/************************************************************************
 * making of Brouwer_Haemers_Graph                                      *
 * Copyright (C) 2010                                                   *
 *   Claudio Rocchini                                                   *
 *   All rights reserved.                                               *
 * This program is free software: you can redistribute it and/or modify *
 * it under the terms of the GNU General Public License as published by *
 * the Free  Software Foundation,  either version  3 of the License, or *
 * (at your option) any later version.                                  *
 *   This program is distributed in the hope that it will be useful,    *
 *   but WITHOUT ANY WARRANTY; without even the implied  warranty of    *
 *   MERCHANTABILITY  or FITNESS  FOR A  PARTICULAR PURPOSE. See the    *
 *   GNU General Public License for more details.                       *
 * You should have  received a  copy of the GNU  General Public License *
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.*
 ************************************************************************/
 
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <vector>
#include <set>
#include <algorithm>

const double PI = 3.1415926535897932384626433832795;

typedef std::pair<int,int> edge;

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();
}

bool is_strong_regular( const int nv, const std::vector<edge> & edges ){
	int i,j,k;
	std::vector<bool> MA(nv*nv); std::fill(MA.begin(),MA.end(),false);
	std::vector<edge>::const_iterator q;
	for(q=edges.begin();q!=edges.end();++q)
	{
		MA[(*q).first+nv*(*q).second] = true;
		MA[(*q).second+nv*(*q).first] = true;
	}
	std::vector<int> adj(nv);
	std::fill(adj.begin(),adj.end(),0);
	for(k=0;k<nv*nv;++k) if(MA[k]) {
		i = k%nv; j = k/nv;
		if(i<j) { ++adj[i]; ++adj[j]; }
	}
	for(i=1;i<nv;++i) if(adj[0]!=adj[i]) {
		printf("Error: different rank: %d, %d\n",adj[0],adj[i]);
		return false;
	}
	printf("OK rank: %d\n",adj[0]);
	int gni = -1; int gno = -1;		// lambda mu
	for(i=0;i<nv-1;++i)
	for(j=i+1;j<nv;++j) {
		int n = 0;
		for(k=0;k<nv;++k) if(k!=i && k!=j)
			if( MA[i*nv+k] && MA[j*nv+k] ) ++n;
		if( MA[i*nv+j] ) {
			if(gni==-1) gni = n;
			else if(gni!=n ) {
				printf("Error: different ni\n");
				return false;
			}
		} else {
			if(gno==-1) gno = n;
			else if(gno!=n ) {
				printf("Error: different no\n");
				return false;
			}
		}
	}
	printf("OK l:%d m:%d\n",gni,gno);
	return true;
}

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\n" "g\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" "p\n" "x\n" "o\n" "q\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();
}

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;
	size_t nsl = sub_loops(p,loops);
	if(size_t(NV)==cs*loops.size() && cs>3)	{ // TODO 3?? 
		printf("GOOD! %u %u\n",cs,nsl);
		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, bool all = false ) {
	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)) {
						if(!all) return;
					}
					active.push_back(cu);
				}
			}
		}
	}
	printf("%u autos\n",perms.size());
}

void random_perm( size_t n, size_t m, int per[] ) {
	size_t i,j;
	std::vector<size_t> shu(m);
	for(i=0;i<m;++i) shu[i] = i; std::random_shuffle(shu.begin(),shu.end());
	std::vector<size_t> fas(m);
	for(i=0;i<m;++i) fas[i] = std::rand()%n;
	std::vector<size_t> o_per(n*m); std::copy(per,per+(n*m),o_per.begin());
	for(i=0;i<m;++i) for(j=0;j<n;++j)
		per[i+j*m] = o_per[ shu[i] + ((j+fas[i])%n) * m];
}

void save_svg_random_try( const char * filename, int NV, std::vector<edge> & edges, int perm[], int simm ) {
	const double SX = 800; const double SY = 800;
	const double RR = 2;   const double BO = 5;
	const int N = 4;
	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/N)/2;
	for(size_t vx=0;vx<size_t(N);++vx)
	for(size_t vy=0;vy<size_t(N);++vy){
		fprintf(fp,"<g id=\"edges\" style=\"stroke:#000000;stroke-width:0.1;stroke-opacity:1.0;\">\n");
		for(i=0;i<NV;++i) {
			const double a = 2*PI*i/NV;
			px[perm[i]] = R + (R-BO)*cos(a) + vx*(R*2);
			py[perm[i]] = R + (R-BO)*sin(a) + vy*(R*2);
		}
		for(i=0;i<int(edges.size());++i) {
			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:#000000;stroke-width:1;stroke-opacity:1.0;fill:#FF0000\">\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");
		random_perm(simm,NV/simm,perm);
	}
	fprintf(fp,"</svg>\n");
	fclose(fp);
}

int main() {
		// Make over GF(3): adjacent whe full quadric of difference=0
	const size_t NV = 81;
	size_t i,j,a,b;
	std::vector<edge> edges;
	for(a=0;a<NV-1;++a) {
		size_t va[4];
		j = a;
		for(i=0;i<4;++i) { va[i] = j%3; j/=3; }
		for(b=a+1;b<NV;++b) {
			size_t vb[4];
			j = b;
			for(i=0;i<4;++i) { vb[i] = j%3; j/=3; }
			size_t di[4];
			for(i=0;i<4;++i) di[i] = (va[i]+3-vb[i])%3;
			size_t x =
				di[0]*di[0] + di[0]*di[1] + di[0]*di[2] + di[0]*di[3] + di[1]*di[1] +
				di[1]*di[2] + di[1]*di[3] + di[2]*di[2] + di[2]*di[3] + di[3]*di[3] ;
			x = x%3;
			if(x==0) edges.push_back( edge(a,b) );
		}
	}
	is_strong_regular(NV,edges);
	out_nauty(NV,edges,"Brouwer_Haemers.txt");
	system("nauty < Brouwer_Haemers.txt > Brouwer_Haemers_o.txt");
	std::vector< std::vector<int> > auto_base;
	load_nauty(NV,"Brouwer_Haemers_o.txt",auto_base);
	std::vector<int> out_perm;
	find_symmetric(NV,auto_base,out_perm);
	save_svg_random_try("Brouwer_Haemers_Graph.svg",NV,edges, & out_perm.front(),9);
	return 0;
}