convex/dynamic_lichao.hpp

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• Last update: 2025-09-16 20:23:00+09:00
• Include: #include "convex/dynamic_lichao.hpp"
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Depends on

• ds/node_pool.hpp

Verified with

• test/2_library_checker/data_structure/line_add_get_min_lichao.test.cpp
• test/2_library_checker/data_structure/segment_add_get_min.test.cpp

Code

#include "ds/node_pool.hpp"

/*
struct F {
  using value_type = ll;  // operator() の戻り値
  int a;
  ll b;
  ll operator()(ll x) { return a * x + b; }
};
*/

// 直線追加かつ非永続なら空間 Q でよい。
// 関数は ll -> T。[L, R) 上 f が overflow しないように注意。
// evaluate を書き変えると、totally monotone な関数群にも使える
template <typename FUNC, bool PERSISTENT, int NODES, bool MINIMIZE>
struct Dynamic_LiChao_Tree {
  using T = typename FUNC::value_type;
  vc<FUNC> funcs;

  static inline T evaluate(FUNC &f, ll x) { return f(x); }

  struct Node {
    int fid;
    Node *l, *r;
  };
  Node_Pool<Node> pool;
  ll L, R;

  using np = Node *;

  Dynamic_LiChao_Tree(ll L, ll R) : L(L), R(R) {}

  void reset() { funcs.clear(), pool.reset(); }

  np new_root() { return nullptr; }

  np new_node() {
    np c = pool.create();
    c->fid = -1, c->l = c->r = nullptr;
    return c;
  }

  np chmin_line(np root, FUNC f) {
    static_assert(MINIMIZE);
    int fid = len(funcs);
    funcs.eb(f);
    if (!root) root = new_node();
    return add_line_rec(root, fid, L, R);
  }
  np chmax_line(np root, FUNC f) {
    static_assert(!MINIMIZE);
    int fid = len(funcs);
    funcs.eb(f);
    if (!root) root = new_node();
    return add_line_rec(root, fid, L, R);
  }

  // [xl, xr)
  np chmin_segment(np root, ll xl, ll xr, FUNC f) {
    static_assert(MINIMIZE);
    int fid = len(funcs);
    funcs.eb(f);
    if (!root) root = new_node();
    return add_segment_rec(root, xl, xr, fid, L, R);
  }
  // [xl, xr)
  np chmax_segment(np root, ll xl, ll xr, FUNC f) {
    static_assert(!MINIMIZE);
    int fid = len(funcs);
    funcs.eb(f);
    if (!root) root = new_node();
    return add_segment_rec(root, xl, xr, fid, L, R);
  }

  // (値・関数番号)
  pair<T, int> query(np root, ll x) {
    assert(L <= x && x < R);
    if (!root) {
      if (MINIMIZE) return {infty<T>, -1};
      if (!MINIMIZE) return {-infty<T>, -1};
    }
    return query_rec(root, x, L, R);
  }

 private:
  np clone(np c) {
    if (!c || !PERSISTENT) return c;
    return pool.lone(c);
  }

  inline T evaluate_inner(int fid, ll x) {
    if (fid == -1) {
      return (MINIMIZE ? infty<T> : -infty<T>);
    };
    return evaluate(funcs[fid], x);
  }

  np add_segment_rec(np c, ll xl, ll xr, int fid, ll node_l, ll node_r) {
    chmax(xl, node_l), chmin(xr, node_r);
    if (xl >= xr) return c;
    if (node_l < xl || xr < node_r) {
      c = clone(c);
      ll node_m = (node_l + node_r) / 2;
      if (!c->l) c->l = new_node();
      if (!c->r) c->r = new_node();
      c->l = add_segment_rec(c->l, xl, xr, fid, node_l, node_m);
      c->r = add_segment_rec(c->r, xl, xr, fid, node_m, node_r);
      return c;
    }
    return add_line_rec(c, fid, node_l, node_r);
  }

  np add_line_rec(np c, int fid, ll node_l, ll node_r) {
    int gid = c->fid;
    T fl = evaluate_inner(fid, node_l), fr = evaluate_inner(fid, node_r - 1);
    T gl = evaluate_inner(gid, node_l), gr = evaluate_inner(gid, node_r - 1);
    bool bl = (MINIMIZE ? fl < gl : fl > gl);
    bool br = (MINIMIZE ? fr < gr : fr > gr);
    if (bl && br) {
      c = clone(c);
      c->fid = fid;
      return c;
    }
    if (!bl && !br) {
      return c;
    }

