結果

問題 No.2296 Union Path Query (Hard)
ユーザー noshi91noshi91
提出日時 2023-05-05 21:51:54
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,580 ms / 7,000 ms
コード長 15,212 bytes
コンパイル時間 1,214 ms
コンパイル使用メモリ 99,044 KB
実行使用メモリ 38,832 KB
最終ジャッジ日時 2023-08-15 03:46:23
合計ジャッジ時間 34,249 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge13
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
4,380 KB
testcase_01 AC 7 ms
20,432 KB
testcase_02 AC 7 ms
20,384 KB
testcase_03 AC 8 ms
20,336 KB
testcase_04 AC 203 ms
27,324 KB
testcase_05 AC 206 ms
27,984 KB
testcase_06 AC 388 ms
30,608 KB
testcase_07 AC 770 ms
33,468 KB
testcase_08 AC 760 ms
34,648 KB
testcase_09 AC 910 ms
22,064 KB
testcase_10 AC 984 ms
21,736 KB
testcase_11 AC 1,038 ms
21,672 KB
testcase_12 AC 1,055 ms
19,664 KB
testcase_13 AC 850 ms
4,876 KB
testcase_14 AC 724 ms
4,376 KB
testcase_15 AC 702 ms
32,388 KB
testcase_16 AC 861 ms
26,912 KB
testcase_17 AC 1,181 ms
11,708 KB
testcase_18 AC 1,239 ms
37,124 KB
testcase_19 AC 1,580 ms
20,164 KB
testcase_20 AC 1,222 ms
36,412 KB
testcase_21 AC 1,412 ms
32,476 KB
testcase_22 AC 1,409 ms
32,600 KB
testcase_23 AC 549 ms
38,832 KB
testcase_24 AC 860 ms
20,960 KB
testcase_25 AC 309 ms
31,940 KB
testcase_26 AC 309 ms
32,320 KB
testcase_27 AC 353 ms
31,872 KB
testcase_28 AC 362 ms
32,932 KB
testcase_29 AC 128 ms
33,940 KB
testcase_30 AC 127 ms
35,064 KB
testcase_31 AC 163 ms
33,672 KB
testcase_32 AC 280 ms
32,852 KB
testcase_33 AC 482 ms
31,600 KB
testcase_34 AC 170 ms
29,628 KB
testcase_35 AC 296 ms
28,500 KB
testcase_36 AC 965 ms
26,272 KB
testcase_37 AC 368 ms
25,524 KB
testcase_38 AC 376 ms
25,516 KB
testcase_39 AC 371 ms
25,484 KB
testcase_40 AC 371 ms
25,456 KB
testcase_41 AC 1 ms
4,376 KB
testcase_42 AC 2 ms
4,380 KB
testcase_43 AC 1 ms
4,376 KB
testcase_44 AC 485 ms
37,320 KB
testcase_45 AC 496 ms
37,576 KB
testcase_46 AC 635 ms
37,324 KB
testcase_47 AC 632 ms
37,324 KB
testcase_48 AC 639 ms
37,336 KB
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 <array>
#include <cassert>
#include <utility>
#include <variant>
#include <vector>

/*

struct Info {
  using V;
  using E;
  using Point;
  using Path;
  static Point rake(Point, Point);
  static Point id();
  static Path to_path(V, Point);
  static Path compress(Path, E, Path);
  static Path reverse(Path);
  static Point to_point(E, Path);
};

*/

template <class Info> class top_tree {
  using V = typename Info::V;
  using E = typename Info::E;
  using Point = typename Info::Point;
  using Path = typename Info::Path;

  struct node_type;
  using node_ptr = node_type *;

  struct vertex_node {
    V v;
    Path path;

    vertex_node(V v_, Path path_) : v(std::move(v_)), path(std::move(path_)) {}
  };

  struct solid_edge_node {
    bool rev;
    E e;
    Path sum;

    solid_edge_node(E e_, Path sum_)
        : rev(false), e(std::move(e_)), sum(std::move(sum_)) {}
  };

  struct dashed_edge_node {
    E e;
    Point point;
    Point sum;

