結果

問題 No.1194 Replace
コンテスト
ユーザー hitonanode
提出日時 2020-08-22 14:43:00
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 379 ms / 2,000 ms
コード長 12,172 bytes
コンパイル時間 3,016 ms
コンパイル使用メモリ 216,632 KB
最終ジャッジ日時 2025-01-13 08:51:51
ジャッジサーバーID
（参考情報） 		judge2 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 27
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template <typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template <typename V, typename T> void ndfill(V &x, const T &val) { x = val; }
template <typename V, typename T> void ndfill(vector<V> &vec, const T &val) { for (auto &v : vec) ndfill(v, val); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
#else
#define dbg(x)
#endif

// 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; }

    void _consolidate()
    {
        std::array<Node *, 30> arr;
        arr.fill(nullptr);

        auto fmerge = [&](auto &&func, Node *ptr) -> void {
            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;
                func(func, ptr);
            }
        };
        for (auto ptr : roots) if (ptr != nullptr) {
            if (ptr->deg < 0) delete ptr;
            else fmerge(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 clear()
    {
        auto deldfs = [&](auto &&f, Node *now) -> void {
            while (now != nullptr)
            {
                if (now->child != nullptr) f(f, now->child);
                Node *nxt = now->right;
                delete now;
                now = nxt;
            }
        };
        for (auto root : roots)
        {
            deldfs(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();
    }
};

int main()
{
    int N, M;
    cin >> N >> M;
    vector<int> B(M), C(M);
    REP(i, M) cin >> B[i] >> C[i];

    vector<int> Z = B;
    Z.insert(Z.end(), ALL(C));
    Z = srtunq(Z);
    int V = Z.size();
    vector<vector<pint>> to(V);
    heap<int> hp(V, 0);
    REP(i, M)
    {
        int s = lower_bound(ALL(Z), B[i]) - Z.begin();
        int t = lower_bound(ALL(Z), C[i]) - Z.begin();
        to[t].emplace_back(s, B[i] - C[i]);
        hp.chmin(s, B[i] - C[i]);
    }
    vector<int> visited(V);
    vector<int> result(V);
    queue<int> q;
    IREP(i, V) if (!visited[i])
    {
        q.emplace(i);
        while (q.size())
        {
            int now = q.front();
            visited[now] = true;
            q.pop();
            for (auto [j, adv] : to[now]) if (!visited[j])
            {
                result[j] = result[now] + adv;
                q.emplace(j);
            }
        }
    }
    dbg(to);
    int last_idx = -1;
    // while (hp.size())
    // {
    //     auto [val, i] = hp.top();
    //     if (i == last_idx)
    //     {
    //         hp.pop();
    //         continue;
    //     }
    //     last_idx = i;
    //     for (auto [j, adv] : to[i])
    //     {
    //         hp.chmin(j, val + adv);
    //     }
    // }
    // dbg(hp.result);
    cout << 1LL * (1 + N) * N / 2 - accumulate(ALL(result), 0LL) << '\n';
}
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