#866625 (C++23) No.2296 Union Path Query (Hard)

提出ソース
結果

問題	No.2296 Union Path Query (Hard)
コンテスト
ユーザー	hitonanode
提出日時	2023-05-05 22:51:33
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	513 ms / 7,000 ms
コード長	15,646 bytes
コンパイル時間	3,907 ms
コンパイル使用メモリ	189,056 KB
実行使用メモリ	34,504 KB
最終ジャッジ日時	2024-11-23 10:42:52
合計ジャッジ時間	19,388 ms
ジャッジサーバーID （参考情報）	judge4 / judge3
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 * 4
other	AC * 45
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ソースコード

raw source code
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
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, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif

// Link-Cut Tree
// Reference:
// - https://www.slideshare.net/iwiwi/2-12188845
// - https://ei1333.github.io/library/structure/lct/link-cut-tree-lazy-path.cpp
template <class S, class F, S (*op)(S, S), S (*reversal)(S), S (*mapping)(F, S),
          F (*composition)(F, F), F (*id)()>
class lazy_linkcuttree {
public:
    struct Node {
        Node *l, *r, *p;
        S d, sum;
        F lz;
        bool is_reversed;
        int sz;
        Node(S val)
            : l(nullptr), r(nullptr), p(nullptr), d(val), sum(val), lz(id()), is_reversed(false),
              sz(1) {}
        bool is_root() const { return !p || (p->l != this and p->r != this); }
        template <class OStream> friend OStream &operator<<(OStream &os, const Node &n) {
            os << '[';
            if (n.l) os << *(n.l) << ',';
            os << n.d << ',';
            if (n.r) os << *(n.r);
            return os << ']';
        }
    };

protected:
    void update(Node *t) {
        if (t == nullptr) return;
        t->sz = 1;
        t->sum = t->d;
        if (t->l) {
            t->sz += t->l->sz;
            t->sum = op(t->l->sum, t->sum);
        }
        if (t->r) {
            t->sz += t->r->sz;
            t->sum = op(t->sum, t->r->sum);
        }
    }
    void all_apply(Node *a, F b) {
        a->d = mapping(b, a->d);
        a->sum = mapping(b, a->sum);
        a->lz = composition(b, a->lz);
    }
    void _toggle(Node *t) {
        auto tmp = t->l;
        t->l = t->r, t->r = tmp;
        t->sum = reversal(t->sum);
        t->is_reversed ^= true;
    }

    void push(Node *&t) {
        if (t->lz != id()) {
            if (t->l) all_apply(t->l, t->lz);
            if (t->r) all_apply(t->r, t->lz);
            t->lz = id();
        }
        if (t->is_reversed) {
            if (t->l) _toggle(t->l);
            if (t->r) _toggle(t->r);
            t->is_reversed = false;
        }
    }

    void _rot_r(Node *t) {
        Node *x = t->p, *y = x->p;
        if ((x->l = t->r)) t->r->p = x;
        t->r = x, x->p = t;
        update(x), update(t);
        if ((t->p = y)) {
            if (y->l == x) y->l = t;
            if (y->r == x) y->r = t;
            update(y);
        }
    }
    void _rot_l(Node *t) {
        Node *x = t->p, *y = x->p;
        if ((x->r = t->l)) t->l->p = x;
        t->l = x, x->p = t;
        update(x), update(t);
        if ((t->p = y)) {
            if (y->l == x) y->l = t;
            if (y->r == x) y->r = t;
            update(y);
        }
    }

    void _splay(Node *t) {
        push(t);
        while (!t->is_root()) {
            Node *q = t->p;
            if (q->is_root()) {
                push(q), push(t);
                if (q->l == t)
                    _rot_r(t);
                else
                    _rot_l(t);
            } else {
                Node *r = q->p;
                push(r), push(q), push(t);
                if (r->l == q) {
                    if (q->l == t)
                        _rot_r(q), _rot_r(t);
                    else
                        _rot_l(t), _rot_r(t);
                } else {
                    if (q->r == t)
                        _rot_l(q), _rot_l(t);
                    else
                        _rot_r(t), _rot_l(t);
                }
            }
        }
    }

public:
    [[nodiscard]] Node *make_node(S val) { return new Node(val); }

    void evert(Node *t) { expose(t), _toggle(t), push(t); }

    Node *expose(Node *t) {
        Node *rp = nullptr;
        for (Node *cur = t; cur; cur = cur->p) {
            _splay(cur);
            cur->r = rp;
            update(cur);
            rp = cur;
        }
        _splay(t);
        return rp;
    }

    void link(Node *chi, Node *par) {
        evert(chi);
        expose(par);
        chi->p = par;
        par->r = chi;
        update(par);
    }

    void cut(Node *chi) {
        expose(chi);
        Node *par = chi->l;
        chi->l = nullptr;
        update(chi);
        par->p = nullptr;
    }

    void cut(Node *u, Node *v) { evert(u), cut(v); }

    Node *lca(Node *u, Node *v) { return expose(u), expose(v); }

    void set(Node *t, S x) { expose(t), t->d = x, update(t); }

    S get(Node *t) { return expose(t), t->d; }

    void apply(Node *u, Node *v, const F &x) {
        evert(u);
        expose(v);
        all_apply(v, x);
        push(v);
    }