    dashed_edge_node(E e_, Point point_, Point sum_)
        : e(std::move(e_)), point(std::move(point_)), sum(std::move(sum_)) {}
  };

  using data_variant =
      std::variant<vertex_node, solid_edge_node, dashed_edge_node>;

  struct node_type {
    node_ptr p;
    std::array<node_ptr, 3> c;
    data_variant data;

    template <class... Args>
    node_type(Args &&... args)
        : p(nullptr), c({nullptr, nullptr, nullptr}),
          data(std::forward<Args>(args)...) {}
  };

  static void link_child(node_type &par, const node_ptr ch, const int dir) {
    par.c[dir] = ch;
    if (ch) {
      ch->p = &par;
    }
  }

  static int get_dir(const node_type &node) {
    if (node.p) {
      for (int i = 0; i < 3; i++) {
        if (node.p->c[i] == &node) {
          return i;
        }
      }
      assert(false);
    } else {
      return 1;
    }
  }

  static void p_replace(node_type &prev, node_type &n) {
    if (prev.p) {
      prev.p->c[get_dir(prev)] = &n;
      n.p = prev.p;
    } else {
      n.p = nullptr;
    }
  }

  static Point get_sum_point(const node_ptr ptr) {
    if (ptr) {
      return std::get<dashed_edge_node>(ptr->data).sum;
    } else {
      return Info::id();
    }
  }

  static const Path &get_sum_path(const node_type &node) {
    struct {
      const Path &operator()(const vertex_node &v) const { return v.path; }
      const Path &operator()(const solid_edge_node &s) const { return s.sum; }
      const Path &operator()(const dashed_edge_node &) const {
        throw "top_tree: internal error";
      }
    } visitor{};
    return std::visit(visitor, node.data);
  }

  static void update(node_type &node) {
    struct {
      node_type &node;
      void operator()(vertex_node &) const { throw "top_tree: internal error"; }
      void operator()(solid_edge_node &s) const {
        s.sum = Info::compress(get_sum_path(*node.c[0]), s.e,
                               get_sum_path(*node.c[2]));
      }
      void operator()(dashed_edge_node &d) const {
        d.sum = Info::rake(d.point, Info::rake(get_sum_point(node.c[0]),
                                               get_sum_point(node.c[2])));
      }
    } visitor{node};
    std::visit(visitor, node.data);
  }

  static void rotate(node_type &node, const int dir) {
    node_type &ch = *node.c[dir ^ 2];
    ch.p = node.p;
    if (node.p) {
      node.p->c[get_dir(node)] = &ch;
    }
    link_child(node, ch.c[dir], dir ^ 2);
    update(node);
    link_child(ch, &node, dir);
  }

  static void splay(node_type &node) {
    while (true) {
      const int d0 = get_dir(node);
      if (d0 == 1) {
        break;
      }
      node_type &p = *node.p;
      const int d1 = get_dir(p);
      if (d1 == 1) {
        rotate(p, d0 ^ 2);
        break;
      }
      node_type &pp = *p.p;
      if (d0 == d1) {
        rotate(pp, d1 ^ 2);
        rotate(p, d0 ^ 2);
      } else {
        rotate(p, d0 ^ 2);
        rotate(pp, d1 ^ 2);
      }
    }
    update(node);
  }

  static void reverse(node_type &node) {
    struct {
      void operator()(vertex_node &) const {}
      void operator()(solid_edge_node &s) const {
        s.sum = Info::reverse(std::move(s.sum));
        s.rev = !s.rev;
      }
      void operator()(dashed_edge_node &) const {
        throw "top_tree: internal error";
      }
    } visitor{};
    std::visit(visitor, node.data);
  }

  static void propagate(node_type &node) {
    if (node.p) {
      propagate(*node.p);
    }
    struct {
      node_type &node;
      void operator()(vertex_node &) const {}
      void operator()(solid_edge_node &s) const {
        if (s.rev) {
          s.rev = false;
          std::swap(node.c[0], node.c[2]);
          reverse(*node.c[0]);
          reverse(*node.c[2]);
        }
      }
      void operator()(dashed_edge_node &) const {}
    } visitor{node};
    std::visit(visitor, node.data);
  }

