test/verify/yosupo-dynamic-tree-vertex-add-path-sum-2.test.cpp

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: https://judge.yosupo.jp/problem/dynamic_tree_vertex_add_path_sum

Depends on

• Link-Cut-Tree (structure/develop/link-cut-tree.hpp)
• Reversible-Splay-Tree(反転可能Splay木) (structure/develop/reversible-splay-tree.hpp)
• Splay-Tree-Base(Splay木) (structure/develop/splay-tree-base.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/dynamic_tree_vertex_add_path_sum

#include "../../template/template.hpp"

#include "../../structure/develop/splay-tree-base.hpp"
#include "../../structure/develop/reversible-splay-tree.hpp"
#include "../../structure/develop/link-cut-tree.hpp"

int main() {
  int N, Q;
  cin >> N >> Q;
  using LCT = LinkCutTree< RST< int64 > >;

  auto add = [](int64 a, int64 b) { return a + b; };
  auto s = [](int64 a) { return a; };
  LCT lct(add, s, 0);

  vector< int > A(N);
  cin >> A;

  vector< LCT::Node * > vs(N);
  for(int i = 0; i < N; i++) {
    vs[i] = lct.alloc(A[i]);
  }
  for(int i = 1; i < N; i++) {
    int a, b;
    cin >> a >> b;
    lct.evert(vs[a]);
    lct.link(vs[a], vs[b]);
  }

  while(Q--) {
    int T;
    cin >> T;
    if(T == 0) {
      int U, V, W, X;
      cin >> U >> V >> W >> X;
      lct.evert(vs[U]);
      lct.cut(vs[V]);
      lct.evert(vs[W]);
      lct.link(vs[W], vs[X]);
    } else if(T == 1) {
      int P, X;
      cin >> P >> X;
      lct.expose(vs[P]);
      vs[P]->key += X;
      lct.update(vs[P]);
    } else {
      int U, V;
      cin >> U >> V;
      lct.evert(vs[U]);
      lct.expose(vs[V]);
      cout << vs[V]->sum << "\n";
    }
  }
}

#line 1 "test/verify/yosupo-dynamic-tree-vertex-add-path-sum-2.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/dynamic_tree_vertex_add_path_sum

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

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(forward<F>(f)) {}

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

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-dynamic-tree-vertex-add-path-sum-2.test.cpp"

#line 1 "structure/develop/splay-tree-base.hpp"
/**
 * @brief Splay-Tree-Base(Splay木)
 */
template <typename Node>
struct SplayTreeBase {
 public:
  using NP = Node *;

  bool is_root(const NP &t) const {
    return !t->p || (t->p->l != t && t->p->r != t);
  }

  inline size_t count(const NP &t) const { return t ? t->sz : 0; }

  void splay(NP t) {
    push(t);
    while (!is_root(t)) {
      auto *q = t->p;
      if (!is_root(t)) {
        push(q), push(t);
        if (q->l == t)
          rotr(t);
        else
          rotl(t);
      } else {
        auto *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);
        }
      }
    }
  }

  NP erase(NP t) {
    splay(t);
    Node *x = t->l, *y = t->r;
    delete t;
    if (!x) {
      t = y;
      if (t) t->p = nullptr;
    } else if (!y) {
      t = x;
      t->p = nullptr;
    } else {
      x->p = nullptr;
      t = get_right(x);
      splay(t);
      t->r = y;
      y->p = t;
    }
    return t;
  }

  NP splay_front(NP t) {
    splay(t);
    while (t->l) t = t->l;
    splay(t);
    return t;
  }

  NP splay_back(NP t) {
    splay(t);
    while (t->r) t = t->r;
    splay(t);
    return t;
  }

  pair<NP, NP> split(NP t, int k) {
    if (!t) return {nullptr, nullptr};
    push(t);
    if (k <= count(t->l)) {
      auto x = split(t->l, k);
      t->l = x.second;
      t->p = nullptr;
      if (x.second) x.second->p = t;
      return {x.first, update(t)};
    } else {
      auto x = split(t->r, k - count(t->l) - 1);
      t->r = x.first;
      t->p = nullptr;
      if (x.first) x.first->p = t;
      return {update(t), x.second};
    }
  }

  template <typename... Args>
  NP merge(NP p, Args... args) {
    return merge(p, merge(args...));
  }

