結果

問題 No.2296 Union Path Query (Hard)
コンテスト
ユーザー t98slider
提出日時 2023-03-20 14:24:15
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 602 ms / 7,000 ms
コード長 6,577 bytes
コンパイル時間 2,686 ms
コンパイル使用メモリ 202,164 KB
実行使用メモリ 46,268 KB
最終ジャッジ日時 2024-11-23 04:46:19
合計ジャッジ時間 22,100 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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ファイルパターン 結果
sample AC * 4
other AC * 45
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 ll = long long;

/**
 * @brief Link Cut Tree
 * @docs docs/link-cut-tree.md
 */
template< typename T>
struct LinkCutTree {

private:

  struct Node {
    Node *l, *r, *p;
    T key, sum;
    bool rev;

    explicit Node(const T &v) : key(v), sum(v), rev(false),
                                l(nullptr), r(nullptr), p(nullptr) {}

    bool is_root() const {
      return not p or (p->l != this and p->r != this);
    }
  };

public:
  using NP = Node *;

private:
  NP update(NP t) {
    t->sum = t->key;
    if(t->l) t->sum += t->l->sum;
    if(t->r) t->sum += t->r->sum;
    return t;
  }

  void rotr(NP t) {
    NP 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 rotl(NP t) {
    NP 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 toggle(NP t) {
    swap(t->l, t->r);
    //t->sum = s(t->sum);
    t->rev ^= true;
  }

  void push(NP t) {
    if(t->rev) {
      if(t->l) toggle(t->l);
      if(t->r) toggle(t->r);
      t->rev = false;
    }
  }

  void splay(NP t) {
    push(t);
    while(not t->is_root()) {
      NP q = t->p;
      if(q->is_root()) {
        push(q), push(t);
        if(q->l == t) rotr(t);
        else rotl(t);
      } else {
        NP r = q->p;
        push(r), push(q), push(t);
        if(r->l == q) {
          if(q->l == t) rotr(q), rotr(t);
          else rotl(t), rotr(t);
        } else {
          if(q->r == t) rotl(q), rotl(t);
          else rotr(t), rotl(t);
        }
      }
    }
  }

public:
  LinkCutTree() {}

  NP alloc(const T &v = T()) {
    return new Node(v);
  }

  vector< NP > build(vector< T > &vs) {
    vector< NP > nodes(vs.size());
    for(int i = 0; i < (int) vs.size(); i++) {
      nodes[i] = alloc(vs[i]);
    }
    return nodes;
  }

  NP expose(NP t) {
    NP rp = nullptr;
    for(NP cur = t; cur; cur = cur->p) {
      splay(cur);
      cur->r = rp;
      update(cur);
      rp = cur;
    }
    splay(t);
    return rp;
  }

  void evert(NP t) {
    expose(t);
    toggle(t);
    push(t);
  }

  void link(NP child, NP parent) {
    if(is_connected(child, parent)) {
      throw runtime_error("child and parent must be different connected components");
    }
    if(child->l) {
      throw runtime_error("child must be root");
    }
    child->p = parent;
    parent->r = child;
    update(parent);
  }

  void cut(NP child) {
    expose(child);
    NP parent = child->l;
    if(not parent) {
      throw runtime_error("child must not be root");
    }
    child->l = nullptr;
    parent->p = nullptr;
    update(child);
  }

  bool is_connected(NP u, NP v) {
    expose(u), expose(v);
    return u == v or u->p;
  }

  NP lca(NP u, NP v) {
    if(not is_connected(u, v)) return nullptr;
    expose(u);
    return expose(v);
  }

  const T &query(NP u) {
    expose(u);
    return u->sum;
  }

  const T &query(NP u, NP v) {
    evert(u);
    return query(v);
  }

  void set_key(NP t, T v) {
    expose(t);
    t->key = v;
    update(t);
  }
};

struct dsu {
    public:
    int csz;
    dsu() : _n(0) {}
    dsu(int n) : _n(n), csz(n), parent_or_size(n, -1) {}

    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        csz--;
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }

    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

    private:
    int _n;
    // root node: -1 * component size
    // otherwise: parent
    std::vector<int> parent_or_size;
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  ll N, X, Q;
  cin >> N >> X >> Q;
  auto add = [](ll a, ll b) { return a + b; };
  LinkCutTree<ll> lct;

  vector<ll> A(N + Q);
  vector<tuple<ll,int,int>> B(N);
  for(int i = 0; i < N; i++){
    B[i] = make_tuple(0, i, i);
  }
  dsu uf(N);
  auto vs = lct.build(A);

  auto update = [&](int x, int y){
    int r = uf.merge(x, y);
    auto mx = max(B[x], B[y]);
    mx = max(mx, make_tuple(lct.query(vs[get<1>(B[x])], vs[get<1>(B[y])]), get<1>(B[x]), get<1>(B[y])));
    mx = max(mx, make_tuple(lct.query(vs[get<1>(B[x])], vs[get<2>(B[y])]), get<1>(B[x]), get<2>(B[y])));
    mx = max(mx, make_tuple(lct.query(vs[get<2>(B[x])], vs[get<1>(B[y])]), get<2>(B[x]), get<1>(B[y])));
    mx = max(mx, make_tuple(lct.query(vs[get<2>(B[x])], vs[get<2>(B[y])]), get<2>(B[x]), get<2>(B[y])));
    B[r] = mx;
  };

  int type, x, u, v, w;
  for(int i = 0; i < Q; i++){
    cin >> type;
    if(type == 1){
      cin >> v >> w;
      int s = N + i, x = uf.leader(v), y = uf.leader(X);
      lct.evert(vs[v]);
      lct.link(vs[v], vs[s]);
      lct.evert(vs[X]);
      lct.link(vs[X], vs[s]);
      lct.set_key(vs[s], w);
      update(x, y);
    }else if(type == 2){
      cin >> u >> v;
      if(!uf.same(u, v)){
        cout << -1 << '\n';
        continue;
      }
      ll d = lct.query(vs[u], vs[v]);
      (X += d) %= N;
      cout << d << '\n';
    }else if(type == 3){
      cin >> v;
      cout << get<0>(B[uf.leader(v)]) << '\n';
    }else{
      cin >> v;
      (X += v) %= N;
    }
  }
}
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