  static node_ptr merge(const node_ptr x, node_ptr y) {
    if (!y) {
      return x;
    }
    y->p = nullptr;
    while (y->c[0]) {
      y = y->c[0];
    }
    link_child(*y, x, 0);
    splay(*y);
    return y;
  }

  static void expose_edge(node_type &node) {
    propagate(node);
    node_ptr ptr = &node;
    if (ptr->data.index() == 1) {
      splay(*ptr);
      ptr = ptr->p;
    }
    while (ptr) {
      splay(*ptr);
      node_type &v = *ptr->p;
      if (get_dir(v) != 1) {
        splay(*v.p);
      }
      if (get_dir(v) != 1) {
        splay(*v.p);
      }
      if (get_dir(v) == 2 && get_dir(*v.p) == 0) {
        splay(*v.p);
      }
      if (get_dir(v) == 0) {
        node_type &p = *v.p;
        p_replace(p, *ptr);
        link_child(v, &p, 1);
        link_child(p, p.c[2], 1);
        link_child(p, ptr->c[0], 0);
        link_child(p, ptr->c[2], 2);
        E e = std::move(std::get<solid_edge_node>(p.data).e);
        Point point = Info::to_point(e, get_sum_path(*p.c[1]));
        Point sum = Info::rake(
            point, Info::rake(get_sum_point(p.c[0]), get_sum_point(p.c[2])));
        p.data = data_variant(std::in_place_type<dashed_edge_node>,
                              std::move(e), std::move(point), std::move(sum));
      } else {
        link_child(v, merge(ptr->c[0], ptr->c[2]), 1);
        p_replace(v, *ptr);
      }
      vertex_node &inner = std::get<vertex_node>(v.data);
      inner.path = Info::to_path(inner.v, get_sum_point(v.c[1]));
      link_child(*ptr, &v, 0);
      link_child(*ptr, ptr->c[1], 2);
      ptr->c[1] = nullptr;
      E e = std::move(std::get<dashed_edge_node>(ptr->data).e);
      Path sum =
          Info::compress(get_sum_path(*ptr->c[0]), e, get_sum_path(*ptr->c[2]));
      ptr->data = data_variant(std::in_place_type<solid_edge_node>,
                               std::move(e), std::move(sum));
      splay(*ptr);
      ptr = ptr->p;
    }
    splay(node);
  }

  static void check(const node_type &n) {
    if (n.p) {
      get_dir(n);
    }
    for (int i = 0; i < 3; i++) {
      if (n.c[i]) {
        assert(n.c[i]->p == &n);
      }
    }
    struct {
      const node_type &n;
      void operator()(const vertex_node &) const {
        assert(n.c[0] == nullptr);
        if (n.c[1]) {
          assert(n.c[1]->data.index() == 2);
        }
        assert(n.c[2] == nullptr);
        if (n.p) {
          assert(n.p->data.index() == 1 || n.p->data.index() == 2);
        }
      }
      void operator()(const solid_edge_node &) const {
        assert(n.c[0] != nullptr);
        assert(n.c[0]->data.index() == 0 || n.c[0]->data.index() == 1);
        assert(n.c[1] == nullptr);
        assert(n.c[2] != nullptr);
        assert(n.c[2]->data.index() == 0 || n.c[2]->data.index() == 1);
        if (n.p) {
          assert(n.p->data.index() == 1 || n.p->data.index() == 2);
        }
      }
      void operator()(const dashed_edge_node &) const {
        if (n.c[0]) {
          assert(n.c[0]->data.index() == 2);
        }
        assert(n.c[1] != nullptr);
        assert(n.c[1]->data.index() == 0 || n.c[1]->data.index() == 1);
        if (n.c[2]) {
          assert(n.c[2]->data.index() == 2);
        }
        assert(n.p != nullptr);
        assert(n.p->data.index() == 0 || n.p->data.index() == 2);
      }
    } visitor{n};
    std::visit(visitor, n.data);
  }

