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LCT.h
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/*
最后修改:
20231013
测试环境:
gcc11.2,c++11
clang12.0,C++11
msvc14.2,C++14
*/
#ifndef __OY_LCT__
#define __OY_LCT__
#include <algorithm>
#include <cstdint>
#include <functional>
#include <numeric>
namespace OY {
namespace LCT {
using size_type = uint32_t;
struct Ignore {};
template <typename Node>
struct BaseNode {};
template <template <typename> typename NodeWrap, typename Node, bool MakeRoot, bool UpdateSubtree>
struct NodeBase : NodeWrap<Node> {
size_type m_parent, m_lchild, m_rchild, m_vroot, m_vparent, m_vlchild, m_vrchild;
bool m_reversed;
};
template <template <typename> typename NodeWrap, typename Node>
struct NodeBase<NodeWrap, Node, true, false> : NodeWrap<Node> {
size_type m_parent, m_lchild, m_rchild;
bool m_reversed;
};
template <template <typename> typename NodeWrap, typename Node>
struct NodeBase<NodeWrap, Node, false, true> : NodeWrap<Node> {
size_type m_parent, m_lchild, m_rchild, m_vroot, m_vparent, m_vlchild, m_vrchild;
};
template <template <typename> typename NodeWrap, typename Node>
struct NodeBase<NodeWrap, Node, false, false> : NodeWrap<Node> {
size_type m_parent, m_lchild, m_rchild;
};
#ifdef __cpp_lib_void_t
template <typename... Tp>
using void_t = std::void_t<Tp...>;
#else
template <typename... Tp>
struct make_void {
using type = void;
};
template <typename... Tp>
using void_t = typename make_void<Tp...>::type;
#endif
template <typename Tp, typename NodePtr, typename VRoot, typename = void>
struct Has_pushup : std::false_type {};
template <typename Tp, typename NodePtr>
struct Has_pushup<Tp, NodePtr, void, void_t<decltype(std::declval<Tp>().pushup(std::declval<NodePtr>(), std::declval<NodePtr>()))>> : std::true_type {};
template <typename Tp, typename NodePtr>
struct Has_pushup<Tp, NodePtr, NodePtr, void_t<decltype(std::declval<Tp>().pushup(std::declval<NodePtr>(), std::declval<NodePtr>(), std::declval<NodePtr>()))>> : std::true_type {};
template <typename Tp, typename NodePtr, typename = void>
struct Has_vpushup : std::false_type {};
template <typename Tp, typename NodePtr>
struct Has_vpushup<Tp, NodePtr, void_t<decltype(std::declval<Tp>().vpushup(std::declval<NodePtr>(), std::declval<NodePtr>()))>> : std::true_type {};
template <typename Tp, typename NodePtr, typename VRoot, typename = void>
struct Has_pushdown : std::false_type {};
template <typename Tp, typename NodePtr>
struct Has_pushdown<Tp, NodePtr, void, void_t<decltype(std::declval<Tp>().pushdown(std::declval<NodePtr>(), std::declval<NodePtr>()))>> : std::true_type {};
template <typename Tp, typename NodePtr>
struct Has_pushdown<Tp, NodePtr, NodePtr, void_t<decltype(std::declval<Tp>().pushdown(std::declval<NodePtr>(), std::declval<NodePtr>(), std::declval<NodePtr>()))>> : std::true_type {};
template <typename Tp, typename NodePtr, typename = void>
struct Has_vpushdown : std::false_type {};
template <typename Tp, typename NodePtr>
struct Has_vpushdown<Tp, NodePtr, void_t<decltype(std::declval<Tp>().vpushdown(std::declval<NodePtr>(), std::declval<NodePtr>()))>> : std::true_type {};
template <typename Tp, typename NodePtr, typename = void>
struct Has_add_virtual_subtree : std::false_type {};
template <typename Tp, typename NodePtr>
