Tifa's CP Library

:heavy_check_mark: link_cut_tree (src/code/ds/link_cut_tree.hpp)

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#ifndef TIFALIBS_DS_LINK_CUT_TREE
#define TIFALIBS_DS_LINK_CUT_TREE

#include "../util/util.hpp"

namespace tifa_libs::ds {

template <class T, auto op, auto inv_op>
requires requires(T x, T y) {
  { op(x, y) } -> std::same_as<T>;
  { inv_op(x, y) } -> std::same_as<T>;
}
class link_cut_tree {
  // function in private: index of node should start from 1
  // wait for updating
  struct YYZ {
    T w, val;
    T s, sv;  // requirement of maintaining subtree
    u32 fa, rev;
    arr<u32, 2> son;
  };

 public:
  vec<YYZ> tr;

  constexpr link_cut_tree(u32 n, vec<T> A) : tr(n + 1) {
    for (u32 i = 1; i <= n; ++i) tr[i].val = A[i - 1];
  }

  constexpr void access(u32 x) { access_(x + 1); }
  constexpr void makeroot(u32 x) { makeroot_(x + 1); }
  constexpr u32 findroot(u32 x) { return findroot_(x + 1) - 1; }
  constexpr void split(u32 x, u32 y) { split_(x + 1, y + 1); }
  constexpr bool con(u32 x, u32 y) { return con_(x + 1, y + 1); }
  constexpr bool link(u32 x, u32 y) { return link_(x + 1, y + 1); }
  constexpr bool cut(u32 x, u32 y) { return cut_(x + 1, y + 1); }
  constexpr void node_update(u32 x, T k) {
    x += 1;
    access_(x);  // requirement of maintaining subtree
    splay_(x), tr[x].val = k, update_(x);
  }
  constexpr void node_add(u32 x, T k) {
    x += 1;
    access_(x);  // requirement of maintaining subtree
    splay_(x), tr[x].val = op(tr[x].val, k), update_(x);
  }
  constexpr u32 lca(u32 u, u32 v, u32 root = 0) {
    if (u == v) return u;
    ++u, ++v, ++root;
    makeroot_(root);
    access_(u);
    u32 ret = access_(v) - 1;
    return tr[u].fa ? ret : -1u;
  }
  constexpr ptt<T> query_subtree(u32 x, u32 y) {
    ++x, ++y;
    split_(x, y);
    return {op(tr[x].sv, tr[x].val), op(tr[y].sv, tr[y].val)};
  }
  constexpr T query_path(u32 x, u32 y) {
    ++x, ++y;
    split_(x, y);
    return tr[y].w;
  }

