#pragma once
#include "../../util/alias/others/lib.hpp"
namespace tifa_libs {
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 TIFA {
T w, val;
T s, sv; // requirement of maintaining subtree
u32 fa, rev;
arr<u32, 2> son;
};
public:
vec<TIFA> tr;
CEXP link_cut_tree(u32 n, vec<T> A) NE : tr(n + 1) {
flt_ (u32, i, 1, n + 1) tr[i].val = A[i - 1];
}
CEXP void access(u32 x) NE { access_(x + 1); }
CEXP void makeroot(u32 x) NE { makeroot_(x + 1); }
CEXP u32 findroot(u32 x) NE { return findroot_(x + 1) - 1; }
CEXP void split(u32 x, u32 y) NE { split_(x + 1, y + 1); }
CEXP bool con(u32 x, u32 y) NE { return con_(x + 1, y + 1); }
CEXP bool link(u32 x, u32 y) NE { return link_(x + 1, y + 1); }
CEXP bool cut(u32 x, u32 y) NE { return cut_(x + 1, y + 1); }
CEXP void node_update(u32 x, T k) NE {
x += 1;
access_(x); // requirement of maintaining subtree
splay_(x), tr[x].val = k, update_(x);
}
CEXP void node_add(u32 x, T k) NE {
x += 1;
access_(x); // requirement of maintaining subtree
splay_(x), tr[x].val = op(tr[x].val, k), update_(x);
}
CEXP u32 lca(u32 u, u32 v, u32 root = 0) NE {
if (u == v) return u;
++u, ++v, ++root, makeroot_(root), access_(u);
u32 ret = access_(v) - 1;
retif_((tr[u].fa), ret, -1u);
}
CEXP ptt<T> query_subtree(u32 x, u32 y) NE {
split_(++x, ++y);
return {op(tr[x].sv, tr[x].val), op(tr[y].sv, tr[y].val)};
}
CEXP T query_path(u32 x, u32 y) NE {
split_(++x, ++y);
return tr[y].w;
}
private:
CEXP void update_(u32 x) NE {
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
}
CEXP bool which_(u32 x) NE { return tr[tr[x].fa].son[1] == x; }
CEXP bool noroot_(u32 x) NE { return tr[tr[x].fa].son[0] == x || tr[tr[x].fa].son[1] == x; }
CEXP void all_update_(u32 x) NE {
if (x) swap(tr[x].son[0], tr[x].son[1]), tr[x].rev ^= 1;
}
CEXP void pushdown_(u32 x) NE {
if (tr[x].rev) all_update_(tr[x].son[0]), all_update_(tr[x].son[1]), tr[x].rev ^= 1;
}
CEXP void ppushdown_(u32 x) NE {
if (noroot_(x)) ppushdown_(tr[x].fa);
pushdown_(x);
}
CEXP void rotate(u32 x) NE {
cu32 y = tr[x].fa, z = tr[y].fa, y_son = which_(x), z_son = which_(y), B = tr[x].son[y_son ^ 1];
if (noroot_(y)) tr[z].son[z_son] = x;
if (tr[x].fa = z, tr[y].fa = x, tr[x].son[y_son ^ 1] = y; B) tr[B].fa = y;
tr[y].son[y_son] = B, update_(y);
}
CEXP void splay_(u32 x) NE {
ppushdown_(x);
while (noroot_(x)) {
if (cu32 fa = tr[x].fa; noroot_(fa)) {
if (which_(fa) ^ which_(x)) rotate(x);
else rotate(fa);
}
rotate(x);
}
update_(x);
}
CEXP u32 access_(u32 x) NE {
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;
}
CEXP void makeroot_(u32 x) NE { access_(x), splay_(x), all_update_(x); }
CEXP u32 findroot_(u32 x) NE {
access_(x), splay_(x);
while (tr[x].son[0]) x = tr[x].son[0];
return x;
}
CEXP void split_(u32 x, u32 y) NE { makeroot_(x), access_(y), splay_(y); }
CEXP bool con_(u32 x, u32 y) NE {
makeroot_(x);
if (findroot_(y) != x) return true;
return false;
}
CEXP bool link_(u32 x, u32 y) NE {
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;
}
CEXP bool cut_(u32 x, u32 y) NE {
if (makeroot_(x); 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
#line 2 "src/ds/link_cut_tree/lib.hpp"
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<T>;
template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>; template <class T, usz N> using carr = std::array<const T, N>;