    c = clone(c);
    ll node_m = (node_l + node_r) / 2;
    auto fm = evaluate_inner(fid, node_m), gm = evaluate_inner(gid, node_m);
    bool bm = (MINIMIZE ? fm < gm : fm > gm);
    if (bm) {
      c->fid = fid;
      if (bl) {
        if (!c->r) c->r = new_node();
        c->r = add_line_rec(c->r, gid, node_m, node_r);
      } else {
        if (!c->l) c->l = new_node();
        c->l = add_line_rec(c->l, gid, node_l, node_m);
      }
    }
    if (!bm) {
      if (!bl) {
        if (!c->r) c->r = new_node();
        c->r = add_line_rec(c->r, fid, node_m, node_r);
      } else {
        if (!c->l) c->l = new_node();
        c->l = add_line_rec(c->l, fid, node_l, node_m);
      }
    }
    return c;
  }

  pair<T, int> query_rec(np c, ll x, ll node_l, ll node_r) {
    int fid = c->fid;
    pair<T, int> res = {evaluate_inner(fid, x), fid};
    ll node_m = (node_l + node_r) / 2;
    if (x < node_m && c->l) {
      pair<T, int> res1 = query_rec(c->l, x, node_l, node_m);
      res = (MINIMIZE ? min(res, res1) : max(res, res1));
    }
    if (x >= node_m && c->r) {
      pair<T, int> res1 = query_rec(c->r, x, node_m, node_r);
      res = (MINIMIZE ? min(res, res1) : max(res, res1));
    }
    return res;
  }
};

#line 1 "ds/node_pool.hpp"
template <class Node>
struct Node_Pool {
  struct Slot {
    union alignas(Node) {
      Slot* next;
      unsigned char storage[sizeof(Node)];
    };
  };
  using np = Node*;

  static constexpr int CHUNK_SIZE = 1 << 16;

  vc<unique_ptr<Slot[]>> chunks;
  Slot* cur = nullptr;
  int cur_used = 0;
  Slot* free_head = nullptr;

  Node_Pool() { alloc_chunk(); }

  template <class... Args>
  np create(Args&&... args) {
    Slot* s = new_slot();
    return ::new (s) Node(forward<Args>(args)...);
  }

  np clone(const np x) {
    assert(x);
    Slot* s = new_slot();
    return ::new (s) Node(*x);  // コピーコンストラクタ呼び出し
  }

  void destroy(np x) {
    if (!x) return;
    x->~Node();
    auto s = reinterpret_cast<Slot*>(x);
    s->next = free_head;
    free_head = s;
  }

  void reset() {
    free_head = nullptr;
    if (!chunks.empty()) {
      cur = chunks[0].get();
      cur_used = 0;
    }
  }

 private:
  void alloc_chunk() {
    chunks.emplace_back(make_unique<Slot[]>(CHUNK_SIZE));
    cur = chunks.back().get();
    cur_used = 0;
  }

  Slot* new_slot() {
    if (free_head) {
      Slot* s = free_head;
      free_head = free_head->next;
      return s;
    }
    if (cur_used == CHUNK_SIZE) alloc_chunk();
    return &cur[cur_used++];
  }
};
#line 2 "convex/dynamic_lichao.hpp"

/*
struct F {
  using value_type = ll;  // operator() の戻り値
  int a;
  ll b;
  ll operator()(ll x) { return a * x + b; }
};
*/

// 直線追加かつ非永続なら空間 Q でよい。
// 関数は ll -> T。[L, R) 上 f が overflow しないように注意。
// evaluate を書き変えると、totally monotone な関数群にも使える
template <typename FUNC, bool PERSISTENT, int NODES, bool MINIMIZE>
struct Dynamic_LiChao_Tree {
  using T = typename FUNC::value_type;
  vc<FUNC> funcs;

  static inline T evaluate(FUNC &f, ll x) { return f(x); }

  struct Node {
    int fid;
    Node *l, *r;
  };
  Node_Pool<Node> pool;
  ll L, R;

  using np = Node *;

