       Node a=g.u(*ei);

       Node b=g.v(*ei);

       g.erase(*ei);

       bfs.run(a,b);

       if(bfs.predArc(b)==INVALID || bfs.dist(b)>d)

         g.addEdge(a,b);

       else cnt++;

     }

 }

 void sparse2(int d)

 {

   Counter cnt("Number of arcs removed: ");

   for(std::vector<Edge>::reverse_iterator ei=arcs.rbegin();

       ei!=arcs.rend();++ei)

     {

       Node a=g.u(*ei);

       Node b=g.v(*ei);

       g.erase(*ei);

       ConstMap<Arc,int> cegy(1);

       Suurballe<ListGraph,ConstMap<Arc,int> > sur(g,cegy);

       int k=sur.run(a,b,2);

       if(k<2 || sur.totalLength()>d)

         g.addEdge(a,b);

       else cnt++;

 //       else std::cout << "Remove arc " << g.id(a) << "-" << g.id(b) << '\n';

     }

 }

 void sparseTriangle(int d)

 {

   Counter cnt("Number of arcs added: ");

   std::vector<Parc> pedges;

   for(NodeIt n(g);n!=INVALID;++n)

     for(NodeIt m=++(NodeIt(n));m!=INVALID;++m)

       {

         Parc p;

         p.a=n;

         p.b=m;

         p.len=(coords[m]-coords[n]).normSquare();

         pedges.push_back(p);

       }

   std::sort(pedges.begin(),pedges.end(),pedgeLess);

   for(std::vector<Parc>::iterator pi=pedges.begin();pi!=pedges.end();++pi)

     {

       Line li(pi->a,pi->b);

       EdgeIt e(g);

       for(;e!=INVALID && !cross(e,li);++e) ;

       Edge ne;

       if(e==INVALID) {

         ConstMap<Arc,int> cegy(1);

         Suurballe<ListGraph,ConstMap<Arc,int> > sur(g,cegy);

         int k=sur.run(pi->a,pi->b,2);

         if(k<2 || sur.totalLength()>d)

           {

             ne=g.addEdge(pi->a,pi->b);

             arcs.push_back(ne);

             cnt++;

           }

       }

     }

 }

 template <typename Graph, typename CoordMap>

 class LengthSquareMap {

 public:

   typedef typename Graph::Edge Key;

   typedef typename CoordMap::Value::Value Value;

   LengthSquareMap(const Graph& graph, const CoordMap& coords)

     : _graph(graph), _coords(coords) {}

   Value operator[](const Key& key) const {

     return (_coords[_graph.v(key)] -

             _coords[_graph.u(key)]).normSquare();

   }

 private:

   const Graph& _graph;

   const CoordMap& _coords;

 };

 void minTree() {

   std::vector<Parc> pedges;

   Timer T;

   std::cout << T.realTime() << "s: Creating delaunay triangulation...\n";

   delaunay();

   std::cout << T.realTime() << "s: Calculating spanning tree...\n";

   LengthSquareMap<ListGraph, ListGraph::NodeMap<Point> > ls(g, coords);

   ListGraph::EdgeMap<bool> tree(g);

   kruskal(g, ls, tree);

   std::cout << T.realTime() << "s: Removing non tree arcs...\n";

   std::vector<Edge> remove;

   for (EdgeIt e(g); e != INVALID; ++e) {

     if (!tree[e]) remove.push_back(e);

   }

   for(int i = 0; i < int(remove.size()); ++i) {

     g.erase(remove[i]);

   }

   std::cout << T.realTime() << "s: Done\n";

 }

 void tsp2()

 {

   std::cout << "Find a tree..." << std::endl;

   minTree();

   std::cout << "Total arc length (tree) : " << totalLen() << std::endl;

   std::cout << "Make it Euler..." << std::endl;

   {

     std::vector<Node> leafs;

     for(NodeIt n(g);n!=INVALID;++n)

       if(countIncEdges(g,n)%2==1) leafs.push_back(n);

 //    for(unsigned int i=0;i<leafs.size();i+=2)

 //       g.addArc(leafs[i],leafs[i+1]);

     std::vector<Parc> pedges;

     for(unsigned int i=0;i<leafs.size()-1;i++)

       for(unsigned int j=i+1;j<leafs.size();j++)

         {

           Node n=leafs[i];

           Node m=leafs[j];