  NP merge(NP l, NP r) {
    if (!l && !r) return nullptr;
    if (!l) return splay(r), r;
    if (!r) return splay(l), l;
    splay(l), splay(r);
    l = splay_back(l);
    l->r = r;
    r->p = l;
    update(l);
    return l;
  }

  tuple<NP, NP, NP> split3(NP t, int a, int b) {
    splay(t);
    auto x = split(t, a);
    auto y = split(x.second, b - a);
    return make_tuple(x.first, y.first, y.second);
  }

  virtual void push(NP t) = 0;

  virtual Node *update(NP t) = 0;

 private:
  void rotr(NP t) {
    auto *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) {
    auto *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);
    }
  }

  NP build(int l, int r, const vector<NP> &v) {
    if (l + 1 >= r) return v[l];
    return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
  }

 protected:
  NP build_node(const vector<NP> &v) { return build(0, v.size(), v); }

  NP insert_node(NP t, int k, NP v) {
    splay(t);
    auto x = split(t, k);
    return merge(x.first, v, x.second);
  }

  NP erase_node(NP t, int k) {
    splay(t);
    auto x = split(t, k);
    auto y = split(x.second, 1);
    delete y.first;
    return merge(x.first, y.second);
  }
};
#line 1 "structure/develop/reversible-splay-tree.hpp"
/**
 * @brief Reversible-Splay-Tree(反転可能Splay木)
 */
template <typename Tp>
struct ReversibleSplayTreeNode {
  using T = Tp;
  ReversibleSplayTreeNode *l, *r, *p;
  T key, sum;
  bool rev;
  size_t sz;

  ReversibleSplayTreeNode() : ReversibleSplayTreeNode(Tp()) {}

  ReversibleSplayTreeNode(const T &key)
      : key(key),
        sum(key),
        rev(false),
        l(nullptr),
        r(nullptr),
        p(nullptr),
        sz(1) {}
};

template <typename Np>
struct ReversibleSplayTree : SplayTreeBase<Np> {
 public:
  using Node = Np;
  using T = typename Node::T;
  using F = function<T(T, T)>;
  using S = function<T(T)>;
  using super = SplayTreeBase<Node>;
  using NP = typename super::NP;

  explicit ReversibleSplayTree(const F &f, const S &s, const T &M1)
      : f(f), s(s), M1(M1) {}

  using super::build_node;
  using super::count;
  using super::insert_node;
  using super::merge;
  using super::splay;
  using super::split;

  inline const T &sum(const NP t) { return t ? t->sum : M1; }

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

  T query(NP &t, int a, int b) {
    splay(t);
    auto x = split(t, a);
    auto y = split(x.second, b - a);
    auto ret = sum(y.first);
    t = merge(x.first, y.first, y.second);
    return ret;
  }

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

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

  NP update(NP t) override {
    t->sz = 1;
    t->sum = t->key;
    if (t->l) t->sz += t->l->sz, t->sum = f(t->l->sum, t->sum);
    if (t->r) t->sz += t->r->sz, t->sum = f(t->sum, t->r->sum);
    return t;
  }

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

  NP insert(NP t, int k, const T &x) { return insert_node(t, k, alloc(x)); }

  NP set_element(NP t, int k, const T &x) {
    splay(t);
    return imp_set_element(t, k, x);
  }

  pair<NP, NP> split_lower_bound(NP t, const T &key) {
    if (!t) return {nullptr, nullptr};
    push(t);
    if (key <= t->key) {
      auto x = split_lower_bound(t->l, key);
      t->l = x.second;
      t->p = nullptr;
      if (x.second) x.second->p = t;
      return {x.first, update(t)};
    } else {
      auto x = split_lower_bound(t->r, key);
      t->r = x.first;
      t->p = nullptr;
      if (x.first) x.first->p = t;
      return {update(t), x.second};
    }
  }

 private:
  const T M1;
  const F f;
  const S s;

