test/verify/aoj-grl-5-a-3.test.cpp

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• Last update: 2024-07-28 19:56:12+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_A

Depends on

• structure/dynamic-tree/diameter.hpp
• Dynamic Tree Builder (for Edge) (structure/dynamic-tree/dynamic-tree-builder-for-edge.hpp)
• Top Tree (structure/dynamic-tree/top-tree.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_A

#include "../../template/template.hpp"
#include "../../structure/dynamic-tree/diameter.hpp"
#include "../../structure/dynamic-tree/dynamic-tree-builder-for-edge.hpp"

int main() {
  int N;
  cin >> N;
  DynamicTreeBuilderForEdge< TopTree, Diameter< int64 > > g(N);
  for(int i = 0; i < N; i++) {
    g.set_vertex(i, {true, 0});
  }
  for(int i = 1; i < N; i++) {
    int a, b;
    int64 w;
    cin >> a >> b >> w;
    g.add_edge(a, b, {false, w});
  }
  g.build();
  cout << g.query(g.vs[0]).dia << endl;
}

#line 1 "test/verify/aoj-grl-5-a-3.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_A

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 1 "structure/dynamic-tree/top-tree.hpp"
template <typename TreeDPInfo>
struct SplayTreeForDashedEdge {
  using Point = typename TreeDPInfo::Point;
  struct Node {
    Node *l, *r, *p;
    Point key, sum;

    explicit Node(const Point &key)
        : key(key), sum(key), l(nullptr), r(nullptr), p(nullptr) {}
  };

  SplayTreeForDashedEdge() = default;

  using NP = Node *;

  void rotr(NP t) const {
    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;
    }
  }

  void rotl(NP t) const {
    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;
    }
  }

  void update(NP t) const {
    t->sum = t->key;
    if (t->l) t->sum = TreeDPInfo::rake(t->sum, t->l->sum);
    if (t->r) t->sum = TreeDPInfo::rake(t->sum, t->r->sum);
  }

  NP get_right(NP t) const {
    while (t->r) t = t->r;
    return t;
  }

  NP alloc(const Point &v) const {
    auto t = new Node(v);
    update(t);
    return t;
  }

  void splay(NP t) const {
    while (t->p) {
      NP q = t->p;
      if (!q->p) {
        if (q->l == t)
          rotr(t);
        else
          rotl(t);
      } else {
        NP r = q->p;
        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);
        }
      }
    }
  }

  NP insert(NP t, const Point &v) const {
    if (not t) {
      t = alloc(v);
      return t;
    } else {
      NP cur = get_right(t), z = alloc(v);
      splay(cur);
      z->p = cur;
      cur->r = z;
      update(cur);
      splay(z);
      return z;
    }
  }

  NP erase(NP t) const {
    splay(t);
    NP x = t->l, y = t->r;
    delete t;
    if (not x) {
      t = y;
      if (t) t->p = nullptr;
    } else if (not y) {
      t = x;
      t->p = nullptr;
    } else {
      x->p = nullptr;
      t = get_right(x);
      splay(t);
      t->r = y;
      y->p = t;
      update(t);
    }
    return t;
  }
};

template <typename TreeDPInfo>
struct TopTree {
  using Path = typename TreeDPInfo::Path;
  using Info = typename TreeDPInfo::Info;

 private:
  struct Node {
    Node *l, *r, *p;
    Info info;
    Path sum, mus;
    typename SplayTreeForDashedEdge<TreeDPInfo>::Node *light, *belong;
    bool rev;

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

    Node(const Info &info)
        : info(info),
          l(nullptr),
          r(nullptr),
          p(nullptr),
          rev(false),
          light(nullptr),
          belong(nullptr) {}
  };

 public:
  using NP = Node *;
  const SplayTreeForDashedEdge<TreeDPInfo> splay_tree;

 private:
  void toggle(NP t) {
    swap(t->l, t->r);
    swap(t->sum, t->mus);
    t->rev ^= true;
  }

  void rotr(NP t) {
    NP x = t->p, y = x->p;
    push(x), push(t);
    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;
    }
  }

  void rotl(NP t) {
    NP x = t->p, y = x->p;
    push(x), push(t);
    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;
    }
  }

 public:
  TopTree() : splay_tree{} {}

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

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

  void update(NP t) {
    Path key = t->light ? TreeDPInfo::add_vertex(t->light->sum, t->info)
                        : TreeDPInfo::vertex(t->info);
    t->sum = key;
    t->mus = key;
    if (t->l) {
      t->sum = TreeDPInfo::compress(t->l->sum, t->sum);
      t->mus = TreeDPInfo::compress(t->mus, t->l->mus);
    }
    if (t->r) {
      t->sum = TreeDPInfo::compress(t->sum, t->r->sum);
      t->mus = TreeDPInfo::compress(t->r->mus, t->mus);
    }
  }