 private:
  constexpr void update_(u32 x) {
    tr[x].w = op(op(tr[tr[x].son[0]].w, tr[x].val), tr[tr[x].son[1]].w);
    tr[x].s = op(op(op(tr[tr[x].son[0]].s, tr[x].val), tr[tr[x].son[1]].s), tr[x].sv);  // requirement of maintaining subtree
  }
  constexpr bool which_(u32 x) { return tr[tr[x].fa].son[1] == x; }
  constexpr bool noroot_(u32 x) { return tr[tr[x].fa].son[0] == x || tr[tr[x].fa].son[1] == x; }
  constexpr void all_update_(u32 x) {
    if (x) std::swap(tr[x].son[0], tr[x].son[1]), tr[x].rev ^= 1;
  }
  constexpr void pushdown_(u32 x) {
    if (tr[x].rev) all_update_(tr[x].son[0]), all_update_(tr[x].son[1]), tr[x].rev ^= 1;
  }
  constexpr void ppushdown_(u32 x) {
    if (noroot_(x)) ppushdown_(tr[x].fa);
    pushdown_(x);
  }
  constexpr void rotate(u32 x) {
    u32 y = tr[x].fa, z = tr[y].fa, ySon = which_(x), zSon = which_(y), B = tr[x].son[ySon ^ 1];
    if (noroot_(y)) tr[z].son[zSon] = x;
    tr[x].fa = z;
    tr[y].fa = x, tr[x].son[ySon ^ 1] = y;
    if (B) tr[B].fa = y;
    tr[y].son[ySon] = B;
    update_(y);
  }
  constexpr void splay_(u32 x) {
    ppushdown_(x);
    while (noroot_(x)) {
      u32 fa = tr[x].fa;
      if (noroot_(fa)) {
        if (which_(fa) ^ which_(x)) rotate(x);
        else rotate(fa);
      }
      rotate(x);
    }
    update_(x);
  }
  constexpr u32 access_(u32 x) {
    u32 y = 0;
    for (; x; x = tr[y = x].fa) {
      splay_(x);
      tr[x].sv = inv_op(op(tr[x].sv, tr[tr[x].son[1]].s), tr[y].s);  // requirement of maintaining subtree
      tr[x].son[1] = y;
      update_(x);
    }
    return y;
  }
  constexpr void makeroot_(u32 x) { access_(x), splay_(x), all_update_(x); }
  constexpr u32 findroot_(u32 x) {
    access_(x), splay_(x);
    while (tr[x].son[0]) x = tr[x].son[0];
    return x;
  }
  constexpr void split_(u32 x, u32 y) { makeroot_(x), access_(y), splay_(y); }
  constexpr bool con_(u32 x, u32 y) {
    makeroot_(x);
    if (findroot_(y) != x) return true;
    return false;
  }
  constexpr bool link_(u32 x, u32 y) {
    makeroot_(x);
    if (findroot_(y) == x) return false;
    tr[y].sv = op(tr[y].sv, tr[x].s);  // requirement of maintaining subtree
    tr[x].fa = y;
    update_(y);
    return true;
  }
  constexpr bool cut_(u32 x, u32 y) {
    makeroot_(x);
    if (findroot_(y) == x && tr[x].fa == y && tr[y].son[0] == x) {
      tr[y].son[0] = tr[x].fa = 0, update_(y);
      return true;
    }
    return false;
  }
};

}  // namespace tifa_libs::ds

#endif
#line 1 "src/code/ds/link_cut_tree.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };


#line 5 "src/code/ds/link_cut_tree.hpp"

namespace tifa_libs::ds {

template <class T, auto op, auto inv_op>
requires requires(T x, T y) {
  { op(x, y) } -> std::same_as<T>;
  { inv_op(x, y) } -> std::same_as<T>;
}
class link_cut_tree {
  // function in private: index of node should start from 1
  // wait for updating
  struct YYZ {
    T w, val;
    T s, sv;  // requirement of maintaining subtree
    u32 fa, rev;
    arr<u32, 2> son;
  };

 public:
  vec<YYZ> tr;

  constexpr link_cut_tree(u32 n, vec<T> A) : tr(n + 1) {
    for (u32 i = 1; i <= n; ++i) tr[i].val = A[i - 1];
  }

  constexpr void access(u32 x) { access_(x + 1); }
  constexpr void makeroot(u32 x) { makeroot_(x + 1); }
  constexpr u32 findroot(u32 x) { return findroot_(x + 1) - 1; }
  constexpr void split(u32 x, u32 y) { split_(x + 1, y + 1); }
  constexpr bool con(u32 x, u32 y) { return con_(x + 1, y + 1); }
  constexpr bool link(u32 x, u32 y) { return link_(x + 1, y + 1); }
  constexpr bool cut(u32 x, u32 y) { return cut_(x + 1, y + 1); }
  constexpr void node_update(u32 x, T k) {
    x += 1;
    access_(x);  // requirement of maintaining subtree
    splay_(x), tr[x].val = k, update_(x);
  }
  constexpr void node_add(u32 x, T k) {
    x += 1;
    access_(x);  // requirement of maintaining subtree
    splay_(x), tr[x].val = op(tr[x].val, k), update_(x);
  }
  constexpr u32 lca(u32 u, u32 v, u32 root = 0) {
    if (u == v) return u;
    ++u, ++v, ++root;
    makeroot_(root);
    access_(u);
    u32 ret = access_(v) - 1;
    return tr[u].fa ? ret : -1u;
  }
  constexpr ptt<T> query_subtree(u32 x, u32 y) {
    ++x, ++y;
    split_(x, y);
    return {op(tr[x].sv, tr[x].val), op(tr[y].sv, tr[y].val)};
  }
  constexpr T query_path(u32 x, u32 y) {
    ++x, ++y;
    split_(x, y);
    return tr[y].w;
  }

