test/verify/yosupo-dynamic-tree-vertex-set-path-composite-4.test.cpp

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• Last update: 2024-07-28 19:56:12+09:00
• Problem: https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite

Depends on

• math/combinatorics/montgomery-mod-int.hpp
• Dynamic Tree Builder (for Vertex) (structure/dynamic-tree/dynamic-tree-builder-for-vertex.hpp)
• Link Cut Tree (structure/dynamic-tree/link-cut-tree.hpp)
• structure/dynamic-tree/vertex-set-path-composite.hpp
• template/template.hpp

Code

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

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

#include "../../math/combinatorics/montgomery-mod-int.hpp"
#include "../../structure/dynamic-tree/vertex-set-path-composite.hpp"
#include "../../structure/dynamic-tree/dynamic-tree-builder-for-vertex.hpp"

using mint = modint998244353;

int main() {
  int N, Q;
  cin >> N >> Q;
  DynamicTreeBuilderForVertex< LinkCutTree, VertexSetPathComposite< mint > > g(N);
  for(int i = 0; i < N; i++) {
    mint a, b;
    cin >> a >> b;
    g.set_vertex(i, {a, b});
  }
  for(int i = 1; i < N; i++) {
    int a, b;
    cin >> a >> b;
    g.add_edge(a, b);
  }
  g.build();
  while(Q--) {
    int t;
    cin >> t;
    if(t == 0) {
      int u, v, w, x;
      cin >> u >> v >> w >> x;
      g.evert(g.vs[u]);
      g.cut(g.vs[v]);
      g.evert(g.vs[w]);
      g.link(g.vs[w], g.vs[x]);
    } else if(t == 1) {
      int p;
      mint c, d;
      cin >> p >> c >> d;
      g.set_key(g.vs[p], {c, d});
    } else {
      int u, v;
      mint x;
      cin >> u >> v >> x;
      auto sum = g.query_path(g.vs[u], g.vs[v]);
      cout << sum.a * x + sum.b << "\n";
    }
  }
}

#line 1 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite-4.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>
#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 4 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite-4.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 1 "structure/dynamic-tree/link-cut-tree.hpp"
template <typename TreeDPInfo>
struct LinkCutTree {
  using Path = typename TreeDPInfo::Path;
  using Info = typename TreeDPInfo::Info;

 private:
  struct Node {
    Node *l, *r, *p;

    Info info;

    Path sum, mus;

    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) {}
  };

 public:
  using NP = Node *;

 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:
  LinkCutTree() = default;

  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 = 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);
    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);
      cur->r = rp;
      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_path(NP u) {
    expose(u);
    return u->sum;
  }

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

  template <typename C>
  pair<NP, Path> find_first(NP u, const C &check) {
    expose(u);
    Path sum = TreeDPInfo::vertex(u->info);
    if (check(sum)) return {u, sum};
    u = u->l;
    while (u) {
      push(u);
      if (u->r) {
        Path nxt = TreeDPInfo::compress(u->r->sum, sum);
        if (check(nxt)) {
          u = u->r;
          continue;
        }
        sum = nxt;
      }
      Path nxt = TreeDPInfo::compress(TreeDPInfo::vertex(u->info), sum);
      if (check(nxt)) {
        splay(u);
        return {u, nxt};
      }
      sum = nxt;
      u = u->l;
    }
    return {nullptr, sum};
  }
};

/*
struct TreeDPInfo {
  struct Path {};
  struct Info {};
  static Path vertex(const Info& u) {}
  static Path compress(const Path& p, const Path& c) {}
};
*/
#line 2 "structure/dynamic-tree/vertex-set-path-composite.hpp"

template <typename T>
struct VertexSetPathComposite {
  struct Path {
    T a, b;
  };
  struct Info {
    T x, y;
  };

  static Path vertex(const Info& u) { return {u.x, u.y}; }
  static Path compress(const Path& p, const Path& c) {
    return {p.a * c.a, p.b * c.a + c.b};
  }
};
#line 1 "structure/dynamic-tree/dynamic-tree-builder-for-vertex.hpp"
template <template <typename> typename DynamicTree, typename TreeDPInfo>
struct DynamicTreeBuilderForVertex : DynamicTree<TreeDPInfo> {
 private:
  using DT = DynamicTree<TreeDPInfo>;
  using Info = typename TreeDPInfo::Info;

  int n;
  vector<vector<int> > g;