    S prod(Node *u, Node *v) {
        evert(u);
        expose(v);
        return v->sum;
    }

    Node *kth_parent(Node *t, int k) {
        expose(t);
        while (t) {
            push(t);
            if (t->r and t->r->sz > k) {
                t = t->r;
            } else {
                if (t->r) k -= t->r->sz;
                if (k == 0) return t;
                k--;
                t = t->l;
            }
        }
        return nullptr;
    }

    bool is_connected(Node *u, Node *v) {
        expose(u), expose(v);
        return u == v or u->p;
    }
};
/* example usage:
struct S {
    int sz, sum, lhi, rhi, inhi;
    S(int x) : sz(1), sum(x), lhi(x), rhi(x), inhi(x) {}
    S(int sz_, int sum_, int lhi_, int rhi_, int inhi_)
        : sz(sz_), sum(sum_), lhi(lhi_), rhi(rhi_), inhi(inhi_) {}
};
using F = pair<bool, int>;
S op(S l, S r) {
    return S(l.sz + r.sz, l.sum + r.sum, max(l.sum + r.lhi, l.lhi), max(l.rhi + r.sum, r.rhi),
max<int>({l.inhi, r.inhi, l.rhi + r.lhi}));
}
S reversal(S x) { return S(x.sz, x.sum, x.rhi, x.lhi, x.inhi); }
S mapping(F f, S x) {
    if (f.first) {
        auto v = f.second;
        auto sum = x.sz * v;
        return S{x.sz, sum, max(v, sum), max(v, sum), max(v, sum)};
    } else {
        return x;
    }
}
F composition(F fnew, F gold) { return fnew.first ? fnew : gold; }
F id() { return {false, 0}; }
using LCT = lazy_linkcuttree<S, F, op, reversal, mapping, composition, id>;
vector<LCT::Node*> vs;
*/

// using S = lint;
using S = lint;
using F = tuple<>;
S op(S l, S r) { return l + r; }
S reversal(S x) { return x; }
S mapping(F, S x) { return x; }
F composition(F, F) { return F(); }
F id() { return F(); }
using LCT = lazy_linkcuttree<S, F, op, reversal, mapping, composition, id>;

// UnionFind Tree (0-indexed), based on size of each disjoint set
struct UnionFind {
    std::vector<int> par, cou;
    UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); }
    int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
    bool unite(int x, int y) {
        x = find(x), y = find(y);
        if (x == y) return false;
        if (cou[x] < cou[y]) std::swap(x, y);
        par[y] = x, cou[x] += cou[y];
        return true;
    }
    int count(int x) { return cou[find(x)]; }
    bool same(int x, int y) { return find(x) == find(y); }
    std::vector<std::vector<int>> groups() {
        std::vector<std::vector<int>> ret(par.size());
        for (int i = 0; i < int(par.size()); ++i) ret[find(i)].push_back(i);
        ret.erase(std::remove_if(ret.begin(), ret.end(),
                                 [&](const std::vector<int> &v) { return v.empty(); }),
                  ret.end());
        return ret;
    }
};

struct Component {
    int u;
    int v;
    lint len;
};

int main() {
    int N, x, Q;
    cin >> N >> x >> Q;

    LCT tree;
    vector<LCT::Node *> vs;
    REP(i, N) vs.push_back(tree.make_node(0));

    UnionFind uf(N);

    vector<Component> comps(N);
    REP(i, N) comps.at(i) = {i, i, 0};

    REP(q, Q) {
        int tp;
        cin >> tp;
        if (tp == 1) {
            int v, w;
            cin >> v >> w;
            int a = uf.find(v), b = uf.find(x);
            uf.unite(v, x);
            if (uf.find(a) != a) swap(a, b);


            auto n = tree.make_node(w);
            tree.link(vs[v], n);
            tree.link(vs[x], n);

            int bu = comps.at(a).u, bv = comps.at(a).v;
            lint blen = comps.at(a).len;
            if (chmax(blen, comps.at(b).len)) bu = comps.at(b).u, bv = comps.at(b).v;

            for (int c : {comps.at(a).u, comps.at(a).v}) {
                for (int d : {comps.at(b).u, comps.at(b).v}) {
                    if (chmax(blen, tree.prod(vs.at(c), vs.at(d)))) bu = c, bv = d;
                }
            }
            comps.at(a) = {bu, bv, blen};

        } else if (tp == 2) {
            int u, v;
            cin >> u >> v;
            if (uf.same(u, v)) {
                lint ret = tree.prod(vs.at(u), vs.at(v));
                cout << ret << '\n';
                x = (x + ret) % N;
            } else {
                cout << "-1\n";
            }
        } else if (tp == 3) {
            int v;
            cin >> v;
            cout << comps.at(uf.find(v)).len << '\n';
        } else if (tp == 4) {
            int v;
            cin >> v;
            x = (x + v) % N;
        }
    }
}
yukicoder

結果

ソースコード