struct Has_add_virtual_subtree<Tp, NodePtr, void_t<decltype(std::declval<Tp>().add_vtree(std::declval<NodePtr>()))>> : std::true_type {};
template <typename Tp, typename NodePtr, typename = void>
struct Has_remove_virtual_subtree : std::false_type {};
template <typename Tp, typename NodePtr>
struct Has_remove_virtual_subtree<Tp, NodePtr, void_t<decltype(std::declval<Tp>().remove_vtree(std::declval<NodePtr>()))>> : std::true_type {};
template <typename Tp, typename NodePtr, typename = void>
struct Has_reverse : std::false_type {};
template <typename Tp, typename NodePtr>
struct Has_reverse<Tp, NodePtr, void_t<decltype(std::declval<Tp>().reverse(std::declval<NodePtr>(), std::declval<NodePtr>()))>> : std::true_type {};
template <template <typename> typename NodeWrap, bool MakeRoot, bool UpdateSubtree, size_type MAX_NODE = 1 << 20>
struct Tree {
struct node : NodeBase<NodeWrap, node, MakeRoot, UpdateSubtree> {
bool is_null() const { return this == s_buffer; }
node *parent() const { return s_buffer + this->m_parent; }
node *lchild() const { return s_buffer + this->m_lchild; }
node *rchild() const { return s_buffer + this->m_rchild; }
node *vroot() const { return s_buffer + this->m_vroot; }
node *vparent() const { return s_buffer + this->m_vparent; }
node *vlchild() const { return s_buffer + this->m_vlchild; }
node *vrchild() const { return s_buffer + this->m_vrchild; }
};
struct LchildGetter {
size_type &operator()(node &x) const { return x.m_lchild; }
const size_type &operator()(const node &x) const { return x.m_lchild; }
};
struct RchildGetter {
size_type &operator()(node &x) const { return x.m_rchild; }
const size_type &operator()(const node &x) const { return x.m_rchild; }
};
struct ParentGetter {
size_type &operator()(node &x) const { return x.m_parent; }
const size_type &operator()(const node &x) const { return x.m_parent; }
void operator()(size_type x) const { _pushup(x); }
};
struct VirtualLchildGetter {
size_type &operator()(node &x) const { return x.m_vlchild; }
const size_type &operator()(const node &x) const { return x.m_vlchild; }
};
struct VirtualRchildGetter {
size_type &operator()(node &x) const { return x.m_vrchild; }
const size_type &operator()(const node &x) const { return x.m_vrchild; }
};
struct VirtualParentGetter {
size_type &operator()(node &x) const { return x.m_vparent; }
const size_type &operator()(const node &x) const { return x.m_vparent; }
void operator()(size_type x) const { _vpushup(x); }
};
static constexpr bool update_virtual = UpdateSubtree || Has_add_virtual_subtree<node, node *>::value;
static node s_buffer[MAX_NODE + 1];
static size_type s_use_count;
size_type m_cursor, m_vertex_cnt;
static void _pushdown(size_type x) {
if constexpr (MakeRoot)
if (s_buffer[x].m_reversed) {
if (s_buffer[x].m_lchild) _reverse(s_buffer[x].m_lchild);
if (s_buffer[x].m_rchild) _reverse(s_buffer[x].m_rchild);
s_buffer[x].m_reversed = false;
}
if constexpr (Has_pushdown<node, node *, node *>::value)
s_buffer[x].pushdown(s_buffer[x].lchild(), s_buffer[x].rchild(), s_buffer[x].vroot());
else if constexpr (Has_pushdown<node, node *, void>::value)
s_buffer[x].pushdown(s_buffer[x].lchild(), s_buffer[x].rchild());
}
static void _pushup(size_type x) {
if constexpr (Has_pushup<node, node *, node *>::value)
s_buffer[x].pushup(s_buffer[x].lchild(), s_buffer[x].rchild(), s_buffer[x].vroot());
else if constexpr (Has_pushup<node, node *, void>::value)
