fibonacci_heap.hpp

#pragma once
#include <array>
#include <cassert>
#include <iostream>
#include <list>

// CUT begin
// Fibonacci heap
// - Complexity:
//   - empty(), size(), top(), push(), meld(): O(1)
//   - pop(), decrease(): O(lg N) amortized
// - Reference:
//   - "Introduction to Algorithms, Third Edition", Chapter 19
//   - <https://www.cs.princeton.edu/~wayne/teaching/fibonacci-heap.pdf>
//   - <https://rsk0315.hatenablog.com/entry/2019/10/29/151823>
template <typename Tp> struct fibonacci_heap {
    struct Node {
        Tp val;
        int deg;
        Node *parent, *left, *right, *child;
        bool mark;
        Node() = default;
        Node(Node const &) = default;
        Node(Node &&) = default;
        Node &operator=(Node const &) = default;
        Node &operator=(Node &&) = default;
        Node(Tp v)
            : val(v), deg(0), parent(nullptr), left(nullptr), right(nullptr), child(nullptr),
              mark(false) {}
        friend std::ostream &operator<<(std::ostream &os, const Node &n) {
            os << '(' << n.val << ',';
            if (n.child != nullptr) os << *(n.child) << ',';
            Node *now = n.right;
            while (now != &n) {
                os << now->val << ',';
                if (now->child != nullptr) os << *now->child << ',';
                now = now->right;
            }
            os << ')';
            return os;
        }
    };

    int sz;
    std::list<Node *> roots;
    Node *ptop;
    inline void _chmin(Node *cand) noexcept {
        if (ptop == nullptr or cand->val < ptop->val) ptop = cand;
    }
    fibonacci_heap() : sz(0), roots({}), ptop(nullptr) {}

    bool empty() const noexcept { return sz == 0; }
    int size() const noexcept { return sz; }

    std::array<Node *, 30> _arr;
    void _fmerge(Node *ptr) {
        int d = ptr->deg;
        if (_arr[d] == nullptr)
            _arr[d] = ptr;
        else {
            Node *cptr = _arr[d];
            if (cptr->val < ptr->val) std::swap(ptr, cptr);
            ptr->deg++;
            cptr->parent = ptr;
            if (ptr->child == nullptr)
                ptr->child = cptr;
            else {
                Node *cl = ptr->child, *cr = ptr->child->right;
                assert(cl->right == cr and cr->left == cl);
                cptr->left = cl, cptr->right = cr, cl->right = cr->left = cptr;
            }
            _arr[d] = nullptr;
            _fmerge(ptr);
        }
    }
    void _consolidate() {
        _arr.fill(nullptr);
        for (auto ptr : roots)
            if (ptr != nullptr) {
                if (ptr->deg < 0)
                    delete ptr;
                else
                    _fmerge(ptr);
            }
        roots.clear(), ptop = nullptr;
        for (auto ptr : _arr)
            if (ptr != nullptr) _add_tree(ptr);
    }

    void _add_tree(Node *root) noexcept {
        root->parent = nullptr;
        root->left = root->right = root;
        roots.emplace_back(root);
        _chmin(root);
    }

    Node *push(const Tp &val) noexcept {
        sz++;
        Node *ptr = new Node(val);
        _add_tree(ptr);
        return ptr;
    }

    void meld(fibonacci_heap &&hp) {
        sz += hp.sz;
        roots.splice(roots.end(), hp.roots);
        if (hp.ptop != nullptr) _chmin(hp.ptop);
    }

    void pop() {
        assert(sz > 0);
        sz--;
        Node *ch1 = ptop->child;
        if (ch1 != nullptr) {
            Node *now = ch1;
            while (true) {
                Node *nxt = now->right;
                _add_tree(now);
                now = nxt;
                if (now == ch1) break;
            }
        }
        ptop->deg = -1;
        _consolidate();
    }

    void _deldfs(Node *now) {
        while (now != nullptr) {
            if (now->child != nullptr) _deldfs(now->child);
            Node *nxt = now->right;
            delete now;
            now = nxt;
        }
    }
    void clear() {
        for (auto root : roots) _deldfs(root);
        sz = 0;
        roots.clear();
        ptop = nullptr;
    }

    void _cut(Node *x) noexcept {
        Node *y = x->parent;
        assert(y != nullptr and y->deg > 0);
        Node *xr = x->right, *xl = x->left;
        if (x == xr) {
            y->child = nullptr;
        } else {
            y->child = xr;
            xl->right = xr, xr->left = xl;
        }
        y->deg--;
        _add_tree(x);
        x->mark = false;
    }
    void _cascading_cut(Node *now) noexcept {
        assert(now != nullptr);
        Node *par = now->parent;
        if (par == nullptr) return;
        if (!now->mark)
            now->mark = true;
        else {
            _cut(now);
            _cascading_cut(par);
        }
    }
    void erase(Node *r) {
        if (r->parent != nullptr) {
            Node *rpar = r->parent;
            _cut(r);
            _cascading_cut(rpar);
        }
        ptop = r;
        pop();
    }
    bool decrease(Node *r, const Tp new_val) {
        assert(r != nullptr);
        if (!(new_val < r->val)) return false;
        r->val = new_val;
        if (r->parent != nullptr and new_val < r->parent->val) {
            Node *rpar = r->parent;
            _cut(r);
            _cascading_cut(rpar);
        }
        _chmin(r);
        return true;
    }
    Tp top() const {
        assert(ptop != nullptr);
        return ptop->val;
    }
    friend std::ostream &operator<<(std::ostream &os, const fibonacci_heap &hp) {
        os << "[(fibonacci_heap: sz=" << hp.sz << ", top=" << hp.ptop->val
           << ", #tree = " << hp.roots.size() << ")";
        for (auto x : hp.roots) { os << *x << ", "; }
        os << ']';
        return os;
    }
};

#include <utility>
#include <vector>
template <typename Tp> struct heap {
    using P = std::pair<Tp, int>;
    fibonacci_heap<P> _heap;
    std::vector<typename fibonacci_heap<P>::Node *> vp;
    std::vector<Tp> result;
    void initialize(int N, Tp initval) {
        _heap.clear();
        vp.resize(N);
        result.assign(N, initval);
        for (int i = 0; i < N; i++) { vp[i] = _heap.push(std::make_pair(initval, i)); }
    }
    heap(int N, Tp initval) { initialize(N, initval); }
    bool chmin(int i, Tp val) {
        if (val < result[i]) {
            result[i] = val;
            if (vp[i] == nullptr) {
                vp[i] = _heap.push(std::make_pair(result[i], i));
            } else {
                _heap.decrease(vp[i], std::make_pair(result[i], i));
            }
            return true;
        }
        return false;
    }
    Tp operator[](int i) const { return result.at(i); }
    P top() { return _heap.top(); }
    P pop() {
        P ret = _heap.top();
        _heap.pop();
        return ret;
    }
    int size() { return _heap.size(); }
    bool empty() { return _heap.empty(); }
};