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+/*
+ * Skeleton_blocker_simplifiable_complex.h
+ *
+ *  Created on: Feb 4, 2014
+ *      Author: dsalinas
+ */
+
+#ifndef GUDHI_SKELETON_BLOCKERS_SIMPLIFIABLE_COMPLEX_H_
+#define GUDHI_SKELETON_BLOCKERS_SIMPLIFIABLE_COMPLEX_H_
+
+#include "gudhi/Skeleton_blocker/Skeleton_blocker_sub_complex.h"
+
+namespace Gudhi{
+
+namespace skbl {
+
+/**
+ *  \brief Class that allows simplification operation on a simplicial complex represented
+ *  by a skeleton/blockers pair.
+ */
+template<typename SkeletonBlockerDS>
+class Skeleton_blocker_simplifiable_complex : public Skeleton_blocker_complex<SkeletonBlockerDS>
+{
+	template<class ComplexType> friend class Skeleton_blocker_sub_complex;
+
+public:
+
+	typedef Skeleton_blocker_complex<SkeletonBlockerDS> SkeletonBlockerComplex;
+
+	typedef typename SkeletonBlockerComplex::Graph_edge Graph_edge;
+
+	typedef typename SkeletonBlockerComplex::boost_adjacency_iterator boost_adjacency_iterator;
+	typedef typename SkeletonBlockerComplex::Edge_handle Edge_handle;
+	typedef typename SkeletonBlockerComplex::boost_vertex_handle boost_vertex_handle;
+	typedef typename SkeletonBlockerComplex::Vertex_handle Vertex_handle;
+	typedef typename SkeletonBlockerComplex::Root_vertex_handle Root_vertex_handle;
+	typedef typename SkeletonBlockerComplex::Simplex_handle Simplex_handle;
+	typedef typename SkeletonBlockerComplex::Root_simplex_handle Root_simplex_handle;
+	typedef typename SkeletonBlockerComplex::Blocker_handle Blocker_handle;
+
+
+	typedef typename SkeletonBlockerComplex::Root_simplex_iterator Root_simplex_iterator;
+	typedef typename SkeletonBlockerComplex::Simplex_handle_iterator Simplex_handle_iterator;
+	typedef typename SkeletonBlockerComplex::BlockerMap BlockerMap;
+	typedef typename SkeletonBlockerComplex::BlockerPair BlockerPair;
+	typedef typename SkeletonBlockerComplex::BlockerMapIterator BlockerMapIterator;
+	typedef typename SkeletonBlockerComplex::BlockerMapConstIterator BlockerMapConstIterator;
+
+	typedef typename SkeletonBlockerComplex::Visitor Visitor;
+
+
+	/** @name Constructors / Destructors / Initialization
+	 */
+	//@{
+	Skeleton_blocker_simplifiable_complex(int num_vertices_ = 0,Visitor* visitor_=NULL):
+		Skeleton_blocker_complex<SkeletonBlockerDS>(num_vertices_,visitor_){	}
+
+
+	/**
+	 * @brief Constructor with a list of simplices
+	 * @details The list of simplices must be the list
+	 * of simplices of a simplicial complex, sorted with increasing dimension.
+	 * todo take iterator instead
+	 */
+	Skeleton_blocker_simplifiable_complex(std::list<Simplex_handle>& simplices,Visitor* visitor_=NULL):
+		Skeleton_blocker_complex<SkeletonBlockerDS>(simplices,visitor_)
+		{}
+
+
+
+	virtual ~Skeleton_blocker_simplifiable_complex(){
+	}
+
+	//@}
+
+	/**
+	 * Returns true iff the blocker 'sigma' is popable.
+	 * To define popable, let us call 'L' the complex that
+	 * consists in the current complex without the blocker 'sigma'.
+	 * A blocker 'sigma' is then "popable" if the link of 'sigma'
+	 * in L is reducible.