           Parc p;

           p.a=n;

           p.b=m;

           p.len=(coords[m]-coords[n]).normSquare();

           pedges.push_back(p);

         }

     std::sort(pedges.begin(),pedges.end(),pedgeLess);

     for(unsigned int i=0;i<pedges.size();i++)

       if(countIncEdges(g,pedges[i].a)%2 &&

          countIncEdges(g,pedges[i].b)%2)

         g.addEdge(pedges[i].a,pedges[i].b);

   }

   for(NodeIt n(g);n!=INVALID;++n)

     if(countIncEdges(g,n)%2 || countIncEdges(g,n)==0 )

       std::cout << "GEBASZ!!!" << std::endl;

   for(EdgeIt e(g);e!=INVALID;++e)

     if(g.u(e)==g.v(e))

       std::cout << "LOOP GEBASZ!!!" << std::endl;

   std::cout << "Number of arcs : " << countEdges(g) << std::endl;

   std::cout << "Total arc length (euler) : " << totalLen() << std::endl;

   ListGraph::EdgeMap<Arc> enext(g);

   {

     EulerIt<ListGraph> e(g);

     Arc eo=e;

     Arc ef=e;

 //     std::cout << "Tour arc: " << g.id(Edge(e)) << std::endl;

     for(++e;e!=INVALID;++e)

       {

 //         std::cout << "Tour arc: " << g.id(Edge(e)) << std::endl;

         enext[eo]=e;

         eo=e;

       }

     enext[eo]=ef;

   }

   std::cout << "Creating a tour from that..." << std::endl;

   int nnum = countNodes(g);

   int ednum = countEdges(g);

   for(Arc p=enext[EdgeIt(g)];ednum>nnum;p=enext[p])

     {

 //       std::cout << "Checking arc " << g.id(p) << std::endl;

       Arc e=enext[p];

       Arc f=enext[e];

       Node n2=g.source(f);

       Node n1=g.oppositeNode(n2,e);

       Node n3=g.oppositeNode(n2,f);

       if(countIncEdges(g,n2)>2)

         {

 //           std::cout << "Remove an Arc" << std::endl;

           Arc ff=enext[f];

           g.erase(e);

           g.erase(f);

           if(n1!=n3)

             {

               Arc ne=g.direct(g.addEdge(n1,n3),n1);

               enext[p]=ne;

               enext[ne]=ff;

               ednum--;

             }

           else {

             enext[p]=ff;

             ednum-=2;

           }

         }

     }

   std::cout << "Total arc length (tour) : " << totalLen() << std::endl;

   std::cout << "2-opt the tour..." << std::endl;

   tsp_improve();

   std::cout << "Total arc length (2-opt tour) : " << totalLen() << std::endl;

 }

 int main(int argc,const char **argv)

 {

   ArgParser ap(argc,argv);

 //   bool eps;

   bool disc_d, square_d, gauss_d;

 //   bool tsp_a,two_a,tree_a;

   int num_of_cities=1;

   double area=1;

   N=100;

 //   girth=10;

   std::string ndist("disc");

   ap.refOption("n", "Number of nodes (default is 100)", N)

     .intOption("g", "Girth parameter (default is 10)", 10)

     .refOption("cities", "Number of cities (default is 1)", num_of_cities)

     .refOption("area", "Full relative area of the cities (default is 1)", area)

     .refOption("disc", "Nodes are evenly distributed on a unit disc (default)",

                disc_d)

     .optionGroup("dist", "disc")

     .refOption("square", "Nodes are evenly distributed on a unit square",

                square_d)

     .optionGroup("dist", "square")

     .refOption("gauss", "Nodes are located according to a two-dim Gauss "

                "distribution", gauss_d)

     .optionGroup("dist", "gauss")

     .onlyOneGroup("dist")

     .boolOption("eps", "Also generate .eps output (<prefix>.eps)")

     .boolOption("nonodes", "Draw only the edges in the generated .eps output")

     .boolOption("dir", "Directed graph is generated (each edge is replaced by "

                 "two directed arcs)")

     .boolOption("2con", "Create a two connected planar graph")

     .optionGroup("alg","2con")

     .boolOption("tree", "Create a min. cost spanning tree")

     .optionGroup("alg","tree")

     .boolOption("tsp", "Create a TSP tour")

     .optionGroup("alg","tsp")

