/***************************
 * (C) 2010 Claudio Rocchini
 * GPL License
 ***************************/
#include <stdio.h>
#include <math.h>
#include <vector>
#include <set>
#include <algorithm>

const double PI = 3.1415926535897932384626433832795;
typedef std::pair<int,int> edge;

static inline unsigned char f2b( double f ) {
	if(f<0) f = 0; if(f>1) f = 1;
	int i = int(f*256);
	if(i>255) i = 255;
	else if(i<0) i=0;
	return i;
}

void HSV2RGB(double h, double s, double v, unsigned char rgb[3] ) {
	if (s == 0) {
		rgb[0] = rgb[1] = rgb[2] = f2b(v);
	} else {
		double v_h = h * 6;
		double v_i = floor(v_h);
		double v_1 = v * (1 - s);
		double v_2 = v * (1 - s * (v_h - v_i));
		double v_3 = v * (1 - s * (1 - (v_h - v_i)));
		double v_r,v_g,v_b;
		     if (v_i == 0) {v_r = v;   v_g = v_3; v_b = v_1;}
		else if (v_i == 1) {v_r = v_2; v_g = v;   v_b = v_1;}
		else if (v_i == 2) {v_r = v_1; v_g = v;   v_b = v_3;}
		else if (v_i == 3) {v_r = v_1; v_g = v_2; v_b = v  ;}
		else if (v_i == 4) {v_r = v_3; v_g = v_1; v_b = v  ;}
		else               {v_r = v;   v_g = v_1; v_b = v_2;};
		
		rgb[0] = f2b(v_r);
		rgb[1] = f2b(v_g);
		rgb[2] = f2b(v_b);
	}
}

class permu
{
public:
	std::vector<size_t> p;
	void ident( size_t n ) {
		p.resize(n); for(size_t i=0;i<n;++i) p[i] = i;
	}
};

void copy( permu & dst, const permu & src ) {
	dst.p.resize(src.p.size());
	std::copy(src.p.begin(),src.p.end(),dst.p.begin());
}

void apply( permu & dst, const size_t perm[] ) {
	permu t; copy(t,dst);
	for(size_t i=0;i<dst.p.size();++i)
		dst.p[i] = t.p[perm[i]];
}

void apply( permu & dst, const int perm[] ) {
	permu t; copy(t,dst);
	for(size_t i=0;i<dst.p.size();++i)
		dst.p[i] = t.p[perm[i]];
}

bool operator== (const permu & a, const permu & b) {
	std::vector<size_t>::const_iterator i,j;
	for(i=a.p.begin(),j=b.p.begin();i!=a.p.end();++i,++j)
		if(*i!=*j) return false;
	return true;
}

bool operator< (const permu & a, const permu & b) {
	std::vector<size_t>::const_iterator i,j;
	for(i=a.p.begin(),j=b.p.begin();i!=a.p.end();++i,++j)
		if(*i!=*j) return *i < *j;
	return false;
}

size_t fix_point( const permu & pe ) {
	size_t fix = 0;
	for(size_t j=0;j<pe.p.size();++j)
		if(pe.p[j]==j) ++fix;
	return fix;
}

size_t cicle_size( const permu & pe ) {
	permu t; copy(t,pe); size_t cs = 0;
	for(;;) {
		apply(t,& pe.p.front());
		++cs; if(t==pe) break;
	}
	return cs;
}

size_t sub_loops( const permu & pe, std::vector< std::vector<size_t> > & loops ) {
	std::vector<bool> done(pe.p.size()); std::fill(done.begin(),done.end(),false);
	loops.clear();
	for(;;) {
		size_t i;
		for(i=0;i<pe.p.size();++i) if(!done[i]) break;
		if(i==pe.p.size()) break;
		loops.push_back( std::vector<size_t>() );
		size_t j = i;
		do {
			done[j] = true;
			loops.back().push_back(j);
			j = pe.p[j];
		} while(j!=i);
	}
	return loops.size();
}