s_buffer[x].pushup(s_buffer[x].lchild(), s_buffer[x].rchild());
}
static void _reverse(size_type x) {
if constexpr (MakeRoot) {
s_buffer[x].m_reversed = !s_buffer[x].m_reversed, std::swap(s_buffer[x].m_lchild, s_buffer[x].m_rchild);
if constexpr (Has_reverse<node, node *>::value) s_buffer[x].reverse(s_buffer[x].lchild(), s_buffer[x].rchild());
}
}
static void _vpushdown(size_type x) {
if constexpr (Has_vpushdown<node, node *>::value) s_buffer[x].vpushdown(s_buffer[x].vlchild(), s_buffer[x].vrchild());
}
static void _vpushup(size_type x) {
if constexpr (Has_vpushup<node, node *>::value) s_buffer[x].vpushup(s_buffer[x].vlchild(), s_buffer[x].vrchild());
}
static void _add_virtual_child(size_type x, size_type c) {
if constexpr (Has_add_virtual_subtree<node, node *>::value) s_buffer[x].add_vtree(s_buffer + c);
}
static void _remove_virtual_child(size_type x, size_type c) {
if constexpr (Has_remove_virtual_subtree<node, node *>::value) s_buffer[x].remove_vtree(s_buffer + c);
}
template <typename Child, typename Parent>
static void _set_child(size_type x, size_type c) { Child()(s_buffer[x]) = c, Parent()(s_buffer[c]) = x; }
template <typename Child>
static void _set_child_null(size_type x) { Child()(s_buffer[x]) = 0; }
template <typename Child, typename Parent>
static void _set_child_or(size_type x, size_type c) { c ? _set_child<Child, Parent>(x, c) : _set_child_null<Child>(x); }
template <typename Child1, typename Child2, typename Parent>
static void _rotate1(size_type x, size_type p) { _set_child_or<Child2, Parent>(p, Child1()(s_buffer[x])), Parent()(p), _set_child<Child1, Parent>(x, p); }
template <typename Child1, typename Child2, typename Parent>
static void _rotate2(size_type x, size_type p, size_type g) { _set_child_or<Child2, Parent>(g, Child1()(s_buffer[p])), Parent()(g), _set_child<Child1, Parent>(p, g), _set_child_or<Child2, Parent>(p, Child1()(s_buffer[x])), Parent()(p), _set_child<Child1, Parent>(x, p); }
template <typename Child1, typename Child2, typename Parent>
static void _rotate3(size_type x, size_type p, size_type g) { _set_child_or<Child1, Parent>(g, Child2()(s_buffer[x])), Parent()(g), _set_child_or<Child2, Parent>(p, Child1()(s_buffer[x])), Parent()(p), _set_child<Child1, Parent>(x, p), _set_child<Child2, Parent>(x, g); }
static void _pre_pushdown(size_type x) {
if (!_is_root(x))
_pre_pushdown(s_buffer[x].m_parent);
else if (s_buffer[x].m_parent)
_erase_virtual_child(s_buffer[x].m_parent, x);
_pushdown(x);
}
static bool _is_root(size_type x) {
size_type p = s_buffer[x].m_parent;
return s_buffer[p].m_lchild != x && s_buffer[p].m_rchild != x;
}
template <typename Child1, typename Child2, typename Parent>
static bool _splay(size_type x, size_type p) {
size_type g = Parent()(s_buffer[p]);
if (p == Child1()(s_buffer[g])) {
size_type gp = Parent()(s_buffer[g]);
_rotate2<Child2, Child1, Parent>(x, p, g), Parent()(s_buffer[x]) = gp;
if (g == Child1()(s_buffer[gp]))
Child1()(s_buffer[gp]) = x;
else if (g == Child2()(s_buffer[gp]))
Child2()(s_buffer[gp]) = x;
return false;
} else if (p == Child2()(s_buffer[g])) {
size_type gp = Parent()(s_buffer[g]);
_rotate3<Child2, Child1, Parent>(x, p, g), Parent()(s_buffer[x]) = gp;
if (g == Child1()(s_buffer[gp]))
Child1()(s_buffer[gp]) = x;
else if (g == Child2()(s_buffer[gp]))
Child2()(s_buffer[gp]) = x;
return false;
} else {
