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#ifndef TOPLEX_MAP_H
#define TOPLEX_MAP_H
#include <vector>
#include <unordered_set>
#include <unordered_map>
#include <memory>
#include <limits>
#define vertex_upper_bound std::numeric_limits<Toplex_map::Vertex>::max()
namespace Gudhi {
/** A Toplex_map represents the simplicial complex.
* A "toplex" is a maximal simplex.
* \ingroup toplex_map */
class Toplex_map {
public:
/** Vertex is the type of vertices.
* \ingroup toplex_map */
typedef std::size_t Vertex;
/** Simplex is the type of simplices.
* \ingroup toplex_map */
typedef std::unordered_set<Toplex_map::Vertex> Simplex;
/** The type of the pointers to maximal simplices.
* \ingroup toplex_map */
typedef std::shared_ptr<Toplex_map::Simplex> Simplex_ptr;
struct Sptr_hash{ std::size_t operator()(const Toplex_map::Simplex_ptr& s) const; };
struct Sptr_equal{ std::size_t operator()(const Toplex_map::Simplex_ptr& a, const Toplex_map::Simplex_ptr& b) const; };
/** The type of the sets of Toplex_map::Simplex_ptr.
* \ingroup toplex_map */
typedef std::unordered_set<Toplex_map::Simplex_ptr, Sptr_hash, Sptr_equal> Simplex_ptr_set;
/** \brief Adds the given simplex to the complex.
* Nothing happens if the simplex has a coface in the complex.
* \ingroup toplex_map */
template <typename Input_vertex_range>
void insert_simplex(const Input_vertex_range &vertex_range);
/** \brief Removes the given simplex and its cofaces from the complex.
* Its faces are kept inside.
* \ingroup toplex_map */
template <typename Input_vertex_range>
void remove_simplex(const Input_vertex_range &vertex_range);
/** Does a simplex belong to the complex ?
* \ingroup toplex_map */
template <typename Input_vertex_range>
bool membership(const Input_vertex_range &vertex_range) const;
/** Does a simplex is a toplex ?
* \ingroup toplex_map */
template <typename Input_vertex_range>
bool maximality(const Input_vertex_range &vertex_range) const;
/** Gives a set of pointers to the maximal cofaces of a simplex.
* Gives all the toplices if given the empty simplex.
* Gives not more than max_number maximal cofaces if max_number is strictly positive.
* \ingroup toplex_map */
template <typename Input_vertex_range>
Toplex_map::Simplex_ptr_set maximal_cofaces(const Input_vertex_range &vertex_range, const std::size_t max_number = 0) const;
/** Contracts one edge in the complex.
* The edge has to verify the link condition if you want to preserve topology.
* Returns the remaining vertex.
* \ingroup toplex_map */
Toplex_map::Vertex contraction(const Toplex_map::Vertex x, const Toplex_map::Vertex y, bool force=false);
/** Adds the given simplex to the complex.
* The simplex must not have neither maximal face nor coface in the complex.
* \ingroup toplex_map */
template <typename Input_vertex_range>
void insert_independent_simplex(const Input_vertex_range &vertex_range);
/** \internal Removes a toplex without adding facets after.
* \ingroup toplex_map */
void erase_maximal(const Toplex_map::Simplex_ptr& sptr);
/** Removes a vertex from any simplex containing it.
* \ingroup toplex_map */
void remove_vertex(const Toplex_map::Vertex x);
/** \brief Number of maximal simplices.
* \ingroup toplex_map */
std::size_t num_simplices() const;
protected:
/** \internal Gives an index in order to look for a simplex quickly.
