/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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.

///

///\verbatim

/// Usage:

///   ./tools/lgf-gen [-2con|-tree|-tsp|-tsp2|-dela] [-disc|-square|-gauss]

///      [-rand|-seed int] [--help|-h|-help] [-area num] [-cities int] [-dir]

///      [-eps] [-g int] [-n int] [prefix]

/// Where:

///   [prefix]

///      Prefix of the output files. Default is 'lgf-gen-out'

///   --help|-h|-help

///      Print a short help message

///   -2con

///      Create a two connected planar graph

///   -area num

///      Full relative area of the cities (default is 1)

///   -cities int

///      Number of cities (default is 1)

///   -dela

///      Delaunay triangulation graph

///   -dir

///      Directed graph is generated (each edges are replaced by two directed ones)

///   -disc

///      Nodes are evenly distributed on a unit disc (default)

///   -eps

///      Also generate .eps output (prefix.eps)

///   -g int

///      Girth parameter (default is 10)

///   -gauss

///      Nodes are located according to a two-dim gauss distribution

///   -n int

///      Number of nodes (default is 100)

///   -rand

///      Use time seed for random number generator

///   -seed int

///      Random seed

///   -square

///      Nodes are evenly distributed on a unit square

///   -tree

///      Create a min. cost spanning tree

///   -tsp

///      Create a TSP tour

///   -tsp2

///      Create a TSP tour (tree based)

///\endverbatim

/// \image html plane_tree.png

/// \image latex plane_tree.eps "Eucledian spanning tree" width=\textwidth

///

#include <lemon/list_graph.h>

#include <lemon/graph_utils.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/graph_writer.h>

#include <lemon/arg_parser.h>

#include <lemon/euler.h>

#include <lemon/math.h>

#include <algorithm>

#include <lemon/kruskal.h>

#include <lemon/time_measure.h>

using namespace lemon;

typedef dim2::Point<double> Point;

UGRAPH_TYPEDEFS(ListUGraph);

bool progress=true;

int N;

// int girth;

ListUGraph g;

std::vector<Node> nodes;

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

double totalLen(){

  double tlen=0;

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

    tlen+=sqrt((coords[g.source(e)]-coords[g.target(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(findUEdge(g,u,v));

 	g.erase(findUEdge(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 Edge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {}

  Line(const UEdge &e) : a(coords[g.source(e)]),b(coords[g.target(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 Pedge

{

  Node a;

  Node b;

  double len;

};

bool pedgeLess(Pedge a,Pedge b)

{

  return a.len<b.len;

}

std::vector<UEdge> edges;

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) + 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 - 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 edges 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> > edges;

  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> edge;

	edge = prev < curr ? 

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

	if (edges.find(edge) == edges.end()) {

	  edges.insert(edge);

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

	  ++cnt;

	}

	edge = curr < next ? 

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

	if (edges.find(edge) == edges.end()) {

	  edges.insert(edge);

	  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> edge;

    edge = curr < next ? 

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

    if (edges.find(edge) == edges.end()) {

      edges.insert(edge);

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

      ++cnt;

    }

  }

}

void sparse(int d) 

{

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

  Bfs<ListUGraph> bfs(g);

  for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin();

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

    {

      Node a=g.source(*ei);

      Node b=g.target(*ei);

      g.erase(*ei);

      bfs.run(a,b);

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

	g.addEdge(a,b);

      else cnt++;

    }

}

void sparse2(int d) 

{

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

  for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin();

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

    {

      Node a=g.source(*ei);

      Node b=g.target(*ei);

      g.erase(*ei);

      ConstMap<Edge,int> cegy(1);

      Suurballe<ListUGraph,ConstMap<Edge,int> > sur(g,cegy,a,b);

      int k=sur.run(2);

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

	g.addEdge(a,b);

      else cnt++;

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

    }

}

void sparseTriangle(int d)

{

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

  std::vector<Pedge> pedges;

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

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

      {

	Pedge 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<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi)

    {

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

      UEdgeIt e(g);

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

      UEdge ne;

      if(e==INVALID) {

	ConstMap<Edge,int> cegy(1);

	Suurballe<ListUGraph,ConstMap<Edge,int> >

	  sur(g,cegy,pi->a,pi->b);

	int k=sur.run(2);

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

	  {

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

	    edges.push_back(ne);

	    cnt++;

	  }

      }

    }

}

template <typename UGraph, typename CoordMap>

class LengthSquareMap {

public:

  typedef typename UGraph::UEdge Key;

  typedef typename CoordMap::Value::Value Value;

  LengthSquareMap(const UGraph& ugraph, const CoordMap& coords)

    : _ugraph(ugraph), _coords(coords) {}

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

    return (_coords[_ugraph.target(key)] -

	    _coords[_ugraph.source(key)]).normSquare();

  }

private:

  const UGraph& _ugraph;

  const CoordMap& _coords;

};

void minTree() {

  std::vector<Pedge> pedges;

  Timer T;

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

  delaunay();

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

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

  ListUGraph::UEdgeMap<bool> tree(g);

  kruskal(g, ls, tree);

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

  std::vector<UEdge> remove;

  for (UEdgeIt 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 edge 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.addEdge(leafs[i],leafs[i+1]);

    std::vector<Pedge> 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];

	  Pedge 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(UEdgeIt e(g);e!=INVALID;++e)

    if(g.source(e)==g.target(e))

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

  std::cout << "Number of edges : " << countUEdges(g) << std::endl;

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

  ListUGraph::UEdgeMap<Edge> enext(g);

  {

    UEulerIt<ListUGraph> e(g);

    Edge eo=e;

    Edge ef=e;

//     std::cout << "Tour edge: " << g.id(UEdge(e)) << std::endl;      

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

      {

// 	std::cout << "Tour edge: " << g.id(UEdge(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 = countUEdges(g);

  for(Edge p=enext[UEdgeIt(g)];ednum>nnum;p=enext[p]) 

    {

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

      Edge e=enext[p];

      Edge 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 Edge" << std::endl;

	  Edge ff=enext[f];

	  g.erase(e);

	  g.erase(f);

	  if(n1!=n3)

	    {

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

	      enext[p]=ne;

	      enext[ne]=ff;

	      ednum--;

	    }

	  else {

	    enext[p]=ff;

	    ednum-=2;

	  }

	}

    }

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

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

  tsp_improve();

  std::cout << "Total edge 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")

//     .mandatoryGroup("dist")

    .onlyOneGroup("dist")

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

    .boolOption("dir", "Directed graph is generated (each edges are replaced by two directed ones)")

    .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 = 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 (ListUGraph::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 edges    : " << countUEdges(g) << std::endl;

  double tlen=0;

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

    tlen+=sqrt((coords[g.source(e)]-coords[g.target(e)]).normSquare());

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

  if(ap["eps"])

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

      scale(600).nodeScale(.2).edgeWidthScale(.001).preScale(false).

      coords(coords).run();

  if(ap["dir"])

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

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

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

      run();

  else UGraphWriter<ListUGraph>(prefix+".lgf",g).

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

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

	 run();

}