 private:
  constexpr void update_(u32 x) {
    tr[x].w = op(op(tr[tr[x].son[0]].w, tr[x].val), tr[tr[x].son[1]].w);
    tr[x].s = op(op(op(tr[tr[x].son[0]].s, tr[x].val), tr[tr[x].son[1]].s), tr[x].sv);  // requirement of maintaining subtree
  }
  constexpr bool which_(u32 x) { return tr[tr[x].fa].son[1] == x; }
  constexpr bool noroot_(u32 x) { return tr[tr[x].fa].son[0] == x || tr[tr[x].fa].son[1] == x; }
  constexpr void all_update_(u32 x) {
    if (x) std::swap(tr[x].son[0], tr[x].son[1]), tr[x].rev ^= 1;
  }
  constexpr void pushdown_(u32 x) {
    if (tr[x].rev) all_update_(tr[x].son[0]), all_update_(tr[x].son[1]), tr[x].rev ^= 1;
  }
  constexpr void ppushdown_(u32 x) {
    if (noroot_(x)) ppushdown_(tr[x].fa);
    pushdown_(x);
  }
  constexpr void rotate(u32 x) {
    u32 y = tr[x].fa, z = tr[y].fa, ySon = which_(x), zSon = which_(y), B = tr[x].son[ySon ^ 1];
    if (noroot_(y)) tr[z].son[zSon] = x;
    tr[x].fa = z;
    tr[y].fa = x, tr[x].son[ySon ^ 1] = y;
    if (B) tr[B].fa = y;
    tr[y].son[ySon] = B;
    update_(y);
  }
  constexpr void splay_(u32 x) {
    ppushdown_(x);
    while (noroot_(x)) {
      u32 fa = tr[x].fa;
      if (noroot_(fa)) {
        if (which_(fa) ^ which_(x)) rotate(x);
        else rotate(fa);
      }
      rotate(x);
    }
    update_(x);
  }
  constexpr u32 access_(u32 x) {
    u32 y = 0;
    for (; x; x = tr[y = x].fa) {
      splay_(x);
      tr[x].sv = inv_op(op(tr[x].sv, tr[tr[x].son[1]].s), tr[y].s);  // requirement of maintaining subtree
      tr[x].son[1] = y;
      update_(x);
    }
    return y;
  }
  constexpr void makeroot_(u32 x) { access_(x), splay_(x), all_update_(x); }
  constexpr u32 findroot_(u32 x) {
    access_(x), splay_(x);
    while (tr[x].son[0]) x = tr[x].son[0];
    return x;
  }
  constexpr void split_(u32 x, u32 y) { makeroot_(x), access_(y), splay_(y); }
  constexpr bool con_(u32 x, u32 y) {
    makeroot_(x);
    if (findroot_(y) != x) return true;
    return false;
  }
  constexpr bool link_(u32 x, u32 y) {
    makeroot_(x);
    if (findroot_(y) == x) return false;
    tr[y].sv = op(tr[y].sv, tr[x].s);  // requirement of maintaining subtree
    tr[x].fa = y;
    update_(y);
    return true;
  }
  constexpr bool cut_(u32 x, u32 y) {
    makeroot_(x);
    if (findroot_(y) == x && tr[x].fa == y && tr[y].son[0] == x) {
      tr[y].son[0] = tr[x].fa = 0, update_(y);
      return true;
    }
    return false;
  }
};

}  // namespace tifa_libs::ds


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