86 lines
1.9 KiB
C++
86 lines
1.9 KiB
C++
#ifndef ITALIANO_H_
|
|
#define ITALIANO_H_
|
|
|
|
#include "algorithm/roditty_zwick.h"
|
|
#include "algorithm/tarjan.h"
|
|
#include "tree/breadth_first_tree.h"
|
|
|
|
#include <forward_list>
|
|
|
|
using namespace graph;
|
|
using namespace tree;
|
|
|
|
namespace algo {
|
|
|
|
template<typename T>
|
|
class Italiano : public RodittyZwick<T> {
|
|
public:
|
|
Italiano(Digraph<T> G) : G(G) {}
|
|
|
|
void init();
|
|
|
|
bool query(const T& u, const T& v);
|
|
|
|
void remove(const T& u, const T& v);
|
|
private:
|
|
Digraph<T> G;
|
|
|
|
// Connect each vertex with its representative SCC
|
|
std::map<T, SCC<T>> TC;
|
|
|
|
// Reachability trees
|
|
std::map<T, std::set<T>> RT;
|
|
|
|
// Incoming / Outgoing edges
|
|
struct Edges {
|
|
std::forward_list<T> Ein;
|
|
std::forward_list<T> Eout;
|
|
};
|
|
std::map<SCC<T>, Edges> E;
|
|
};
|
|
|
|
|
|
template<typename T>
|
|
void Italiano<T>::init() {
|
|
|
|
}
|
|
|
|
template<typename T>
|
|
bool Italiano<T>::query(const T& u, const T& v) {
|
|
return TC[u] == TC[v];
|
|
}
|
|
|
|
template<typename T>
|
|
void Italiano<T>::remove(const T& u, const T& v) {
|
|
|
|
for (const auto& w : G.adjMatrix) {
|
|
// Check if (u,v) edge of T(w) || p(w,v) points to (u,v)
|
|
|
|
// If yes => set p(w, v) to point to the next edge (u',v) in Ein(v)
|
|
// If (u,v) the last edge, then set it to point to null
|
|
|
|
// If T(w) contains u' then the new edge reconnects v to T(w)
|
|
// As this needs to be checked, we set R(w) <- {v}
|
|
|
|
// If (u,v) is not edge of T(w) or is the last edge in Ein(v), R(w) <- phi
|
|
|
|
// Remove (u,v) from Eout(u) and Ein(v)
|
|
}
|
|
|
|
for (const auto& w : G.adjMatrix) {
|
|
|
|
// Check tentative pointers of the vertices in R(w).
|
|
// While there is a vertex x in R(w), scan the edges in Ein(x), starting
|
|
// from the edge pointed to by p(w,x), until an edge (u',x) for which
|
|
// p(w,u') != null is found or Ein(x) is exhausted.
|
|
|
|
// If such edge is found, x is removed from R(w).
|
|
// If the list is exhausted, set p(w,x) to null and M(w,x) to 0
|
|
|
|
// Then scan all Eout(x). If (x,x') is tree edge, add x' to R(w)
|
|
}
|
|
}
|
|
|
|
} // namespace algo
|
|
|
|
#endif |