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

  NP expose(NP t) {
    NP rp = nullptr;
    for (NP cur = t; cur; cur = cur->p) {
      splay(cur);
      if (cur->r) {
        cur->light =
            splay_tree.insert(cur->light, TreeDPInfo::add_edge(cur->r->sum));
        cur->r->belong = cur->light;
      }
      cur->r = rp;
      if (cur->r) {
        push(cur->r);
        cur->light = splay_tree.erase(cur->r->belong);
      }
      update(cur);
      rp = cur;
    }
    splay(t);
    return rp;
  }

  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);
  }

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

  NP alloc(const Info &v) {
    NP t = new Node(v);
    update(t);
    return t;
  }

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

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

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

  void set_key(NP t, const Info &v) {
    expose(t);
    t->info = std::move(v);
    update(t);
  }

  const Path &query(NP u) {
    evert(u);
    return u->sum;
  }

  const Path &query_path(NP u) {
    expose(u);
    return u->sum;
  }

  const Path &query_path(NP u, NP v) {
    evert(u);
    return query_path(v);
  }

  Path query_subtree(NP u) {
    expose(u);
    NP l = u->l;
    u->l = nullptr;
    update(u);
    auto ret = u->sum;
    u->l = l;
    update(u);
    return ret;
  }

  Path query_subtree(NP r, NP u) {
    evert(r);
    return query_subtree(u);
  }
};

/*
struct TreeDPInfo {
  struct Point {};
  struct Path {};
  struct Info {};
  static Path vertex(const Info& u) {}
  static Path add_vertex(const Point& d, const Info& u) {}
  static Point add_edge(const Path& d) {}
  static Point rake(const Point& l, const Point& r) {}
  static Path compress(const Path& p, const Path& c) {}
};
*/
#line 2 "structure/dynamic-tree/diameter.hpp"

// verified: https://www.spoj.com/problems/QTREE4/
template <typename T>
struct Diameter {
  static constexpr T m_inf = numeric_limits<T>::min();
  struct Point {
    T dia, dep1, dep2;
  };
  struct Path {
    T dia, all, pref_max, suf_max;
  };
  struct Info {
    bool is_vertex;
    T w;
  };
  static Path vertex(const Info& u) { return add_vertex({m_inf, m_inf}, u); }
  static Path add_vertex(const Point& d, const Info& u) {
    Path p;
    p.dia = d.dia;
    p.pref_max = m_inf;
    p.all = u.w;
    if (d.dep1 != m_inf) {
      p.pref_max = d.dep1 + u.w;
      if (d.dep2 != m_inf) {
        p.dia = max(p.dia, d.dep1 + u.w + d.dep2);
      }
    }
    if (u.is_vertex) {
      p.pref_max = max(p.pref_max, u.w);
      p.dia = max(p.dia, p.pref_max);
    }
    p.suf_max = p.pref_max;
    return p;
  }
  static Point add_edge(const Path& d) { return {d.dia, d.pref_max, m_inf}; }
  static Point rake(Point l, const Point& r) {
    l.dia = max(l.dia, r.dia);
    if (l.dep1 < r.dep1) {
      l.dep2 = max(l.dep1, r.dep2);
      l.dep1 = r.dep1;
    } else {
      l.dep2 = max(l.dep2, r.dep1);
    }
    return l;
  }
  static Path compress(const Path& p, const Path& c) {
    Path t;
    t.dia = max(p.dia, c.dia);
    if (p.suf_max != m_inf and c.pref_max != m_inf) {
      t.dia = max(t.dia, p.suf_max + c.pref_max);
    }
    t.all = p.all + c.all;
    t.pref_max = p.pref_max;
    t.suf_max = c.suf_max;
    if (c.pref_max != m_inf) {
      t.pref_max = max(t.pref_max, p.all + c.pref_max);
    }
    if (p.suf_max != m_inf) {
      t.suf_max = max(t.suf_max, c.all + p.suf_max);
    }
    return t;
  }
};
#line 1 "structure/dynamic-tree/dynamic-tree-builder-for-edge.hpp"
template <template <typename> typename DynamicTree, typename TreeDPInfo>
struct DynamicTreeBuilderForEdge : DynamicTree<TreeDPInfo> {
 private:
  using DT = DynamicTree<TreeDPInfo>;
  using Info = typename TreeDPInfo::Info;

  int n, e_sz;
  vector<vector<pair<int, int> > > g;

 public:
  using DT::alloc;
  using DT::link;

  vector<typename DT::NP> vs, es;

  explicit DynamicTreeBuilderForEdge(int n)
      : n(n), g(n), vs(n), es(n), e_sz(0) {}

  void set_vertex(int u, const Info &info) {
    assert(0 <= u and u < n);
    vs[u] = this->alloc(info);
  }

  void add_edge(int u, int v, const Info &info, int id = -1) {
    assert(0 <= u and u < n);
    assert(0 <= v and v < n);
    assert(u != v);
    if (id == -1) id = e_sz++;
    assert(0 <= id and id < n);
    g[u].emplace_back(v, id);
    g[v].emplace_back(u, id);
    es[id] = alloc(info);
  }