_rotate1<Child2, Child1, Parent>(x, p), Parent()(s_buffer[x]) = g;
return true;
}
}
template <typename Child1, typename Child2, typename Parent>
static void _splay_as_root_pure(size_type x) {
while (true) {
size_type p = Parent()(s_buffer[x]);
if (x == Child1()(s_buffer[p])) {
if (_splay<Child1, Child2, Parent>(x, p)) break;
} else if (x == Child2()(s_buffer[p])) {
if (_splay<Child2, Child1, Parent>(x, p)) break;
} else
break;
}
}
static void _splay_as_root(size_type x) { _splay_as_root_pure<LchildGetter, RchildGetter, ParentGetter>(x); }
static void _splay_as_vroot(size_type x) { _splay_as_root_pure<VirtualLchildGetter, VirtualRchildGetter, VirtualParentGetter>(x); }
static void _vfetch(size_type x) {
if constexpr (UpdateSubtree) {
if (s_buffer[x].m_vparent)
_vfetch(s_buffer[x].m_vparent);
else
_fetch(s_buffer[x].m_parent);
_vpushdown(x);
}
}
static void _fetch(size_type x) {
if constexpr (UpdateSubtree) {
if (!_is_root(x))
_fetch(s_buffer[x].m_parent);
else if (s_buffer[x].m_parent)
_vfetch(x);
_pushdown(x);
}
}
static size_type _access(size_type x) {
_fetch(x);
size_type r0 = 0, r1 = 0;
do {
if constexpr (UpdateSubtree) {
for (r1 = x; !_is_root(r1); r1 = s_buffer[r1].m_parent) {}
if (s_buffer[r1].m_parent) _erase_virtual_child(s_buffer[r1].m_parent, r1), _remove_virtual_child(s_buffer[r1].m_parent, r1);
} else {
if constexpr (Has_remove_virtual_subtree<node, node *>::value) {
for (r1 = x; !_is_root(r1); r1 = s_buffer[r1].m_parent) {}
if (s_buffer[r1].m_parent) _remove_virtual_child(s_buffer[r1].m_parent, r1);
}
_pre_pushdown(x);
}
_splay_as_root(x);
if (s_buffer[x].m_parent) {
_insert_virtual_child(s_buffer[x].m_parent, x);
if constexpr (Has_add_virtual_subtree<node, node *>::value) _pushup(x), _add_virtual_child(s_buffer[x].m_parent, x);
}
_replace_prefered_subtree(x, s_buffer[x].m_rchild, r0);
if (s_buffer[x].m_rchild) _add_virtual_child(x, s_buffer[x].m_rchild);
if (r0) _remove_virtual_child(x, r0);
s_buffer[x].m_rchild = r0, _pushup(x), r0 = x, x = s_buffer[x].m_parent;
} while (x);
return r0;
}
static void _make_access_root(size_type x) { _access(x), _splay_as_root(x); }
static void _make_root(size_type x) {
static_assert(MakeRoot, "MakeRoot Must Be True");
_make_access_root(x), _pushup(x), _reverse(x);
}
static void _isolate(size_type x) {
if (s_buffer[x].m_lchild) {
x = s_buffer[x].m_lchild;
while (true) {
_pushdown(x);
if (!s_buffer[x].m_rchild) break;
x = s_buffer[x].m_rchild;
}
_splay_as_root(x);
} else if (s_buffer[x].m_parent)
_splay_as_root(s_buffer[x].m_parent);
}
template <typename Child1, typename Child2, typename Parent>
static size_type _get_adjacent(size_type x) {
if (Child1()(s_buffer[x])) {
x = Child1()(s_buffer[x]);
while (true) {
_pushdown(x);
if (!Child2()(s_buffer[x])) break;
x = Child2()(s_buffer[x]);
}
} else
x = Parent()(s_buffer[x]);
_splay_as_root(x);
return x;
}
static size_type _find_root(size_type x) {
_pushdown(x = _access(x));
while (s_buffer[x].m_lchild) _pushdown(x = s_buffer[x].m_lchild);
_splay_as_root(x), _pushup(x);
return x;
}
template <typename Child1, typename Child2, typename Judger>
static size_type _bisect(size_type x, Judger &&judge) {
size_type res = 0;
while (true) {
_pushdown(x);
if (judge(s_buffer + x)) {
res = x;
if (!Child1()(s_buffer[x])) break;
x = Child1()(s_buffer[x]);
} else {
if (!Child2()(s_buffer[x])) break;
x = Child2()(s_buffer[x]);
