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:heavy_check_mark: graph/dijkstra_fibheap.hpp

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#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
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