  static void check_cp(node_type &n) {
    struct {
      node_type &n;
      void operator()(vertex_node &) const { check_ds(n.c[1]); }
      void operator()(solid_edge_node &) const {
        check_cp(*n.c[0]);
        check_cp(*n.c[2]);
      }
      void operator()(dashed_edge_node &) const { assert(false); }
    } visitor{n};
    std::visit(visitor, n.data);
  }
  static void check_ds(const node_ptr ptr) {
    if (ptr) {
      struct {
        node_type &n;
        void operator()(vertex_node &) const { assert(false); }
        void operator()(solid_edge_node &) const { assert(false); }
        void operator()(dashed_edge_node &) const {
          check_ds(n.c[0]);
          check_cp(*n.c[1]);
          check_ds(n.c[2]);
        }
      } visitor{*ptr};
      std::visit(visitor, ptr->data);
    }
  }

  std::vector<node_type> vertex_nodes;
  std::vector<node_type> edge_nodes;
  node_ptr free_list;

  template <class... Args> node_type &allocate(Args &&... args) {
    if (free_list) {
      node_type &n = *free_list;
      free_list = n.c[0];
      n = node_type(std::forward<Args>(args)...);
      return n;
    } else {
      edge_nodes.emplace_back(std::forward<Args>(args)...);
      return edge_nodes.back();
    }
  }

  node_type &expose_vertex(const int v_) {
    node_type &v = vertex_nodes[v_];
    if (v.p) {
      expose_edge(*v.p);
    }
    if (get_dir(v) == 2) {
      splay(*v.p);
    }
    if (get_dir(v) == 0) {
      node_type &p = *v.p;
      splay(p);
      p_replace(p, *p.c[0]);
      link_child(p, v.c[1], 0);
      link_child(p, p.c[2], 1);
      p.c[2] = nullptr;
      link_child(v, &p, 1);
      E e = std::move(std::get<solid_edge_node>(p.data).e);
      Point point = Info::to_point(e, get_sum_path(*p.c[1]));
      Point sum = Info::rake(
          point, Info::rake(get_sum_point(p.c[0]), get_sum_point(p.c[2])));
      p.data = data_variant(std::in_place_type<dashed_edge_node>, std::move(e),
                            std::move(point), std::move(sum));
      vertex_node &inner = std::get<vertex_node>(v.data);
      inner.path = Info::to_path(inner.v, get_sum_point(v.c[1]));
    }
    if (v.p) {
      node_type &p = *v.p;
      splay(p);
      return p;
    } else {
      return v;
    }
  }

  node_type &evert(const int v) {
    node_type &r = expose_vertex(v);
    reverse(r);
    return r;
  }

public:
  class edge_handle {
    friend top_tree;
    node_ptr ptr;

    edge_handle(const node_ptr ptr_) : ptr(ptr_) {}

  public:
    edge_handle() : ptr(nullptr) {}
    E get() const {
      struct {
        E operator()(vertex_node &) const { throw "top_tree: internal error"; }
        E operator()(solid_edge_node &n) const { return n.e; }
        E operator()(dashed_edge_node &n) const { return n.e; }
      } visitor{};
      return std::visit(visitor, *ptr);
    }
  };

  top_tree(std::vector<V> vertices)
      : vertex_nodes(), edge_nodes(), free_list(nullptr) {
    const int n = vertices.size();
    vertex_nodes.reserve(n);
    for (int i = 0; i < n; i++) {
      Path sum = Info::to_path(vertices[i], Info::id());
      vertex_nodes.emplace_back(std::in_place_type<vertex_node>,
                                std::move(vertices[i]), std::move(sum));
    }
    edge_nodes.reserve(n - 1);
  }

  void set_vertex(const int i, V v) {
    node_type &n = vertex_nodes[i];
    vertex_node &inner = std::get<vertex_node>(n.data);
    inner.v = std::move(v);
    inner.path = Info::to_path(inner.v, get_sum_point(n.c[1]));
    // check();
    if (n.p) {
      expose_edge(*n.p);
    }
    // check();
  }

  void set_edge(const edge_handle h, E e) {
    expose_edge(*h.ptr);
    std::get<solid_edge_node>(h.ptr->data).e = std::move(e);
    update(*h.ptr);
  }

