107 lines
2.4 KiB
C++
107 lines
2.4 KiB
C++
#ifndef ITALIANO_H_
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#define ITALIANO_H_
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#include "algorithm/roditty_zwick.h"
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#include "algorithm/tarjan.h"
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#include "graph/breadth_first_tree.h"
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#include <forward_list>
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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 RodittyZwick<T> {
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public:
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Italiano(Digraph<T> G) : G(G) {}
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void init();
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bool query(const T& u, const T& v);
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void remove(const T& u, const T& v);
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private:
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Digraph<T> G;
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// Transitive closure matrix, used to answer reachability queries in O(1)
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std::map<T, std::map<T, bool>> TC;
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// Each vertex's reachability tree
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std::map<T, BreadthFirstTree<T>> RT;
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// Incoming / Outgoing edges
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struct Edges {
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std::forward_list<T> inc;
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std::forward_list<T> out;
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};
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std::map<T, Edges> E;
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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 : std::views::keys(G.adjMatrix)) {
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for (const auto& v : G.adjMatrix[u]) {
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E[v].inc.push_front(u);
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E[u].out.push_front(v);
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TC[u][v] = false;
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}
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RT[u] = BreadthFirstTree(G, u);
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TC[u][u] = true;
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for (const auto& v : std::views::keys(RT[u].adjMatrix)) {
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TC[u][v] = true;
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}
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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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std::map<T, std::forward_list<T>> R;
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for (const auto& w : std::views::keys(G.adjMatrix)) {
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if (RT[w].contains(u, v) &&
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std::distance(E[w].inc.begin(), E[w].inc.end()) > 1) {
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if (E[v].inc.front() == u) {
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E[v].inc.pop_front();
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R[w].push_front(E[v].inc.front());
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E[v].inc.push_front(u);
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} else {
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R[w].push_front(E[v].inc.front());
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}
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}
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}
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E[u].inc.remove(v);
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E[u].out.remove(u);
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G.remove(u, v);
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for (const auto& w : std::views::keys(G.adjMatrix)) {
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bool hooked = false;
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// R contains all vertices that need a hook-parent
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while (!R[w].empty()) {
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// z is a candidate hook-parent if it is in RT[w]
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const auto& toHook = R[w].front();
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for (const auto& z : E[toHook].inc) {
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if (RT[w].contains(u, z)) {
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R[w].remove(toHook);
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hooked = true;
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break;
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}
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}
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if (!hooked) {
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TC[w][toHook] = false;
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for (const auto& z : E[toHook].out) {
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if (RT[w].contains(toHook, z))
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R[w].push_front(z);
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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 |