  Dynamic_LiChao_Tree(ll L, ll R) : L(L), R(R) {}

  void reset() { funcs.clear(), pool.reset(); }

  np new_root() { return nullptr; }

  np new_node() {
    np c = pool.create();
    c->fid = -1, c->l = c->r = nullptr;
    return c;
  }

  np chmin_line(np root, FUNC f) {
    static_assert(MINIMIZE);
    int fid = len(funcs);
    funcs.eb(f);
    if (!root) root = new_node();
    return add_line_rec(root, fid, L, R);
  }
  np chmax_line(np root, FUNC f) {
    static_assert(!MINIMIZE);
    int fid = len(funcs);
    funcs.eb(f);
    if (!root) root = new_node();
    return add_line_rec(root, fid, L, R);
  }

  // [xl, xr)
  np chmin_segment(np root, ll xl, ll xr, FUNC f) {
    static_assert(MINIMIZE);
    int fid = len(funcs);
    funcs.eb(f);
    if (!root) root = new_node();
    return add_segment_rec(root, xl, xr, fid, L, R);
  }
  // [xl, xr)
  np chmax_segment(np root, ll xl, ll xr, FUNC f) {
    static_assert(!MINIMIZE);
    int fid = len(funcs);
    funcs.eb(f);
    if (!root) root = new_node();
    return add_segment_rec(root, xl, xr, fid, L, R);
  }

  // (値・関数番号)
  pair<T, int> query(np root, ll x) {
    assert(L <= x && x < R);
    if (!root) {
      if (MINIMIZE) return {infty<T>, -1};
      if (!MINIMIZE) return {-infty<T>, -1};
    }
    return query_rec(root, x, L, R);
  }

 private:
  np clone(np c) {
    if (!c || !PERSISTENT) return c;
    return pool.lone(c);
  }

  inline T evaluate_inner(int fid, ll x) {
    if (fid == -1) {
      return (MINIMIZE ? infty<T> : -infty<T>);
    };
    return evaluate(funcs[fid], x);
  }

  np add_segment_rec(np c, ll xl, ll xr, int fid, ll node_l, ll node_r) {
    chmax(xl, node_l), chmin(xr, node_r);
    if (xl >= xr) return c;
    if (node_l < xl || xr < node_r) {
      c = clone(c);
      ll node_m = (node_l + node_r) / 2;
      if (!c->l) c->l = new_node();
      if (!c->r) c->r = new_node();
      c->l = add_segment_rec(c->l, xl, xr, fid, node_l, node_m);
      c->r = add_segment_rec(c->r, xl, xr, fid, node_m, node_r);
      return c;
    }
    return add_line_rec(c, fid, node_l, node_r);
  }

  np add_line_rec(np c, int fid, ll node_l, ll node_r) {
    int gid = c->fid;
    T fl = evaluate_inner(fid, node_l), fr = evaluate_inner(fid, node_r - 1);
    T gl = evaluate_inner(gid, node_l), gr = evaluate_inner(gid, node_r - 1);
    bool bl = (MINIMIZE ? fl < gl : fl > gl);
    bool br = (MINIMIZE ? fr < gr : fr > gr);
    if (bl && br) {
      c = clone(c);
      c->fid = fid;
      return c;
    }
    if (!bl && !br) {
      return c;
    }

    c = clone(c);
    ll node_m = (node_l + node_r) / 2;
    auto fm = evaluate_inner(fid, node_m), gm = evaluate_inner(gid, node_m);
    bool bm = (MINIMIZE ? fm < gm : fm > gm);
    if (bm) {
      c->fid = fid;
      if (bl) {
        if (!c->r) c->r = new_node();
        c->r = add_line_rec(c->r, gid, node_m, node_r);
      } else {
        if (!c->l) c->l = new_node();
        c->l = add_line_rec(c->l, gid, node_l, node_m);
      }
    }
    if (!bm) {
      if (!bl) {
        if (!c->r) c->r = new_node();
        c->r = add_line_rec(c->r, fid, node_m, node_r);
      } else {
        if (!c->l) c->l = new_node();
        c->l = add_line_rec(c->l, fid, node_l, node_m);
      }
    }
    return c;
  }

  pair<T, int> query_rec(np c, ll x, ll node_l, ll node_r) {
    int fid = c->fid;
    pair<T, int> res = {evaluate_inner(fid, x), fid};
    ll node_m = (node_l + node_r) / 2;
    if (x < node_m && c->l) {
      pair<T, int> res1 = query_rec(c->l, x, node_l, node_m);
      res = (MINIMIZE ? min(res, res1) : max(res, res1));
    }
    if (x >= node_m && c->r) {
      pair<T, int> res1 = query_rec(c->r, x, node_m, node_r);
      res = (MINIMIZE ? min(res, res1) : max(res, res1));
    }
    return res;
  }
};

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