}
}
_splay_as_root(x);
if (res && res != x)
_splay_as_root(res), _pushup(res);
else
_pushup(x);
return res;
}
static void _insert_virtual_child(size_type x, size_type c) {
if constexpr (UpdateSubtree) s_buffer[c].m_vlchild = s_buffer[c].m_vparent = 0, _set_child_or<VirtualRchildGetter, VirtualParentGetter>(c, s_buffer[x].m_vroot), s_buffer[x].m_vroot = c, _vpushup(c);
}
static void _erase_virtual_child(size_type x, size_type c) {
if constexpr (UpdateSubtree) {
_splay_as_vroot(c), _vpushdown(c);
if (s_buffer[c].m_vlchild)
if (s_buffer[c].m_vrchild) {
size_type y = s_buffer[c].m_vrchild;
s_buffer[y].m_vparent = 0, _vpushdown(y);
while (s_buffer[y].m_vlchild) _vpushdown(y = s_buffer[y].m_vlchild);
_splay_as_vroot(y), _set_child<VirtualLchildGetter, VirtualParentGetter>(y, s_buffer[c].m_vlchild), s_buffer[y].m_vparent = 0, s_buffer[x].m_vroot = y, _vpushup(y);
} else
s_buffer[s_buffer[c].m_vlchild].m_vparent = 0, s_buffer[x].m_vroot = s_buffer[c].m_vlchild;
else if (s_buffer[c].m_vrchild)
s_buffer[s_buffer[c].m_vrchild].m_vparent = 0, s_buffer[x].m_vroot = s_buffer[c].m_vrchild;
else
s_buffer[x].m_vroot = 0;
s_buffer[c].m_vlchild = s_buffer[c].m_vrchild = 0;
}
}
static void _replace_prefered_child(size_type x, size_type c0, size_type r0) {
if constexpr (UpdateSubtree) _splay_as_vroot(r0), _vpushdown(r0), _set_child_or<VirtualLchildGetter, VirtualParentGetter>(c0, s_buffer[r0].m_vlchild), _set_child_or<VirtualRchildGetter, VirtualParentGetter>(c0, s_buffer[r0].m_vrchild), s_buffer[c0].m_vparent = 0, s_buffer[x].m_vroot = c0, _vpushup(c0);
}
static void _replace_prefered_subtree(size_type x, size_type c0, size_type r0) {
if constexpr (UpdateSubtree)
if (r0)
if (c0)
_replace_prefered_child(x, c0, r0);
else
_erase_virtual_child(x, r0);
else if (c0)
_insert_virtual_child(x, c0);
}
static void _add_child(size_type x, size_type c) {
s_buffer[c].m_parent = x;
if constexpr (update_virtual) _make_access_root(x);
_insert_virtual_child(x, c), _add_virtual_child(x, c);
if constexpr (update_virtual) _pushup(x);
}
template <typename Modify = Ignore>
Tree(size_type vertex_cnt = 0, Modify &&modify = Modify()) { resize(vertex_cnt, modify); }
template <typename Modify = Ignore>
void resize(size_type vertex_cnt, Modify &&modify = Modify()) {
if (!(m_vertex_cnt = vertex_cnt)) return;
m_cursor = s_use_count, s_use_count += m_vertex_cnt;
for (size_type i = 0; i != m_vertex_cnt; i++) {
if constexpr (!std::is_same<typename std::decay<Modify>::type, Ignore>::value) modify(s_buffer + m_cursor + i);
_pushup(m_cursor + i);
}
}
node *get_node(size_type a) const { return s_buffer + m_cursor + a; }
size_type get_id(node *x) const { return x - s_buffer - m_cursor; }
size_type access(size_type a) const { return _access(m_cursor + a) - m_cursor; }
void rooted_access(size_type a) const {
size_type a2 = m_cursor + a;
_make_access_root(a2), _pushup(a2);
}
size_type access(size_type a, size_type b) const {
_make_root(m_cursor + a);
return _access(m_cursor + b) - m_cursor;
}
void make_root(size_type a) const { _make_root(m_cursor + a); }
template <typename Callback>
void do_for_node(size_type a, Callback &&call) {
size_type a2 = m_cursor + a;
_make_access_root(a2), call(s_buffer + a2), _pushup(a2);
}
template <typename Callback>
void do_for_path(size_type a, Callback &&call) {
size_type a2 = m_cursor + a;
