95 lines
2.0 KiB
C++
95 lines
2.0 KiB
C++
#ifndef DECREMENTAL_SCC_H_
|
|
#define DECREMENTAL_SCC_H_
|
|
|
|
#include "algorithm/roditty_zwick.h"
|
|
#include "algorithm/tarjan.h"
|
|
#include "tree/breadth_first_tree.h"
|
|
|
|
using namespace graph;
|
|
using namespace tree;
|
|
|
|
namespace algo {
|
|
|
|
template<typename T>
|
|
class DecrementalSCC : public RodittyZwick<T> {
|
|
public:
|
|
DecrementalSCC(Digraph<T> G) : G(G) {}
|
|
|
|
void init();
|
|
|
|
void findSCC();
|
|
|
|
bool query(const T& u, const T& v);
|
|
|
|
void remove(const T& u, const T& v);
|
|
private:
|
|
Digraph<T> G;
|
|
|
|
// Array used to answer strong connectivity queries in O(1) time
|
|
std::map<T, T> A;
|
|
|
|
// Maintain in-out bfs trees
|
|
std::map<T, BreadthFirstTree<T>> inTree;
|
|
std::map<T, BreadthFirstTree<T>> outTree;
|
|
|
|
// Connect each representative with its SCC
|
|
std::map<T, SCC<T>> connection;
|
|
};
|
|
|
|
template<typename T>
|
|
void DecrementalSCC<T>::init() {
|
|
findSCC();
|
|
}
|
|
|
|
template<typename T>
|
|
void DecrementalSCC<T>::findSCC() {
|
|
auto SCCs = Tarjan<T>(G).execute();
|
|
|
|
for (auto& C : SCCs) {
|
|
const auto& w = C.representative();
|
|
|
|
for (const auto& v : C.adjMatrix)
|
|
A[v.first] = w;
|
|
|
|
outTree[w] =
|
|
BreadthFirstTree<T>(BreadthFirstSearch<T>(C).execute(w));
|
|
inTree[w] =
|
|
BreadthFirstTree<T>(BreadthFirstSearch<T>(C.reverse()).execute(w));
|
|
|
|
connection[w] = C;
|
|
}
|
|
}
|
|
|
|
template<typename T>
|
|
bool DecrementalSCC<T>::query(const T& u, const T& v) {
|
|
return A[u] == A[v];
|
|
}
|
|
|
|
template<typename T>
|
|
void DecrementalSCC<T>::remove(const T& u, const T& v) {
|
|
G.adjMatrix[u].erase(v);
|
|
|
|
// If u and v are not in the same SCC, do nothing
|
|
if (A[u] != A[v]) return;
|
|
|
|
const auto& w = A[u];
|
|
connection[w].remove(u, v);
|
|
|
|
// Update In(w) and Out(w) if they contain the edge
|
|
if (inTree[w].contains(u, v) || outTree[w].contains(u, v)) {
|
|
auto C = connection[w];
|
|
inTree[w] =
|
|
BreadthFirstTree<T>(BreadthFirstSearch<T>(C.reverse()).execute(w));
|
|
outTree[w] =
|
|
BreadthFirstTree<T>(BreadthFirstSearch<T>(C).execute(w));
|
|
}
|
|
|
|
// If a SCC is broken, compute all SCCs again
|
|
if (!inTree[w].contains(u) || !outTree[w].contains(v)) {
|
|
findSCC();
|
|
}
|
|
}
|
|
|
|
}; // namespace algo
|
|
|
|
#endif |