     .boolOption("tsp2", "Create a TSP tour (tree based)")

     .optionGroup("alg","tsp2")

     .boolOption("dela", "Delaunay triangulation graph")

     .optionGroup("alg","dela")

     .onlyOneGroup("alg")

     .boolOption("rand", "Use time seed for random number generator")

     .optionGroup("rand", "rand")

     .intOption("seed", "Random seed", -1)

     .optionGroup("rand", "seed")

     .onlyOneGroup("rand")

     .other("[prefix]","Prefix of the output files. Default is 'lgf-gen-out'")

     .run();

   if (ap["rand"]) {

     int seed = int(time(0));

     std::cout << "Random number seed: " << seed << std::endl;

     rnd = Random(seed);

   }

   if (ap.given("seed")) {

     int seed = ap["seed"];

     std::cout << "Random number seed: " << seed << std::endl;

     rnd = Random(seed);

   }

   std::string prefix;

   switch(ap.files().size())

     {

     case 0:

       prefix="lgf-gen-out";

       break;

     case 1:

       prefix=ap.files()[0];

       break;

     default:

       std::cerr << "\nAt most one prefix can be given\n\n";

       exit(1);

     }

   double sum_sizes=0;

   std::vector<double> sizes;

   std::vector<double> cum_sizes;

   for(int s=0;s<num_of_cities;s++)

     {

       //         sum_sizes+=rnd.exponential();

       double d=rnd();

       sum_sizes+=d;

       sizes.push_back(d);

       cum_sizes.push_back(sum_sizes);

     }

   int i=0;

   for(int s=0;s<num_of_cities;s++)

     {

       Point center=(num_of_cities==1?Point(0,0):rnd.disc());

       if(gauss_d)

         for(;i<N*(cum_sizes[s]/sum_sizes);i++) {

           Node n=g.addNode();

           nodes.push_back(n);

           coords[n]=center+rnd.gauss2()*area*

             std::sqrt(sizes[s]/sum_sizes);

         }

       else if(square_d)

         for(;i<N*(cum_sizes[s]/sum_sizes);i++) {

           Node n=g.addNode();

           nodes.push_back(n);

           coords[n]=center+Point(rnd()*2-1,rnd()*2-1)*area*

             std::sqrt(sizes[s]/sum_sizes);

         }

       else if(disc_d || true)

         for(;i<N*(cum_sizes[s]/sum_sizes);i++) {

           Node n=g.addNode();

           nodes.push_back(n);

           coords[n]=center+rnd.disc()*area*

             std::sqrt(sizes[s]/sum_sizes);

         }

     }

 //   for (ListGraph::NodeIt n(g); n != INVALID; ++n) {

 //     std::cerr << coords[n] << std::endl;

 //   }

   if(ap["tsp"]) {

     tsp();

     std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl;

   }

   if(ap["tsp2"]) {

     tsp2();

     std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl;

   }

   else if(ap["2con"]) {

     std::cout << "Make triangles\n";

     //   triangle();

     sparseTriangle(ap["g"]);

     std::cout << "Make it sparser\n";

     sparse2(ap["g"]);

   }

   else if(ap["tree"]) {

     minTree();

   }

   else if(ap["dela"]) {

     delaunay();

   }

   std::cout << "Number of nodes    : " << countNodes(g) << std::endl;

   std::cout << "Number of arcs    : " << countEdges(g) << std::endl;

   double tlen=0;

   for(EdgeIt e(g);e!=INVALID;++e)

     tlen+=std::sqrt((coords[g.v(e)]-coords[g.u(e)]).normSquare());

   std::cout << "Total arc length  : " << tlen << std::endl;

   if(ap["eps"])

     graphToEps(g,prefix+".eps").scaleToA4().

       scale(600).nodeScale(.005).arcWidthScale(.001).preScale(false).

       coords(coords).hideNodes(ap.given("nonodes")).run();

   if(ap["dir"])

     DigraphWriter<ListGraph>(g,prefix+".lgf").

       nodeMap("coordinates_x",scaleMap(xMap(coords),600)).

       nodeMap("coordinates_y",scaleMap(yMap(coords),600)).

       run();

   else GraphWriter<ListGraph>(g,prefix+".lgf").

          nodeMap("coordinates_x",scaleMap(xMap(coords),600)).

          nodeMap("coordinates_y",scaleMap(yMap(coords),600)).

          run();

 }