  Path get_path(const int u, const int v) {
    evert(u);
    // check();
    node_type &r = expose_vertex(v);
    // check();
    return get_sum_path(r);
  }

  edge_handle link(const int u, const int v, E e) {
    node_type &u_ = expose_vertex(u);
    node_type &v_ = evert(v);
    Path sum = Info::compress(get_sum_path(u_), e, get_sum_path(v_));
    node_type &r = allocate(std::in_place_type<solid_edge_node>, std::move(e),
                            std::move(sum));
    link_child(r, &u_, 0);
    link_child(r, &v_, 2);
    return edge_handle(&r);
  }

  void cut(const edge_handle h) {
    node_type &n = *h.ptr;
    expose_edge(n);
    n.c[0]->p = nullptr;
    n.c[2]->p = nullptr;
    n.c[0] = free_list;
    free_list = &n;
  }

  bool connected(const int u, const int v) {
    node_type &u_ = expose_vertex(u);
    node_type &v_ = expose_vertex(v);
    return &u_ == &v_ || u_.p != nullptr;
  }

  void check() {
    for (auto &v : vertex_nodes) {
      check(v);
    }
    std::vector<bool> used(edge_nodes.size(), true);
    {
      node_ptr p = free_list;
      while (p) {
        used[p - edge_nodes.data()] = false;
        p = p->c[0];
      }
    }
    for (int i = 0; i < edge_nodes.size(); i++) {
      if (used[i]) {
        check(edge_nodes[i]);
      }
    }

    for (auto &v : vertex_nodes) {
      if (!v.p) {
        check_cp(v);
      }
    }
    for (int i = 0; i < edge_nodes.size(); i++) {
      if (used[i] && !edge_nodes[i].p) {
        check_cp(edge_nodes[i]);
      }
    }
  }
};

#include <algorithm>

using i64 = long long;

struct yuki {
  struct V {};
  using E = i64;
  struct Point {
    i64 far, diam;
  };

  struct Path {
    i64 dist;
    i64 l, r;
    i64 diam;
  };

  static Point rake(Point x, Point y) {
    return Point{std::max(x.far, y.far),
                 std::max({x.diam, y.diam, x.far + y.far})};
  }
  static Point id() { return Point{0, 0}; }
  static Path to_path(V, Point p) { return Path{0, p.far, p.far, p.diam}; }
  static Path compress(Path l, E e, Path r) {
    return Path{l.dist + e + r.dist, std::max(l.l, l.dist + e + r.l),
                std::max(l.r + e + r.dist, r.r),
                std::max({l.diam, r.diam, l.r + e + r.l})};
  }
  static Path reverse(Path p) {
    std::swap(p.l, p.r);
    return p;
  }
  static Point to_point(E e, Path p) {
    return Point{e + p.l, std::max(e + p.l, p.diam)};
  }
};

#include <iostream>
#include <utility>
#include <vector>

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);

  int N, X, Q;
  std::cin >> N >> X >> Q;
  std::vector<yuki::V> vs(N);

  top_tree<yuki> tree(vs);

  while (Q--) {
    int type;
    std::cin >> type;
    if (type == 1) {
      int v;
      i64 w;
      std::cin >> v >> w;
      tree.link(v, X, w);
    } else if (type == 2) {
      int u, v;
      std::cin >> u >> v;
      if (tree.connected(u, v)) {
        const i64 d = tree.get_path(u, v).dist;
        std::cout << d << "\n";
        X = (X + d % N) % N;
      } else {
        std::cout << "-1"
                  << "\n";
      }
    } else if (type == 3) {
      int v;
      std::cin >> v;
      std::cout << tree.get_path(v, v).diam << "\n";
    } else {
      int value;
      std::cin >> value;
      X = (X + value) % N;
    }
  }

  return 0;
}
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