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 U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, T)
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 4 "src/ds/link_cut_tree/lib.hpp"
namespace tifa_libs {
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 TIFA {
T w, val;
T s, sv; // requirement of maintaining subtree
u32 fa, rev;
arr<u32, 2> son;
};
public:
vec<TIFA> tr;
CEXP link_cut_tree(u32 n, vec<T> A) NE : tr(n + 1) {
flt_ (u32, i, 1, n + 1) tr[i].val = A[i - 1];
}
CEXP void access(u32 x) NE { access_(x + 1); }
CEXP void makeroot(u32 x) NE { makeroot_(x + 1); }
CEXP u32 findroot(u32 x) NE { return findroot_(x + 1) - 1; }
CEXP void split(u32 x, u32 y) NE { split_(x + 1, y + 1); }
CEXP bool con(u32 x, u32 y) NE { return con_(x + 1, y + 1); }
CEXP bool link(u32 x, u32 y) NE { return link_(x + 1, y + 1); }
CEXP bool cut(u32 x, u32 y) NE { return cut_(x + 1, y + 1); }
CEXP void node_update(u32 x, T k) NE {
x += 1;
access_(x); // requirement of maintaining subtree
splay_(x), tr[x].val = k, update_(x);
}
CEXP void node_add(u32 x, T k) NE {
x += 1;
access_(x); // requirement of maintaining subtree
splay_(x), tr[x].val = op(tr[x].val, k), update_(x);
}
CEXP u32 lca(u32 u, u32 v, u32 root = 0) NE {
if (u == v) return u;
++u, ++v, ++root, makeroot_(root), access_(u);
u32 ret = access_(v) - 1;
retif_((tr[u].fa), ret, -1u);
}
CEXP ptt<T> query_subtree(u32 x, u32 y) NE {
split_(++x, ++y);
return {op(tr[x].sv, tr[x].val), op(tr[y].sv, tr[y].val)};
}
CEXP T query_path(u32 x, u32 y) NE {
split_(++x, ++y);
return tr[y].w;
}
private:
CEXP void update_(u32 x) NE {
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
}
CEXP bool which_(u32 x) NE { return tr[tr[x].fa].son[1] == x; }
CEXP bool noroot_(u32 x) NE { return tr[tr[x].fa].son[0] == x || tr[tr[x].fa].son[1] == x; }
CEXP void all_update_(u32 x) NE {
if (x) swap(tr[x].son[0], tr[x].son[1]), tr[x].rev ^= 1;
}
CEXP void pushdown_(u32 x) NE {
if (tr[x].rev) all_update_(tr[x].son[0]), all_update_(tr[x].son[1]), tr[x].rev ^= 1;
}
CEXP void ppushdown_(u32 x) NE {
if (noroot_(x)) ppushdown_(tr[x].fa);
pushdown_(x);
}
CEXP void rotate(u32 x) NE {
cu32 y = tr[x].fa, z = tr[y].fa, y_son = which_(x), z_son = which_(y), B = tr[x].son[y_son ^ 1];
if (noroot_(y)) tr[z].son[z_son] = x;
if (tr[x].fa = z, tr[y].fa = x, tr[x].son[y_son ^ 1] = y; B) tr[B].fa = y;
tr[y].son[y_son] = B, update_(y);
}
CEXP void splay_(u32 x) NE {
ppushdown_(x);
while (noroot_(x)) {
if (cu32 fa = tr[x].fa; noroot_(fa)) {
if (which_(fa) ^ which_(x)) rotate(x);
else rotate(fa);
}
rotate(x);
}
update_(x);
}
CEXP u32 access_(u32 x) NE {
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;
}
CEXP void makeroot_(u32 x) NE { access_(x), splay_(x), all_update_(x); }
CEXP u32 findroot_(u32 x) NE {
access_(x), splay_(x);
while (tr[x].son[0]) x = tr[x].son[0];
return x;
}
CEXP void split_(u32 x, u32 y) NE { makeroot_(x), access_(y), splay_(y); }
CEXP bool con_(u32 x, u32 y) NE {
makeroot_(x);
if (findroot_(y) != x) return true;
return false;
}
CEXP bool link_(u32 x, u32 y) NE {
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;
}
CEXP bool cut_(u32 x, u32 y) NE {
if (makeroot_(x); 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
src/ds/link_cut_tree/lib.hpp