+	 *
+	 */
+	virtual bool is_popable_blocker(Blocker_handle sigma) const{
+		assert(this->contains_blocker(*sigma));
+		Skeleton_blocker_link_complex<Skeleton_blocker_simplifiable_complex> link_blocker_sigma;
+		build_link_of_blocker(*this,*sigma,link_blocker_sigma);
+
+		bool res = link_blocker_sigma.is_contractible()==CONTRACTIBLE;
+		return res;
+	}
+
+
+
+
+private:
+	/**
+	 * @returns the list of blockers of the simplex
+	 *
+	 * @todo a enlever et faire un iterateur sur tous les blockers a la place
+	 */
+	std::list<Blocker_handle> get_blockers(){
+		std::list<Blocker_handle> res;
+		for (auto blocker : this->blocker_range()){
+			res.push_back(blocker);
+		}
+		return res;
+	}
+
+
+
+public:
+
+	/**
+	 * Removes all the popable blockers of the complex and delete them.
+	 * @returns the number of popable blockers deleted
+	 */
+	void remove_popable_blockers(){
+		std::list<Vertex_handle> vertex_to_check;
+		for(auto v : this->vertex_range())
+			vertex_to_check.push_front(v);
+
+		while(!vertex_to_check.empty()){
+			Vertex_handle v = vertex_to_check.front();
+			vertex_to_check.pop_front();
+
+			bool blocker_popable_found=true;
+			while (blocker_popable_found){
+				blocker_popable_found = false;
+				for(auto block : this->blocker_range(v)){
+					if (this->is_popable_blocker(block)) {
+						for(Vertex_handle nv : *block)
+							if(nv!=v) vertex_to_check.push_back(nv);
+						this->delete_blocker(block);
+						blocker_popable_found = true;
+						break;
+					}
+				}
+			}
+		}
+	}
+
+
+	/**
+	 * Removes all the popable blockers of the complex passing through v and delete them.
+	 */
+	void remove_popable_blockers(Vertex_handle v){
+		bool blocker_popable_found=true;
+		while (blocker_popable_found){
+			blocker_popable_found = false;
+			for(auto block : this->blocker_range(v)){
+				if (is_popable_blocker(block)) {
+					this->delete_blocker(block);
+					blocker_popable_found = true;
+				}
+			}
+		}
+	}
+
+
+	/**
+	 * Remove the star of the vertex 'v'
+	 */
+	void remove_star(Vertex_handle v){
+		// we remove the blockers that are not consistent anymore
+
+		update_blockers_after_remove_star_of_vertex_or_edge(v);
+
+		while (this->degree(v) > 0)
+		{
+			Vertex_handle w( * (adjacent_vertices(v.vertex, this->skeleton).first));
+			this->remove_edge(v,w);
+		}
+		this->remove_vertex(v);
+	}
+
+private:
+	/**
+	 * after removing the star of a simplex, blockers sigma that contains this simplex must be removed.
+	 * Furthermore, all simplices tau of the form sigma \setminus simplex_to_be_removed must be added
+	 * whenever the dimension of tau is at least 2.
+	 */
+	void update_blockers_after_remove_star_of_vertex_or_edge(const Simplex_handle& simplex_to_be_removed){
+		std::list <Blocker_handle> blockers_to_update;
+		if(simplex_to_be_removed.empty()) return;
+
+		auto v0 = simplex_to_be_removed.first_vertex();
+		for (auto blocker : this->blocker_range(v0)){
+			if(blocker->contains(simplex_to_be_removed))
+				blockers_to_update.push_back(blocker);
+		}
+
+		for(auto blocker_to_update : blockers_to_update){
+			Simplex_handle sub_blocker_to_be_added;
+			bool sub_blocker_need_to_be_added =
+					(blocker_to_update->dimension()-simplex_to_be_removed.dimension()) >= 2;
+			if(sub_blocker_need_to_be_added){
+				sub_blocker_to_be_added = *blocker_to_update;
+				sub_blocker_to_be_added.difference(simplex_to_be_removed);
+			}
+			this->delete_blocker(blocker_to_update);
+			if(sub_blocker_need_to_be_added)
+				this->add_blocker(sub_blocker_to_be_added);
+		}
+	}
+
+
+
+public:
+	/**
+	 * Remove the star of the edge connecting vertices a and b.