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

  vector<typename DT::NP> vs;

  explicit DynamicTreeBuilderForVertex(int n) : n(n), g(n), vs(n) {}

  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) {
    assert(0 <= u and u < n);
    assert(0 <= v and v < n);
    assert(u != v);
    g[u].emplace_back(v);
    g[v].emplace_back(u);
  }

  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 : g[u]) {
        if (v == p) continue;
        que.emplace_back(v, u);
        link(vs[v], vs[u]);
      }
    }
  }
};
#line 8 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite-4.test.cpp"

using mint = modint998244353;

int main() {
  int N, Q;
  cin >> N >> Q;
  DynamicTreeBuilderForVertex< LinkCutTree, VertexSetPathComposite< mint > > g(N);
  for(int i = 0; i < N; i++) {
    mint a, b;
    cin >> a >> b;
    g.set_vertex(i, {a, b});
  }
  for(int i = 1; i < N; i++) {
    int a, b;
    cin >> a >> b;
    g.add_edge(a, b);
  }
  g.build();
  while(Q--) {
    int t;
    cin >> t;
    if(t == 0) {
      int u, v, w, x;
      cin >> u >> v >> w >> x;
      g.evert(g.vs[u]);
      g.cut(g.vs[v]);
      g.evert(g.vs[w]);
      g.link(g.vs[w], g.vs[x]);
    } else if(t == 1) {
      int p;
      mint c, d;
      cin >> p >> c >> d;
      g.set_key(g.vs[p], {c, d});
    } else {
      int u, v;
      mint x;
      cin >> u >> v >> x;
      auto sum = g.query_path(g.vs[u], g.vs[v]);
      cout << sum.a * x + sum.b << "\n";
    }
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	5 ms	3 MB
g++	example_01	AC	5 ms	3 MB
g++	max_random_00	AC	399 ms	28 MB
g++	max_random_01	AC	432 ms	29 MB
g++	max_random_02	AC	390 ms	29 MB
g++	medium_00	AC	6 ms	4 MB
g++	medium_01	AC	5 ms	4 MB
g++	medium_02	AC	5 ms	3 MB
g++	medium_03	AC	5 ms	4 MB
g++	medium_04	AC	6 ms	4 MB
g++	random_00	AC	259 ms	19 MB
g++	random_01	AC	265 ms	22 MB
g++	random_02	AC	154 ms	10 MB
g++	random_03	AC	144 ms	24 MB
g++	random_04	AC	100 ms	5 MB
g++	small_00	AC	5 ms	3 MB
g++	small_01	AC	5 ms	3 MB
g++	small_02	AC	5 ms	3 MB
g++	small_03	AC	5 ms	3 MB
g++	small_04	AC	5 ms	3 MB
clang++	example_00	AC	5 ms	3 MB
clang++	example_01	AC	5 ms	3 MB
clang++	max_random_00	AC	407 ms	29 MB
clang++	max_random_01	AC	432 ms	29 MB
clang++	max_random_02	AC	472 ms	29 MB
clang++	medium_00	AC	6 ms	4 MB
clang++	medium_01	AC	6 ms	4 MB
clang++	medium_02	AC	5 ms	3 MB
clang++	medium_03	AC	5 ms	4 MB
clang++	medium_04	AC	6 ms	3 MB
clang++	random_00	AC	292 ms	19 MB
clang++	random_01	AC	302 ms	22 MB
clang++	random_02	AC	167 ms	10 MB
clang++	random_03	AC	134 ms	24 MB
clang++	random_04	AC	108 ms	5 MB
clang++	small_00	AC	5 ms	3 MB
clang++	small_01	AC	5 ms	3 MB
clang++	small_02	AC	5 ms	3 MB
clang++	small_03	AC	6 ms	3 MB
clang++	small_04	AC	5 ms	3 MB

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