test/verify/yosupo-dynamic-tree-vertex-set-path-composite.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_set_path_composite

Depends on

• math/combinatorics/montgomery-mod-int.hpp
• Link Cut Tree (structure/lct/link-cut-tree.hpp)
• template/template.hpp

Code

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

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

#include "../../structure/lct/link-cut-tree.hpp"

#include "../../math/combinatorics/montgomery-mod-int.hpp"

using mint = modint998244353;

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

  using pi = pair< mint, mint >;
  using pii = pair< pi, pi >;
  auto f = [](const pi &x, const pi &y) { return pi(x.first * y.first, x.second * y.first + y.second); };
  auto ff = [&](const pii &a, const pii &b) { return pii(f(a.first, b.first), f(b.second, a.second)); };
  auto flip = [&](const pii &a) { return pii(a.second, a.first); };
  auto lct = get_link_cut_tree< pii >(ff, flip);

  vector< decltype(lct)::NP > vs(N);
  for(int i = 0; i < N; i++) {
    mint x, y;
    cin >> x >> y;
    vs[i] = lct.alloc(pii(pi(x, y), pi(x, y)));
  }
  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;
      mint a, b;
      cin >> P >> a >> b;
      lct.set_key(vs[P], pii(pi(a, b), pi(a, b)));
    } else {
      int U, V;
      mint X;
      cin >> U >> V >> X;
      auto ret = lct.query(vs[U], vs[V]).first;
      cout << ret.first * X + ret.second << "\n";
    }
  }
}

#line 1 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite

#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-set-path-composite.test.cpp"

#line 1 "structure/lct/link-cut-tree.hpp"
/**
 * @brief Link Cut Tree
 *
 */
template <typename T, typename F, typename S>
struct LinkCutTree {
 private:
  F f;
  S s;

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

    explicit Node(const T &v)
        : key(v),
          sum(v),
          sz(1),
          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->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 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(const F &f, const S &s) : f(f), s(s) {}

  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);
  }

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

  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);
  }
};

template <typename T, typename F, typename S>
LinkCutTree<T, F, S> get_link_cut_tree(const F &f, const S &s) {
  return {f, s};
}
#line 6 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite.test.cpp"

#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

 public:
  MontgomeryModInt() : x{} {}

  MontgomeryModInt(const i64 &a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint &operator+=(const mint &p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator-=(const mint &p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator*=(const mint &p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint &operator/=(const mint &p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint &p) const { return mint(*this) += p; }

  mint operator-(const mint &p) const { return mint(*this) -= p; }

  mint operator*(const mint &p) const { return mint(*this) *= p; }

  mint operator/(const mint &p) const { return mint(*this) /= p; }

  bool operator==(const mint &p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint &p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const { return pow(mod() - 2); }

  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.val();
  }

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 8 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite.test.cpp"

using mint = modint998244353;

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

  using pi = pair< mint, mint >;
  using pii = pair< pi, pi >;
  auto f = [](const pi &x, const pi &y) { return pi(x.first * y.first, x.second * y.first + y.second); };
  auto ff = [&](const pii &a, const pii &b) { return pii(f(a.first, b.first), f(b.second, a.second)); };
  auto flip = [&](const pii &a) { return pii(a.second, a.first); };
  auto lct = get_link_cut_tree< pii >(ff, flip);

  vector< decltype(lct)::NP > vs(N);
  for(int i = 0; i < N; i++) {
    mint x, y;
    cin >> x >> y;
    vs[i] = lct.alloc(pii(pi(x, y), pi(x, y)));
  }
  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;
      mint a, b;
      cin >> P >> a >> b;
      lct.set_key(vs[P], pii(pi(a, b), pi(a, b)));
    } else {
      int U, V;
      mint X;
      cin >> U >> V >> X;
      auto ret = lct.query(vs[U], vs[V]).first;
      cout << ret.first * X + ret.second << "\n";
    }
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	8 ms	4 MB
g++	example_01	AC	8 ms	4 MB
g++	max_random_00	AC	860 ms	21 MB
g++	max_random_01	AC	832 ms	21 MB
g++	max_random_02	AC	858 ms	21 MB
g++	medium_00	AC	9 ms	4 MB
g++	medium_01	AC	8 ms	4 MB
g++	medium_02	AC	8 ms	4 MB
g++	medium_03	AC	8 ms	4 MB
g++	medium_04	AC	9 ms	4 MB
g++	random_00	AC	544 ms	14 MB
g++	random_01	AC	588 ms	16 MB
g++	random_02	AC	282 ms	8 MB
g++	random_03	AC	370 ms	18 MB
g++	random_04	AC	140 ms	5 MB
g++	small_00	AC	8 ms	4 MB
g++	small_01	AC	8 ms	4 MB
g++	small_02	AC	8 ms	4 MB
g++	small_03	AC	9 ms	4 MB
g++	small_04	AC	8 ms	4 MB
clang++	example_00	AC	9 ms	4 MB
clang++	example_01	AC	8 ms	4 MB
clang++	max_random_00	AC	823 ms	21 MB
clang++	max_random_01	AC	888 ms	21 MB
clang++	max_random_02	AC	874 ms	21 MB
clang++	medium_00	AC	9 ms	4 MB
clang++	medium_01	AC	9 ms	4 MB
clang++	medium_02	AC	9 ms	4 MB
clang++	medium_03	AC	8 ms	4 MB
clang++	medium_04	AC	9 ms	4 MB
clang++	random_00	AC	514 ms	14 MB
clang++	random_01	AC	639 ms	16 MB
clang++	random_02	AC	270 ms	8 MB
clang++	random_03	AC	381 ms	18 MB
clang++	random_04	AC	141 ms	5 MB
clang++	small_00	AC	8 ms	4 MB
clang++	small_01	AC	8 ms	4 MB
clang++	small_02	AC	8 ms	4 MB
clang++	small_03	AC	8 ms	4 MB
clang++	small_04	AC	8 ms	4 MB

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