* \ingroup toplex_map */
template <typename Input_vertex_range>
Toplex_map::Vertex best_index(const Input_vertex_range &vertex_range) const;
/** \internal The map from vertices to toplices
* \ingroup toplex_map */
std::unordered_map<Toplex_map::Vertex, Toplex_map::Simplex_ptr_set> t0;
};
// Pointers are also used as key in the hash sets.
template <typename Input_vertex_range>
Toplex_map::Simplex_ptr get_key(const Input_vertex_range &vertex_range);
// Is the first simplex a face of the second ?
template <typename Input_vertex_range1, typename Input_vertex_range2>
bool included(const Input_vertex_range1 &vertex_range1, const Input_vertex_range2 &vertex_range2);
// All the facets of the given simplex.
template <typename Input_vertex_range>
std::vector<Toplex_map::Simplex> facets(const Input_vertex_range &vertex_range);
template <typename Input_vertex_range>
void Toplex_map::insert_simplex(const Input_vertex_range &vertex_range){
if(membership(vertex_range)) return;
bool replace_facets = true;
for(const Toplex_map::Simplex& facet : facets(vertex_range))
if(!maximality(facet))
{
replace_facets=false;
break;
}
if(replace_facets)
for(const Toplex_map::Simplex& facet : facets(vertex_range))
erase_maximal(get_key(facet));
else
for(const Toplex_map::Vertex& v : vertex_range)
if(t0.count(v)) for(const Toplex_map::Simplex_ptr& fptr : Simplex_ptr_set(t0.at(v)))
//Copy constructor needed because the set is modified
if(included(*fptr,vertex_range)) erase_maximal(fptr);
// We erase all the maximal faces of the simplex
insert_independent_simplex(vertex_range);
}
template <typename Input_vertex_range>
void Toplex_map::remove_simplex(const Input_vertex_range &vertex_range){
if(vertex_range.begin()==vertex_range.end())
t0.clear();
// Removal of the empty simplex means cleaning everything
else {
const Toplex_map::Vertex& v = best_index(vertex_range);
if(t0.count(v)) for(const Toplex_map::Simplex_ptr& sptr : Simplex_ptr_set(t0.at(v)))
//Copy constructor needed because the set is modified
if(included(vertex_range, *sptr)){
erase_maximal(sptr);
for(const Toplex_map::Simplex& f : facets(vertex_range))
if(!membership(f)) insert_independent_simplex(f);
// We add the facets which are new maximal simplices
}
}
}
template <typename Input_vertex_range>
bool Toplex_map::membership(const Input_vertex_range &vertex_range) const{
if(t0.size()==0) return false;
const Toplex_map::Vertex& v = best_index(vertex_range);
if(!t0.count(v)) return false;
if(maximality(vertex_range)) return true;
for(const Toplex_map::Simplex_ptr& sptr : t0.at(v))
if(included(vertex_range, *sptr))
return true;
return false;
}
template <typename Input_vertex_range>
bool Toplex_map::maximality(const Input_vertex_range &vertex_range) const{
const Toplex_map::Vertex& v = best_index(vertex_range);
if(!t0.count(v)) return false;
return t0.at(v).count(get_key(vertex_range));
}
template <typename Input_vertex_range>
Toplex_map::Simplex_ptr_set Toplex_map::maximal_cofaces(const Input_vertex_range &vertex_range, const std::size_t max_number) const{
Simplex_ptr_set cofaces;
if(maximality(vertex_range))
cofaces.emplace(get_key(vertex_range));
else if(vertex_range.begin()==vertex_range.end())
for(const auto& kv : t0)
for(const Toplex_map::Simplex_ptr& sptr : kv.second){
//kv.second is a Simplex_ptr_set
cofaces.emplace(sptr);
if(cofaces.size()==max_number)
return cofaces;
}
else {
const Toplex_map::Vertex& v = best_index(vertex_range);