  NP imp_set_element(NP t, int k, const T &x) {
    push(t);
    if (k < count(t->l)) {
      return imp_set_element(t->l, k, x);
    } else if (k == count(t->l)) {
      t->key = x;
      splay(t);
      return t;
    } else {
      return imp_set_element(t->r, k - count(t->l) - 1, x);
    }
  }
};

template <typename T>
using RST = ReversibleSplayTree<ReversibleSplayTreeNode<T> >;
#line 1 "structure/develop/link-cut-tree.hpp"
/**
 * @brief Link-Cut-Tree
 */
template <typename STp>
struct LinkCutTree : STp {
  using ST = STp;
  using ST::ST;
  using Node = typename ST::Node;

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

  void link(Node *child, Node *parent) {
    expose(child);
    expose(parent);
    child->p = parent;
    parent->r = child;
    this->update(parent);
  }

  void cut(Node *child) {
    expose(child);
    auto *parent = child->l;
    child->l = nullptr;
    parent->p = nullptr;
    this->update(child);
  }

  void evert(Node *t) {
    expose(t);
    this->toggle(t);
    this->push(t);
  }

  Node *lca(Node *u, Node *v) {
    if (get_root(u) != get_root(v)) return nullptr;
    expose(u);
    return expose(v);
  }

  Node *get_kth(Node *x, int k) {
    expose(x);
    while (x) {
      this->push(x);
      if (x->r && x->r->sz > k) {
        x = x->r;
      } else {
        if (x->r) k -= x->r->sz;
        if (k == 0) return x;
        k -= 1;
        x = x->l;
      }
    }
    return nullptr;
  }

  Node *get_root(Node *x) {
    expose(x);
    while (x->l) {
      this->push(x);
      x = x->l;
    }
    return x;
  }
};
#line 8 "test/verify/yosupo-dynamic-tree-vertex-add-path-sum-2.test.cpp"

int main() {
  int N, Q;
  cin >> N >> Q;
  using LCT = LinkCutTree< RST< int64 > >;

  auto add = [](int64 a, int64 b) { return a + b; };
  auto s = [](int64 a) { return a; };
  LCT lct(add, s, 0);

  vector< int > A(N);
  cin >> A;

  vector< LCT::Node * > vs(N);
  for(int i = 0; i < N; i++) {
    vs[i] = lct.alloc(A[i]);
  }
  for(int i = 1; i < N; i++) {
    int a, b;
    cin >> a >> b;
    lct.evert(vs[a]);
    lct.link(vs[a], vs[b]);
  }

  while(Q--) {
    int T;
    cin >> T;
    if(T == 0) {
      int U, V, W, X;
      cin >> U >> V >> W >> X;
      lct.evert(vs[U]);
      lct.cut(vs[V]);
      lct.evert(vs[W]);
      lct.link(vs[W], vs[X]);
    } else if(T == 1) {
      int P, X;
      cin >> P >> X;
      lct.expose(vs[P]);
      vs[P]->key += X;
      lct.update(vs[P]);
    } else {
      int U, V;
      cin >> U >> V;
      lct.evert(vs[U]);
      lct.expose(vs[V]);
      cout << vs[V]->sum << "\n";
    }
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	6 ms	4 MB
g++	max_random_00	AC	393 ms	18 MB
g++	max_random_01	AC	381 ms	18 MB
g++	max_random_02	AC	413 ms	18 MB
g++	random_00	AC	249 ms	13 MB
g++	random_01	AC	270 ms	15 MB
g++	random_02	AC	157 ms	7 MB
g++	random_03	AC	175 ms	16 MB
g++	random_04	AC	96 ms	5 MB
g++	small_00	AC	6 ms	4 MB
g++	small_01	AC	6 ms	4 MB
g++	small_02	AC	6 ms	4 MB
clang++	example_00	AC	6 ms	4 MB
clang++	max_random_00	AC	467 ms	18 MB
clang++	max_random_01	AC	427 ms	18 MB
clang++	max_random_02	AC	460 ms	18 MB
clang++	random_00	AC	272 ms	13 MB
clang++	random_01	AC	307 ms	15 MB
clang++	random_02	AC	168 ms	7 MB
clang++	random_03	AC	176 ms	16 MB
clang++	random_04	AC	105 ms	5 MB
clang++	small_00	AC	6 ms	4 MB
clang++	small_01	AC	6 ms	4 MB
clang++	small_02	AC	6 ms	4 MB

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