void out_nauty( int n, const std::vector<std::pair<int,int> > & edges, const char * filename) {
	std::vector< std::vector<int> > vv;
	vv.resize(n);
	std::vector<std::pair<int,int> >::const_iterator i;
	for(i=edges.begin();i!=edges.end();++i)
		if((*i).first < (*i).second)
			vv[(*i).first].push_back( (*i).second );
		else
			vv[(*i).second].push_back( (*i).first );

	std::vector< std::vector<int> >::iterator j;
	for(j=vv.begin();j!=vv.end();++j) std::sort(j->begin(),j->end());

	FILE * fo = fopen(filename,"w");
	fprintf(fo,"n=%d\ng\n",n);
	for(j=vv.begin();j!=vv.end();++j) {
		if(j!=vv.begin()) fprintf(fo,";\n");
		std::vector<int>::iterator k;
		for(k=j->begin();k!=j->end();++k) {
			if(k!=j->begin()) fprintf(fo," ");
			fprintf(fo,"%d",*k);
		}
	}
	fprintf(fo,".\n");
	fprintf(fo, "p\nx\no\nq\n");
	fclose(fo);
}

void load_nauty( int NV, const char * filename, std::vector< std::vector<int> > & auto_base ) {
	const int BSIZE = 1024; static char buff[1024];
	auto_base.clear();
	FILE * fp = fopen(filename,"r");
	auto_base.push_back( std::vector<int>() );
	while(fgets(buff,BSIZE,fp)){
		if(strstr(buff,"grpsize"))
			break;
		else if(strstr(buff,"level"))
			auto_base.push_back( std::vector<int>() );
		else {
			const char * sep = " \n\r\t"; char * p = strtok(buff,sep);
			while(p){
				if(auto_base.back().size()==size_t(NV)) 
					auto_base.push_back( std::vector<int>() );
				auto_base.back().push_back(atoi(p));
				p = strtok(0,sep);
			}
		}
	}
	fclose(fp); auto_base.pop_back();
}

	// n = master set size, m= subsets size
void make_subsets( int m, int n, std::vector< std::vector<int> > & subs ) {
	std::vector<int> ss(m);
	for(int i=0;i<m;++i) ss[i] = i;
	subs.clear();
	for(;;) {
		subs.push_back( ss ); int i = m-1;
		for(;;) {
			if(++ss[i]<n) {
				if(i==m-1) break;
				ss[i+1]=ss[i]; ++i;
			}
			else if(--i<0) break;
		}
		if(i<0) break;
	}
}

	// number of commons element. a,b supposed ordered
int commons( std::vector<int> & a, std::vector<int> & b ) {
	if(a.back()<b.front() || a.front()>b.back()) return 0;
	int c = 0; std::vector<int>::const_iterator ia,ib;
	for(ia=a.begin(),ib=b.begin();ia!=a.end() && ib!=b.end();) {
		if(*ia==*ib) { ++c; ++ia; ++ib; }
		else if(*ia<*ib) ++ia;
		else             ++ib;
	}
	return c;
}

	// n = numero di caratteri, m = lunghezza stringhe, l=sotto-insiemi unici
void make_steiner_system( int l, int m, int n, std::vector< std::vector<int> > & out_blocks ) {
	std::vector< std::vector<int> > blocks;
	make_subsets(m,n,blocks);
	size_t i,j;
	std::vector<bool> oks(blocks.size());
	std::fill(oks.begin(),oks.end(),true);
	for(i=0;i<blocks.size()-1;++i) if(oks[i])
		for(j=i+1;j<blocks.size();++j) if(oks[j])
			if(commons(blocks[i],blocks[j])>=l) oks[j] = false;
	out_blocks.clear();
	for(i=0;i<blocks.size();++i) if(oks[i])
		out_blocks.push_back( blocks[i] );
}