+	 * @returns the number of blocker that have been removed
+	 */
+	void remove_star(Vertex_handle a, Vertex_handle b){
+		update_blockers_after_remove_star_of_vertex_or_edge(Simplex_handle(a,b));
+		// we remove the edge
+		this->remove_edge(a,b);
+	}
+
+
+	/**
+	 * Remove the star of the edge 'e'.
+	 */
+	void remove_star(Edge_handle e){
+		return remove_star(this->first_vertex(e),this->second_vertex(e));
+	}
+
+	/**
+	 * Remove the star of the simplex 'sigma' which needs to belong to the complex
+	 */
+	void remove_star(const Simplex_handle& sigma){
+		assert(this->contains(sigma));
+		if (sigma.dimension()==0)
+			remove_star(sigma.first_vertex());
+		else
+			if (sigma.dimension()==1)
+				remove_star(sigma.first_vertex(),sigma.last_vertex());
+			else
+				update_blockers_after_remove_star_of_simplex(sigma);
+	}
+
+private:
+	void update_blockers_after_remove_star_of_simplex(const Simplex_handle& sigma){
+		std::list <Blocker_handle> blockers_to_remove;
+		for (auto blocker : this->blocker_range(sigma.first_vertex())){
+			if(blocker->contains(sigma))
+				blockers_to_remove.push_back(blocker);
+		}
+		for(auto blocker_to_update : blockers_to_remove)
+			this->delete_blocker(blocker_to_update);
+		this->add_blocker(sigma);
+	}
+
+public:
+
+	enum simplifiable_status{ NOT_HOMOTOPY_EQ,MAYBE_HOMOTOPY_EQ,HOMOTOPY_EQ};
+	simplifiable_status is_remove_star_homotopy_preserving(const Simplex_handle& simplex){
+		return MAYBE_HOMOTOPY_EQ;
+	}
+
+
+
+	enum contractible_status{ NOT_CONTRACTIBLE,MAYBE_CONTRACTIBLE,CONTRACTIBLE};
+	/**
+	 * @brief %Test if the complex is reducible using a strategy defined in the class
+	 * (by default it tests if the complex is a cone)
+	 * @details Note that NO could be returned if some invariant ensures that the complex
+	 * is not a point (for instance if the euler characteristic is different from 1).
+	 * This function will surely have to return MAYBE in some case because the
+	 * associated problem is undecidable but it in practice, it can often
+	 * be solved with the help of geometry.
+	 */
+	virtual contractible_status is_contractible() const{
+		if (this->is_cone()) return CONTRACTIBLE;
+		else return MAYBE_CONTRACTIBLE;
+		//		return this->is_cone();
+	}
+
+
+	/** @Edge contraction operations
+	 */
+	//@{
+
+
+
+	/**
+	 * @return If ignore_popable_blockers is true
+	 * then the result is true iff the link condition at edge ab is satisfied
+	 * or equivalently iff no blocker contains ab.
+	 * If ignore_popable_blockers is false then the
+	 * result is true iff all blocker containing ab are popable.
+	 */
+	bool link_condition(Vertex_handle a, Vertex_handle b,bool ignore_popable_blockers = false) const{
+		for (auto blocker : this->const_blocker_range(a))
+			if ( blocker->contains(b) ){
+				// false if ignore_popable_blockers is false
+				// otherwise the blocker has to be popable
+				return ignore_popable_blockers && is_popable_blocker(blocker);
+			}
+		return true;
+	}
+
+	/**
+	 * @return If ignore_popable_blockers is true
+	 * then the result is true iff the link condition at edge ab is satisfied
+	 * or equivalently iff no blocker contains ab.
+	 * If ignore_popable_blockers is false then the
+	 * result is true iff all blocker containing ab are popable.
