structure/dynamic-tree/vertex-set-tree-path-composite-sum.hpp

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• Last update: 2024-05-12 02:41:24+09:00
• Include: #include "structure/dynamic-tree/vertex-set-tree-path-composite-sum.hpp"

Depends on

• Link Cut Tree (for Subtree) (structure/dynamic-tree/link-cut-tree-for-subtree.hpp)

Verified with

• test/verify/yosupo-point-set-tree-path-composite-sum.test.cpp

Code

#include "link-cut-tree-for-subtree.hpp"

template <typename T>
struct VertexSetTreePathCompositeSum {
  struct Point {
    T s, x;
    static constexpr Point id() { return {0, 0}; }
    Point inv() const { return {-s, -x}; }
  };
  struct Path {
    T a, b, s, x;
  };
  struct Info {
    bool is_vertex;
    T x, y;
  };

  static Path add_vertex(const Point& d, const Info& u) {
    if (u.is_vertex) return {1, 0, d.s + u.x, d.x + 1};
    return {u.x, u.y, d.s * u.x + d.x * u.y, d.x};
  }
  static Point add_edge(const Path& d) { return {d.s, d.x}; }
  static Point rake(const Point& s, const Point& p) {
    return {s.s + p.s, s.x + p.x};
  }
  static Path compress(const Path& p, const Path& c) {
    return {p.a * c.a, p.a * c.b + p.b, p.s + p.a * c.s + p.b * c.x, p.x + c.x};
  }
};

#line 1 "structure/dynamic-tree/link-cut-tree-for-subtree.hpp"
template <typename TreeDPInfo>
struct LinkCutTreeForSubtree {
  using Point = typename TreeDPInfo::Point;
  using Path = typename TreeDPInfo::Path;
  using Info = typename TreeDPInfo::Info;

 private:
  struct Node {
    Node *l, *r, *p;
    Info info;
    Path sum, mus;

    Point point;
    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),
          point(Point::id()) {}
  };

 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:
  LinkCutTreeForSubtree() = 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::add_vertex(t->point, 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);
      if (cur->r) {
        cur->point =
            TreeDPInfo::rake(cur->point, TreeDPInfo::add_edge(cur->r->sum));
      }
      cur->r = rp;
      if (cur->r) {
        cur->point = TreeDPInfo::rake(cur->point,
                                      TreeDPInfo::add_edge(cur->r->sum).inv());
      }
      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 {
    static constexpr Point id() {}
    Point inv() const {}
  };
  struct Path {};
  struct Info {};
  static Path add_vertex(const Point& d, const Info& u) {}
  static Point add_edge(const Path& d) {}
  static Point rake(const Point& s, const Point& p) {}
  static Path compress(const Path& p, const Path& c) {}
};
*/
#line 2 "structure/dynamic-tree/vertex-set-tree-path-composite-sum.hpp"

template <typename T>
struct VertexSetTreePathCompositeSum {
  struct Point {
    T s, x;
    static constexpr Point id() { return {0, 0}; }
    Point inv() const { return {-s, -x}; }
  };
  struct Path {
    T a, b, s, x;
  };
  struct Info {
    bool is_vertex;
    T x, y;
  };

  static Path add_vertex(const Point& d, const Info& u) {
    if (u.is_vertex) return {1, 0, d.s + u.x, d.x + 1};
    return {u.x, u.y, d.s * u.x + d.x * u.y, d.x};
  }
  static Point add_edge(const Path& d) { return {d.s, d.x}; }
  static Point rake(const Point& s, const Point& p) {
    return {s.s + p.s, s.x + p.x};
  }
  static Path compress(const Path& p, const Path& c) {
    return {p.a * c.a, p.a * c.b + p.b, p.s + p.a * c.s + p.b * c.x, p.x + c.x};
  }
};

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