bool analyze_sym( int NV, permu & p, std::vector<int> & out_perm ) {
	if(fix_point(p)!=0) return false;
	size_t cs = cicle_size(p);
	if(cs<4 || NV%cs!=0) return false;
	std::vector< std::vector<size_t> > loops;
	if(size_t(NV)==cs*loops.size()) {
		std::vector< std::vector<size_t> >::iterator q;
		size_t iq;
		for(iq=0,q=loops.begin();q!=loops.end();++iq,++q) {
			std::vector<size_t>::iterator w;
			size_t iw;
			for(iw=0,w=q->begin();w!=q->end();++iw,++w)
				out_perm[ iq + loops.size()*iw ] = *w;
		}
		return true;
	}
	return false;
}

void find_symmetric( int NV, const std::vector< std::vector<int> > & auto_base, std::vector<int> & out_perm )
{
	std::set<permu> perms;
	std::vector<permu> active;
	out_perm.resize(NV);

	permu cu; cu.ident(NV);
	perms.insert(cu); active.push_back(cu);

	while(!active.empty()) {
		std::vector<permu>::iterator i;
		std::pair< std::set<permu>::iterator, bool > r;
		std::vector<permu> old_active;
		std::swap(old_active,active);
		for(i=old_active.begin();i!=old_active.end();++i) {
			for(size_t j=0;j<auto_base.size();++j) {
				copy(cu,*i); apply(cu,&auto_base[j].front());
				r = perms.insert(cu);
				if(r.second) {
					if(analyze_sym(NV,cu,out_perm)) return;
					active.push_back(cu);
				}
			}
		}
	}
}

void save_svg_color( const char * filename, int NV, std::vector<edge> & edges, const int perm[] ) {
	const double SX = 800; const double SY = 800;
	const double RR = 2;   const double BO = 10;

	std::vector<double> px(NV); std::vector<double> py(NV);

	FILE * fp = fopen(filename,"w");
	fprintf(fp,
		"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n"
		"<svg\n"
		"xmlns:svg=\"http://www.w3.org/2000/svg\"\n"
		"xmlns=\"http://www.w3.org/2000/svg\"\n"
		"version=\"1.0\"\n"
		"width=\"%g\"\n" "height=\"%g\"\n"
		"id=\"rockini\">\n"
		,SX,SY
	);

	int i;
	const double R = ((SX-BO*2)/2);
	
	for(i=0;i<NV;++i) {
		const double a = 2*PI*i/NV;
		px[perm[i]] = SX/2 + R*cos(a);
		py[perm[i]] = SY/2 + R*sin(a);
	}

	std::set<int> dist;
	for(i=0;i<int(edges.size());++i) {
		double dx = px[edges[i].first ] - px[edges[i].second];
		double dy = py[edges[i].first ] - py[edges[i].second];
		int di = int(sqrt(dx*dx+dy*dy)+0.5);
		dist.insert(di);
	}
	std::vector<int> vdist;
	std::set<int>::iterator id;
	for(id=dist.begin();id!=dist.end();++id)
		vdist.push_back(*id);

	for(size_t co=0;co<vdist.size();++co) {
		unsigned char rgb[3];
		HSV2RGB(double(co)*2/(3*vdist.size()),0.9,0.8,rgb);
		fprintf(fp,"<g id=\"edges\" style=\"stroke:#%02X%02X%02X;stroke-width:0.1;\">\n",
			rgb[0],rgb[1],rgb[2]);
		for(i=0;i<int(edges.size());++i) {
			double dx = px[edges[i].first ] - px[edges[i].second];
			double dy = py[edges[i].first ] - py[edges[i].second];
			int di = int(sqrt(dx*dx+dy*dy)+0.5);
			if(di!=vdist[co]) continue;
			fprintf(fp,
				"<line x1=\"%5.1lf\" y1=\"%5.1lf\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>\n"
				,px[edges[i].first ],py[edges[i].first ]
				,px[edges[i].second],py[edges[i].second]
			);
		}
		fprintf(fp,"</g>\n");
	}

	fprintf(fp,"<g id=\"nodes\" style=\"stroke:#000;stroke-width:1;stroke-opacity:1.0;fill:#040000\">\n");
	for(i=0;i<NV;++i)
		fprintf(fp,"<circle cx=\"%5.1lf\" cy=\"%5.1lf\" r=\"%5.1lf\"/>\n",px[i],py[i],RR);
	fprintf(fp,"</g>\n");

	fprintf(fp,"</svg>\n");
	fclose(fp);
}

int main(){
	size_t i,j,k,h;
	