  void build(int r = 0) {
    vector<pair<int, int> > que;
    que.reserve(n);
    que.emplace_back(r, -1);
    while (not que.empty()) {
      auto [u, p] = que.back();
      que.pop_back();
      for (auto &[v, id] : g[u]) {
        if (v == p) continue;
        que.emplace_back(v, u);
        link(es[id], vs[u]);
        link(vs[v], es[id]);
      }
    }
  }
};
#line 6 "test/verify/aoj-grl-5-a-3.test.cpp"

int main() {
  int N;
  cin >> N;
  DynamicTreeBuilderForEdge< TopTree, Diameter< int64 > > g(N);
  for(int i = 0; i < N; i++) {
    g.set_vertex(i, {true, 0});
  }
  for(int i = 1; i < N; i++) {
    int a, b;
    int64 w;
    cin >> a >> b >> w;
    g.add_edge(a, b, {false, w});
  }
  g.build();
  cout << g.query(g.vs[0]).dia << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_00.in	AC	5 ms	3 MB
g++	00_sample_01.in	AC	5 ms	3 MB
g++	01_small_00.in	AC	5 ms	3 MB
g++	01_small_01.in	AC	5 ms	3 MB
g++	01_small_02.in	AC	5 ms	3 MB
g++	01_small_03.in	AC	5 ms	3 MB
g++	02_medium_00.in	AC	5 ms	3 MB
g++	02_medium_01.in	AC	5 ms	3 MB
g++	02_medium_02.in	AC	5 ms	3 MB
g++	02_medium_03.in	AC	5 ms	4 MB
g++	03_corner_00.in	AC	5 ms	3 MB
g++	03_corner_01.in	AC	5 ms	3 MB
g++	04_binary_00.in	AC	5 ms	4 MB
g++	04_binary_01.in	AC	5 ms	4 MB
g++	04_binary_02.in	AC	5 ms	4 MB
g++	04_binary_03.in	AC	5 ms	4 MB
g++	05_linear_00.in	AC	5 ms	4 MB
g++	05_linear_01.in	AC	5 ms	4 MB
g++	05_linear_02.in	AC	6 ms	4 MB
g++	05_linear_03.in	AC	7 ms	5 MB
g++	06_rand_00.in	AC	5 ms	4 MB
g++	06_rand_01.in	AC	5 ms	4 MB
g++	06_rand_02.in	AC	9 ms	6 MB
g++	06_rand_03.in	AC	12 ms	7 MB
g++	07_large_00.in	AC	18 ms	12 MB
g++	07_large_01.in	AC	24 ms	15 MB
g++	07_large_02.in	AC	24 ms	15 MB
g++	07_large_03.in	AC	18 ms	12 MB
g++	08_maximum_00.in	AC	64 ms	39 MB
g++	08_maximum_01.in	AC	62 ms	39 MB
g++	08_maximum_02.in	AC	69 ms	43 MB
g++	08_maximum_03.in	AC	55 ms	38 MB
clang++	00_sample_00.in	AC	5 ms	3 MB
clang++	00_sample_01.in	AC	5 ms	3 MB
clang++	01_small_00.in	AC	5 ms	3 MB
clang++	01_small_01.in	AC	5 ms	3 MB
clang++	01_small_02.in	AC	5 ms	3 MB
clang++	01_small_03.in	AC	5 ms	3 MB
clang++	02_medium_00.in	AC	5 ms	3 MB
clang++	02_medium_01.in	AC	5 ms	3 MB
clang++	02_medium_02.in	AC	5 ms	3 MB
clang++	02_medium_03.in	AC	5 ms	4 MB
clang++	03_corner_00.in	AC	5 ms	3 MB
clang++	03_corner_01.in	AC	5 ms	3 MB
clang++	04_binary_00.in	AC	5 ms	3 MB
clang++	04_binary_01.in	AC	5 ms	3 MB
clang++	04_binary_02.in	AC	5 ms	4 MB
clang++	04_binary_03.in	AC	5 ms	4 MB
clang++	05_linear_00.in	AC	5 ms	4 MB
clang++	05_linear_01.in	AC	5 ms	4 MB
clang++	05_linear_02.in	AC	6 ms	4 MB
clang++	05_linear_03.in	AC	7 ms	5 MB
clang++	06_rand_00.in	AC	5 ms	4 MB
clang++	06_rand_01.in	AC	5 ms	4 MB
clang++	06_rand_02.in	AC	8 ms	5 MB
clang++	06_rand_03.in	AC	11 ms	7 MB
clang++	07_large_00.in	AC	18 ms	12 MB
clang++	07_large_01.in	AC	25 ms	15 MB
clang++	07_large_02.in	AC	27 ms	15 MB
clang++	07_large_03.in	AC	19 ms	12 MB
clang++	08_maximum_00.in	AC	67 ms	39 MB
clang++	08_maximum_01.in	AC	67 ms	39 MB
clang++	08_maximum_02.in	AC	74 ms	43 MB
clang++	08_maximum_03.in	AC	58 ms	38 MB

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