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