+	 */
+	bool link_condition(Edge_handle & e,bool ignore_popable_blockers = false) const{
+		const Graph_edge& edge = (*this)[e];
+		assert(this->get_address(edge.first()));
+		assert(this->get_address(edge.second()));
+		Vertex_handle a(*this->get_address(edge.first()));
+		Vertex_handle b(*this->get_address(edge.second()));
+		return link_condition(a,b,ignore_popable_blockers);
+	}
+
+
+protected:
+	/**
+	 * Compute simplices beta such that a.beta is an order 0 blocker
+	 * that may be used to construct a new blocker after contracting ab.
+	 * Suppose that the link condition Link(ab) = Link(a) inter Link(b)
+	 * is satisfied.
+	 */
+	void tip_blockers(Vertex_handle a, Vertex_handle b, std::vector<Simplex_handle> & buffer) const{
+		for (auto const & blocker : this->const_blocker_range(a))
+		{
+			Simplex_handle beta = (*blocker);
+			beta.remove_vertex(a);
+			buffer.push_back(beta);
+		}
+
+		Simplex_handle n;
+		this->add_neighbours(b,n);
+		this->remove_neighbours(a,n);
+		n.remove_vertex(a);
+
+
+		for (Vertex_handle y : n)
+		{
+			Simplex_handle beta;
+			beta.add_vertex( y );
+			buffer.push_back(beta);
+		}
+	}
+
+
+private:
+
+	/**
+	 * @brief "Replace" the edge 'bx' by the edge 'ax'.
+	 * Assume that the edge 'bx' was present whereas 'ax' was not.
+	 * Precisely, it does not replace edges, but remove 'bx' and then add 'ax'.
+	 * The visitor 'on_swaped_edge' is called just after edge 'ax' had been added
+	 * and just before edge 'bx' had been removed. That way, it can
+	 * eventually access to information of 'ax'.
+	 */
+	void swap_edge(Vertex_handle a,Vertex_handle b,Vertex_handle x){
+		this->add_edge(a,x);
+		if (this->visitor) this->visitor->on_swaped_edge(a,b,x);
+		this->remove_edge(b,x);
+	}
+
+
+private:
+	/**
+	 * @brief removes all blockers passing through the edge 'ab'
+	 */
+	void delete_blockers_around_vertex(Vertex_handle v){
+		std::list <Blocker_handle> blockers_to_delete;
+		for (auto blocker : this->blocker_range(v)){
+			blockers_to_delete.push_back(blocker);
+		}
+		while (!blockers_to_delete.empty()){
+			this->remove_blocker(blockers_to_delete.back());
+			blockers_to_delete.pop_back();
+		}
+
+	}
+	/**
+	 * @brief removes all blockers passing through the edge 'ab'
+	 */
+	void delete_blockers_around_edge(Vertex_handle a, Vertex_handle b){
+		std::list<Blocker_handle> blocker_to_delete;
+		for (auto blocker : this->blocker_range(a))
+			if (blocker->contains(b)) blocker_to_delete.push_back(blocker);
+		while (!blocker_to_delete.empty())
+		{
+			this->delete_blocker(blocker_to_delete.back());
+			blocker_to_delete.pop_back();
+		}
+	}
+
+public:
+
+	/**
+	 * Contracts the edge.
+	 * @remark If the link condition Link(ab) = Link(a) inter Link(b) is not satisfied,
+	 * it removes first all blockers passing through 'ab'
+	 */
+	void contract_edge(Edge_handle edge){
+		contract_edge(this->first_vertex(edge),this->second_vertex(edge));
+	}
+
+
+	/**
+	 * Contracts the edge connecting vertices a and b.
+	 * @remark If the link condition Link(ab) = Link(a) inter Link(b) is not satisfied,
+	 * it removes first all blockers passing through 'ab'
+	 */
+	void contract_edge(Vertex_handle a, Vertex_handle b){
+		assert(this->contains_vertex(a));
+		assert(this->contains_vertex(b));
+		assert(this->contains_edge(a,b));
+
+		// if some blockers passes through 'ab', we remove them.
