127 lines
3.0 KiB
C++
127 lines
3.0 KiB
C++
#ifndef ITALIANO_H_
|
|
#define ITALIANO_H_
|
|
|
|
#include "algorithm/decremental_reachability.h"
|
|
#include "graph/breadth_first_tree.h"
|
|
#include <stack>
|
|
|
|
namespace algo {
|
|
|
|
template <typename T> class Italiano : public DecrementalReachability<T> {
|
|
public:
|
|
Italiano() = default;
|
|
|
|
explicit Italiano(graph::Digraph<T> G) { this->G = G; }
|
|
|
|
// Initialize the decremental maintenance data structure for DAGs
|
|
void init() override;
|
|
|
|
// Execute reachability query q(u, v) from vertex u to vertex v
|
|
// in O(1) using the transitive closure matrix
|
|
bool query(const T &u, const T &v) override;
|
|
|
|
// Delete collection of edges
|
|
void remove(const std::vector<std::pair<T, T>> &edges) override;
|
|
|
|
// Delete edge e(u, v) and explicitly maintain the transitive closure
|
|
void remove(const T &u, const T &v);
|
|
|
|
private:
|
|
// Transitive closure matrix
|
|
std::unordered_map<T, std::unordered_map<T, bool>> TC;
|
|
|
|
// For each vertex, store a reachability tree created as a BFS tree
|
|
std::unordered_map<T, BreadthFirstTree<T>> RT;
|
|
|
|
// For each vertex, store collections of its incoming and outgoing edges
|
|
struct Edges {
|
|
std::set<T> inc;
|
|
std::set<T> out;
|
|
};
|
|
std::unordered_map<T, Edges> E;
|
|
|
|
//
|
|
std::unordered_map<T, std::stack<T>> H;
|
|
|
|
// Repair reachability trees after edge deletions
|
|
void repairTrees();
|
|
};
|
|
|
|
template <typename T> void Italiano<T>::init() {
|
|
for (const auto &u : this->G.vertices()) {
|
|
for (const auto &v : this->G.adjList[u]) {
|
|
E[v].inc.insert(u);
|
|
E[u].out.insert(v);
|
|
TC[u][v] = false;
|
|
}
|
|
RT[u] = BreadthFirstTree<T>(this->G, u);
|
|
TC[u][u] = true;
|
|
for (const auto &v : RT[u].vertices())
|
|
TC[u][v] = true;
|
|
}
|
|
}
|
|
|
|
template <typename T> bool Italiano<T>::query(const T &u, const T &v) {
|
|
return TC[u][v];
|
|
}
|
|
|
|
template <typename T>
|
|
void Italiano<T>::remove(const std::vector<std::pair<T, T>> &edges) {
|
|
for (const auto &[u, v] : edges) {
|
|
if (!this->G.adjList[u].contains(v))
|
|
continue;
|
|
remove(u, v);
|
|
}
|
|
}
|
|
|
|
template <typename T> void Italiano<T>::remove(const T &u, const T &v) {
|
|
this->G.remove(u, v);
|
|
E[u].out.erase(v);
|
|
E[v].inc.erase(u);
|
|
|
|
for (const auto &w : this->G.vertices()) {
|
|
if (!RT[w].adjList[u].contains(v))
|
|
continue;
|
|
|
|
RT[w].adjList[u].erase(v);
|
|
if (E[v].inc.size() > 0) {
|
|
H[w].push(v);
|
|
continue;
|
|
}
|
|
TC[w][v] = false;
|
|
for (const auto &c : E[v].out)
|
|
H[w].push(c);
|
|
}
|
|
repairTrees();
|
|
}
|
|
|
|
template <typename T> void Italiano<T>::repairTrees() {
|
|
for (const auto &w : this->G.vertices()) {
|
|
while (H[w].size() > 0) {
|
|
const auto &h = H[w].top();
|
|
H[w].pop();
|
|
bool foundHook = false;
|
|
|
|
for (const auto &i : E[h].inc) {
|
|
if (RT[w].adjList[w].contains(i)) {
|
|
RT[w].adjList[i].insert(h);
|
|
foundHook = true;
|
|
break;
|
|
}
|
|
}
|
|
if (foundHook)
|
|
continue;
|
|
|
|
TC[w][h] = false;
|
|
for (const auto &o : E[h].out) {
|
|
if (RT[w].adjList[h].contains(o)) {
|
|
H[w].push(o);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
} // namespace algo
|
|
|
|
#endif |