		// Make McLaughlin Graph
	const int NVMC = 275;	// 22=steiner char >0, 77 = B blocks contains 0, 176 = C block not-contains 
	std::vector< std::vector<int> > blocks;
	make_steiner_system(4,7,23,blocks);
	
	std::vector<size_t> B; std::vector<size_t> C;
	for(i=0;i<blocks.size();++i)
		if(std::find(blocks[i].begin(),blocks[i].end(),0)!=blocks[i].end())
			B.push_back(i);
		else C.push_back(i);

	std::vector<edge> edges_mc;

	for(i=0;i<22;++i) for(j=0;j<B.size();++j) {
		k = B[j];
		if(std::find(blocks[k].begin(),blocks[k].end(),i+1)==blocks[k].end())
			edges_mc.push_back( edge(i,j+22) );
	}

	for(i=0;i<B.size()-1;++i) for(j=i+1;j<B.size();++j)
	if(commons(blocks[B[i]],blocks[B[j]])==1)
		edges_mc.push_back( edge(i+22,j+22) );

	for(i=0;i<22;++i) for(j=0;j<C.size();++j) {
		k = C[j];
		if(std::find(blocks[k].begin(),blocks[k].end(),i+1)!=blocks[k].end())
			edges_mc.push_back( edge(i,j+99) );
	}

	for(i=0;i<B.size();++i) {
		k = B[i];
		for(j=0;j<C.size();++j) {
			h = C[j];
			if(commons(blocks[k],blocks[h])==3)
				edges_mc.push_back( edge(i+22,j+99) );
		}
	}

	for(i=0;i<C.size()-1;++i) for(j=i+1;j<C.size();++j)
		if(commons(blocks[C[i]],blocks[C[j]])==1)
			edges_mc.push_back( edge(i+99,j+99) );

		// Make Local McLaughlin Graph
	std::vector<bool> deleted(NVMC); std::fill(deleted.begin(),deleted.end(),false);
	deleted[0] = true;
	std::vector<edge>::iterator ie;
	for(ie=edges_mc.begin();ie!=edges_mc.end();++ie) {
		if((*ie).first==0) deleted[(*ie).second] = true;
		if((*ie).second==0) deleted[(*ie).first] = true;
	}

	size_t NV = 0; std::vector<int> reindex(NVMC);
	for(i=0;i<deleted.size();++i)
		if(!deleted[i]) reindex[i] = NV++;
		else reindex[i] = -1;
	printf("%u vertices\n",NV);

	std::vector<edge> edges;
	for(ie=edges_mc.begin();ie!=edges_mc.end();++ie) {
		int rf = reindex[(*ie).first];
		int rs = reindex[(*ie).second];
		if(rf!=-1 && rs!=-1) edges.push_back( edge(rf,rs) );
	}
	printf("%u edges\n",edges.size());

		// nauty
	out_nauty(NV,edges,"lmclaughlin_i.txt");
	system("nauty < lmclaughlin_i.txt > lmclaughlin_o.txt");
	std::vector< std::vector<int> > auto_base;
	load_nauty(NV,"lmclaughlin_o.txt",auto_base);

	std::vector<int> out_perm;
	find_symmetric(NV,auto_base,out_perm);
	save_svg_color("c:\\temp\\lmclaughlin.svg",NV,edges,&out_perm.front());

	return 0;
}