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#include "graph/dijkstra_fibheap.hpp"
#pragma once #include <limits> #include <vector> #include "../data_structure/fibonacci_heap.hpp" #include "../graph/base.hpp" namespace ebi { template <class T> bool op(T a, T b) { return a <= b; } template <class T> std::vector<T> dijkstra_fibheap(int s, int n, const Graph<T> &g) { std::vector<T> d(n, std::numeric_limits<T>::max()); fibonacci_heap<T, int, op> que; d[s] = 0; std::vector<internal::fibheap_node<T, int> *> p(n, nullptr); p[s] = que.push(0, s); while (!que.empty()) { que.is_valid(); int v = que.top(); que.pop(); for (auto e : g[v]) { if (d[e.to] > d[v] + e.cost) { d[e.to] = d[v] + e.cost; if (p[e.to] == nullptr) { p[e.to] = que.push(d[e.to], e.to); continue; } que.prioritize(p[e.to], d[e.to]); } } } return d; } } // namespace ebi
#line 2 "graph/dijkstra_fibheap.hpp" #include <limits> #include <vector> #line 2 "data_structure/fibonacci_heap.hpp" /* reference: http://web.stanford.edu/class/archive/cs/cs166/cs166.1186/lectures/09/Slides09.pdf https://rsk0315.hatenablog.com/entry/2019/10/29/151823 https://en.wikipedia.org/wiki/Fibonacci_heap */ #include <cassert> #include <queue> #line 13 "data_structure/fibonacci_heap.hpp" namespace ebi { namespace internal { template <class K, class T> struct fibheap_node { fibheap_node *par, *prev, *next, *chr; int sz = 0; bool damaged = 0; K ord; T val; fibheap_node(K k, T val) : par(nullptr), prev(this), next(this), chr(nullptr), ord(k), val(val) {} void emplace_back(fibheap_node *e) { if (e == nullptr) return; prev->next = e; e->prev->next = this; std::swap(e->prev, prev); } void cut_par() { if (par == nullptr) return; par->sz--; if (par->sz == 0) { par->chr = nullptr; } if (par->chr == this) { par->chr = next; } cut(); par = nullptr; } void cut() { next->prev = prev; prev->next = next; next = prev = this; } int size() const { return sz; } }; } // namespace internal template <class K, class T, bool (*op)(K, K)> struct fibonacci_heap { private: using Node = internal::fibheap_node<K, T>; using node_ptr = Node *; node_ptr min = nullptr; node_ptr roots = nullptr; int sz = 0; void update(node_ptr a) { assert(a != nullptr); if (!min || op(a->ord, min->ord)) { min = a; } } void merge(node_ptr a, node_ptr b) { assert(a && b); assert(op(a->ord, b->ord)); a->sz++; b->par = a; if (a->chr == nullptr) a->chr = b; else a->chr->emplace_back(b); } int log2ceil(int m) { int n = 1; while ((1 << n) < m) { n++; } return n; } public: node_ptr push(K k, T val) { node_ptr a = new Node(k, val); sz++; update(a); if (roots == nullptr) { roots = a; return a; } roots->emplace_back(a); is_valid(); return a; } void pop() { assert(sz > 0); roots->emplace_back(min->chr); if (roots == min) { roots = roots->next; assert(roots->prev == min); } min->cut(); delete min; min = nullptr; sz--; if (sz == 0) { roots = nullptr; return; } int n = log2ceil(size()) + 5; std::vector<std::queue<node_ptr>> que(n); que[roots->size()].push(roots); roots->par = nullptr; for (node_ptr ptr = roots->next; ptr != roots; ptr = ptr->next) { update(ptr); ptr->par = nullptr; que[ptr->size()].push(ptr); } roots = nullptr; for (int i = 0; i < n; i++) { while (que[i].size() > 1) { node_ptr first = que[i].front(); que[i].pop(); node_ptr second = que[i].front(); que[i].pop(); first->cut(); second->cut(); if (!op(first->ord, second->ord)) std::swap(first, second); merge(first, second); assert(first->sz == i + 1); que[first->size()].push(first); } if (que[i].size() == 1) { node_ptr ptr = que[i].front(); que[i].pop(); update(ptr); ptr->cut(); if (roots == nullptr) { roots = ptr; continue; } roots->emplace_back(ptr); } } } T top() const { return min->val; } void prioritize(node_ptr e, K k) { assert(e && op(k, e->ord)); e->ord = k; update(e); if (e->par == nullptr || op(e->par->ord, e->ord)) return; if (e->par->damaged && e->par->par != nullptr) { e->par->cut_par(); roots->emplace_back(e->par); } e->par->damaged = true; e->cut_par(); roots->emplace_back(e); } int size() const { return sz; } bool empty() const { return sz == 0; } void is_valid() const { K k = roots->ord; for (node_ptr ptr = roots->next; ptr != roots; ptr = ptr->next) { if (op(ptr->ord, k)) { k = ptr->ord; } } assert(k == min->ord); } }; } // namespace ebi #line 2 "graph/base.hpp" #line 4 "graph/base.hpp" #include <iostream> #include <ranges> #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 4 "data_structure/simple_csr.hpp" #include <utility> #line 6 "data_structure/simple_csr.hpp" namespace ebi { template <class E> struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector<std::pair<int, E>>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector<std::vector<E>>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector<int> start; std::vector<E> elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template <class T> struct Edge { int from, to; T cost; int id; }; template <class E> struct Graph { using cost_type = E; using edge_type = Edge<cost_type>; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr<edge_type>(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector<std::pair<int,edge_type>> buff; std::vector<edge_type> edges; simple_csr<edge_type> csr; bool prepared = false; }; } // namespace ebi #line 8 "graph/dijkstra_fibheap.hpp" namespace ebi { template <class T> bool op(T a, T b) { return a <= b; } template <class T> std::vector<T> dijkstra_fibheap(int s, int n, const Graph<T> &g) { std::vector<T> d(n, std::numeric_limits<T>::max()); fibonacci_heap<T, int, op> que; d[s] = 0; std::vector<internal::fibheap_node<T, int> *> p(n, nullptr); p[s] = que.push(0, s); while (!que.empty()) { que.is_valid(); int v = que.top(); que.pop(); for (auto e : g[v]) { if (d[e.to] > d[v] + e.cost) { d[e.to] = d[v] + e.cost; if (p[e.to] == nullptr) { p[e.to] = que.push(d[e.to], e.to); continue; } que.prioritize(p[e.to], d[e.to]); } } } return d; } } // namespace ebi