+		if (!link_condition(a,b))
+			delete_blockers_around_edge(a,b);
+
+		std::set<Simplex_handle> blockers_to_add;
+
+		get_blockers_to_be_added_after_contraction(a,b,blockers_to_add);
+
+		delete_blockers_around_vertices(a,b);
+
+		update_edges_after_contraction(a,b);
+
+		this->remove_vertex(b);
+
+		notify_changed_edges(a);
+
+		for(auto block : blockers_to_add)
+			this->add_blocker(block);
+
+		assert(this->contains_vertex(a));
+		assert(!this->contains_vertex(b));
+	}
+
+
+private:
+
+	void get_blockers_to_be_added_after_contraction(Vertex_handle a,Vertex_handle b,std::set<Simplex_handle>& blockers_to_add){
+		blockers_to_add.clear();
+
+		typedef Skeleton_blocker_link_complex<Skeleton_blocker_complex<SkeletonBlockerDS> > LinkComplexType;
+
+		LinkComplexType link_a(*this,a);
+		LinkComplexType link_b(*this,b);
+
+		std::vector<Simplex_handle> vector_alpha, vector_beta;
+
+		tip_blockers(a,b,vector_alpha);
+		tip_blockers(b,a,vector_beta);
+
+		for (auto alpha = vector_alpha.begin(); alpha != vector_alpha.end(); ++alpha){
+			for (auto beta = vector_beta.begin(); beta != vector_beta.end(); ++beta)
+			{
+				Simplex_handle sigma = *alpha; sigma.union_vertices(*beta);
+				Root_simplex_handle sigma_id = this->get_id(sigma);
+				if ( this->contains(sigma) &&
+						proper_faces_in_union<SkeletonBlockerComplex>(sigma_id,link_a,link_b))
+				{
+					//					Blocker_handle blocker = new Simplex_handle(sigma);
+					sigma.add_vertex(a);
+					blockers_to_add.insert(sigma);
+				}
+			}
+		}
+	}
+
+
+	/**
+	 * delete all blockers that passes through a or b
+	 */
+	void delete_blockers_around_vertices(Vertex_handle a,Vertex_handle b){
+		std::vector<Blocker_handle> blocker_to_delete;
+		for(auto bl : this->blocker_range(a))
+			blocker_to_delete.push_back(bl);
+		for(auto bl : this->blocker_range(b))
+			blocker_to_delete.push_back(bl);
+		while (!blocker_to_delete.empty())
+		{
+			this->delete_blocker(blocker_to_delete.back());
+			blocker_to_delete.pop_back();
+		}
+	}
+
+
+	void update_edges_after_contraction(Vertex_handle a,Vertex_handle b){
+		// We update the set of edges
+		this->remove_edge(a,b);
+
+		// For all edges {b,x} incident to b,
+		// we remove {b,x} and add {a,x} if not already there.
+		while (this->degree(b)> 0)
+		{
+			Vertex_handle x(*(adjacent_vertices(b.vertex, this->skeleton).first));
+			if(!this->contains_edge(a,x))
+				// we 'replace' the edge 'bx' by the edge 'ax'
+				this->swap_edge(a,b,x);
+			else
+				this->remove_edge(b,x);
+		}
+	}
+
+	void notify_changed_edges(Vertex_handle a){
+		// We notify the visitor that all edges incident to 'a' had changed
+		boost_adjacency_iterator v, v_end;
+
+		for (tie(v, v_end) = adjacent_vertices(a.vertex, this->skeleton); v != v_end; ++v)
+			if (this->visitor) this->visitor->on_changed_edge(a,Vertex_handle(*v));
+	}
+
+	//@}
+
+
+};
+
+}
+
+}  // namespace GUDHI
+
+#endif /* GUDHI_SKELETON_BLOCKERS_SIMPLIFIABLE_COMPLEX_H_ */