a2 = _access(a2), call(s_buffer + a2);
}
template <typename Callback>
void do_for_subtree(size_type a, Callback &&call) const {
static_assert(update_virtual, "UpdateSubtree Must Be True, Or Node Must Have 'add_vtree' method");
size_type a2 = m_cursor + a;
_access(a2), _isolate(a2);
call(s_buffer + a2);
if (s_buffer[a2].m_parent) _pushup(s_buffer[a2].m_parent);
}
template <typename Callback>
void do_for_path(size_type a, size_type b, Callback &&call) const {
size_type a2 = m_cursor + a, b2 = m_cursor + b;
_make_root(a2);
size_type r = _access(b2);
call(s_buffer + r);
}
size_type lca(size_type a, size_type b) const {
_access(m_cursor + a);
return _access(m_cursor + b) - m_cursor;
}
template <bool Check>
typename std::conditional<Check, bool, void>::type connect(size_type a, size_type p) {
size_type a2 = m_cursor + a, p2 = m_cursor + p;
_make_root(a2);
if constexpr (Check)
if (_find_root(p2) == a2) return false;
_add_child(p2, a2);
if constexpr (Check) return true;
}
template <bool Check>
typename std::conditional<Check, bool, void>::type disconnect(size_type a, size_type b) {
size_type a2 = m_cursor + a, b2 = m_cursor + b;
_make_root(a2), _make_access_root(b2);
if constexpr (Check)
if (s_buffer[a2].m_rchild || s_buffer[b2].m_lchild != a2) return false;
s_buffer[a2].m_parent = s_buffer[b2].m_lchild = 0, _pushup(b2);
if constexpr (Check) return true;
}
void connect_above(size_type a, size_type p) { _add_child(m_cursor + p, m_cursor + a); }
void disconnect_above(size_type a) {
size_type a2 = m_cursor + a;
_make_access_root(a2), s_buffer[a2].lchild()->m_parent = 0, s_buffer[a2].m_lchild = 0, _pushup(a2);
}
size_type find_root(size_type a) const { return _find_root(m_cursor + a) - m_cursor; }
size_type find_parent(size_type a) const {
size_type a2 = m_cursor + a;
_access(a2);
if (!s_buffer[a2].m_parent && !s_buffer[a2].m_lchild) return -1;
a2 = _get_adjacent<LchildGetter, RchildGetter, ParentGetter>(a2), _pushup(a2);
return a2 - m_cursor;
}
size_type find_son(size_type a, size_type b) const {
size_type a2 = m_cursor + a, b2 = m_cursor + b;
_access(a2), _access(b2), a2 = _get_adjacent<RchildGetter, LchildGetter, ParentGetter>(a2), _pushup(a2);
return a2 - m_cursor;
}
bool in_same_group(size_type a, size_type b) const {
size_type a2 = m_cursor + a, b2 = m_cursor + b;
if constexpr (MakeRoot) {
_make_root(a2);
return _find_root(b2) == a2;
} else
return _find_root(a2) == _find_root(b2);
}
template <typename Judger>
size_type bisect_highest(size_type a, Judger &&judge) const { return _bisect<LchildGetter, RchildGetter>(m_cursor + a, judge) - m_cursor; }
template <typename Judger>
size_type bisect_lowest(size_type a, Judger &&judge) const { return _bisect<RchildGetter, LchildGetter>(m_cursor + a, judge) - m_cursor; }
};
template <template <typename> typename NodeWrap, bool MakeRoot, bool UpdateSubtree, size_type MAX_NODE>
typename Tree<NodeWrap, MakeRoot, UpdateSubtree, MAX_NODE>::node Tree<NodeWrap, MakeRoot, UpdateSubtree, MAX_NODE>::s_buffer[MAX_NODE + 1];
template <template <typename> typename NodeWrap, bool MakeRoot, bool UpdateSubtree, size_type MAX_NODE>
size_type Tree<NodeWrap, MakeRoot, UpdateSubtree, MAX_NODE>::s_use_count = 1;
}
template <bool MakeRoot, bool UpdateSubtree, LCT::size_type MAX_NODE = 1 << 20>
using LCTTree = LCT::Tree<LCT::BaseNode, MakeRoot, UpdateSubtree, MAX_NODE>;
}
#endif