if(t0.count(v)) for(const Toplex_map::Simplex_ptr& sptr : t0.at(v))
if(included(vertex_range, *sptr)){
cofaces.emplace(sptr);
if(cofaces.size()==max_number)
return cofaces;
}
}
return cofaces;
}
Toplex_map::Vertex Toplex_map::contraction(const Toplex_map::Vertex x, const Toplex_map::Vertex y, bool force){
if(!t0.count(x)) return y;
if(!t0.count(y)) return x;
int k, d;
if(force || (t0.at(x).size() > t0.at(y).size()))
k=x, d=y;
else
k=y, d=x;
for(const Toplex_map::Simplex_ptr& sptr : Simplex_ptr_set(t0.at(d))){
//Copy constructor needed because the set is modified
Simplex sigma(*sptr);
Simplex s; s.insert(2);
erase_maximal(sptr);
sigma.erase(d);
sigma.insert(k);
insert_simplex(sigma);
}
return k;
}
template <typename Input_vertex_range>
void Toplex_map::insert_independent_simplex(const Input_vertex_range &vertex_range){
for(const Toplex_map::Vertex& v : vertex_range){
if(!t0.count(v)) t0.emplace(v, Simplex_ptr_set());
auto k = get_key(vertex_range);
t0.at(v).emplace(k);
}
}
void Toplex_map::remove_vertex(const Toplex_map::Vertex x){
for(const Toplex_map::Simplex_ptr& sptr : Simplex_ptr_set(t0.at(x))){
Simplex sigma(*sptr);
erase_maximal(sptr);
sigma.erase(x);
insert_simplex(sigma);
}
}
std::size_t Toplex_map::num_simplices() const{
return maximal_cofaces(Simplex()).size();
}
inline void Toplex_map::erase_maximal(const Toplex_map::Simplex_ptr& sptr){
Simplex sigma(*sptr);
if (sptr->size()==0)
sigma.insert(vertex_upper_bound);
for(const Toplex_map::Vertex& v : sigma){
t0.at(v).erase(sptr);
if(t0.at(v).size()==0) t0.erase(v);
}
}
template <typename Input_vertex_range>
Toplex_map::Vertex Toplex_map::best_index(const Input_vertex_range &vertex_range) const{
std::size_t min = std::numeric_limits<size_t>::max();
Vertex arg_min = vertex_upper_bound;
for(const Toplex_map::Vertex& v : vertex_range)
if(!t0.count(v)) return v;
else if(t0.at(v).size() < min)
min = t0.at(v).size(), arg_min = v;
return arg_min;
}
std::size_t Toplex_map::Sptr_equal::operator()(const Toplex_map::Simplex_ptr& s1, const Toplex_map::Simplex_ptr& s2) const {
if (s1->size() != s2->size()) return false;
return included(*s1,*s2);
// inclusion tests equality for same size simplices
}
std::size_t Toplex_map::Sptr_hash::operator()(const Toplex_map::Simplex_ptr& s) const {
std::hash<double> h_f;
//double hash works better than int hash
size_t h = 0;
for(const Toplex_map::Vertex& v : *s)
h += h_f(static_cast<double>(v));
return h;
}
template <typename Input_vertex_range>
Toplex_map::Simplex_ptr get_key(const Input_vertex_range &vertex_range){
Toplex_map::Simplex s(vertex_range.begin(), vertex_range.end());
return std::make_shared<Toplex_map::Simplex>(s);
}
template <typename Input_vertex_range1, typename Input_vertex_range2>
bool included(const Input_vertex_range1 &vertex_range1, const Input_vertex_range2 &vertex_range2){
Toplex_map::Simplex s2(vertex_range2.begin(), vertex_range2.end());
for(const Toplex_map::Vertex& v : vertex_range1)
if(!s2.count(v)) return false;
return true;
}
template <typename Input_vertex_range>
std::vector<Toplex_map::Simplex> facets(const Input_vertex_range &vertex_range){
std::vector<Toplex_map::Simplex> facets;
Toplex_map::Simplex f(vertex_range.begin(), vertex_range.end());
for(const Toplex_map::Vertex& v : vertex_range){
f.erase(v);
facets.emplace_back(f);
f.insert(v);
}
return facets;
}
} //namespace Gudhi
#endif /* TOPLEX_MAP_H */
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