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#include "structure/develop/dynamic-tree-test.hpp"
#include "super-link-cut-tree.hpp"
/**
* @brief Dynamic Tree Test
* @see https://dmoj.ca/problem/ds5
*/
using T = int;
const T inf_max = numeric_limits<T>::max();
const T inf_min = numeric_limits<T>::min();
// 遅延伝搬をする作用素
struct Lazy {
int type; // 0: none, 1: change, 2:inc
T v;
// 単位元
Lazy() : type(0) {}
// 初期化
constexpr Lazy(int type, T v) : type(type), v(v) {}
inline constexpr void propagate(const Lazy &p) {
if (p.type == 0) {
return;
}
if (type == 0 or p.type == 1) {
type = p.type;
v = p.v;
} else {
v += p.v;
}
}
};
// Light-edge の情報
template <typename Lazy>
struct LInfo {
T min, max, sum, sz;
T all_min, all_max, all_sum, all_sz;
// 単位元(キーの値はアクセスしないので未初期化でもよい
LInfo() : all_min(inf_max), all_max(inf_min), all_sum(0), all_sz(0) {}
// 初期化
LInfo(T min, T max, T sum, T sz) : min(min), max(max), sum(sum), sz(sz) {}
// l, r は Splay-tree の子 (原理上、各ノード区別はない)
void update(const LInfo &l, const LInfo &r) {
all_min = std::min({l.all_min, min, r.all_min});
all_max = std::max({l.all_max, max, r.all_max});
all_sum = l.all_sum + sum + r.all_sum;
all_sz = l.all_sz + sz + r.all_sz;
}
// light-edgeに対する遅延伝搬
void propagate(const Lazy &p) {
if (p.type == 0) {
return;
} else if (p.type == 1) { // change
min = p.v;
max = p.v;
sum = p.v * sz;
all_min = p.v;
all_max = p.v;
all_sum = p.v * all_sz;
} else { // inc
min += p.v;
max += p.v;
sum += p.v * sz;
all_min += p.v;
all_max += p.v;
all_sum += p.v * all_sz;
}
}
};
// Heavy-edge の情報
template <typename LInfo, typename Lazy>
struct Info {
T v;
T path_min, path_max, path_sum, path_sz;
T light_min, light_max, light_sum, light_sz;
// 単位元(キーの値はアクセスしないので未初期化でもよい
Info()
: light_min(inf_max),
light_max(inf_min),
light_sum(0),
light_sz(0),
path_min(inf_max),
path_max(inf_min),
path_sum(0),
path_sz(0) {}
// 初期化
Info(T v) : v(v) {}
// 反転
void toggle() {}
// pが親, cがheavy-edgeで結ばれた子, lがそれ以外の子
void update(const Info &p, const Info &c, const LInfo &l) {
light_min = min({p.light_min, c.light_min, l.all_min});
light_max = max({p.light_max, c.light_max, l.all_max});
light_sum = p.light_sum + c.light_sum + l.all_sum;
light_sz = p.light_sz + c.light_sz + l.all_sz;
path_min = min({p.path_min, v, c.path_min});
path_max = max({p.path_max, v, c.path_max});
path_sum = p.path_sum + v + c.path_sum;
path_sz = p.path_sz + 1 + c.path_sz;
}
// 親と light-edge で繋げる
LInfo link() const {
return LInfo(min(light_min, path_min), max(light_max, path_max),
path_sum + light_sum, light_sz + path_sz);
}
// 遅延伝搬
void propagate(const Lazy &p) {
if (p.type == 0) {
return;
} else if (p.type == 1) { // change
v = p.v;
path_min = p.v;
path_max = p.v;
path_sum = p.v * path_sz;
} else { // inc
v += p.v;
path_min += p.v;
path_max += p.v;
path_sum += p.v * path_sz;
}
}
// light-edgeに対する遅延伝搬
// pathとsubtreeの遅延伝搬が両方ある場合に実装する
void propagate_light(const Lazy &p) {
if (p.type == 0 or light_min == inf_max) {
return;
} else if (p.type == 1) { // change
light_min = p.v;
light_max = p.v;
light_sum = p.v * light_sz;
} else { // inc
light_min += p.v;
light_max += p.v;
light_sum += p.v * light_sz;
}
}
};
using LCT = SuperLinkCutTree<Info, LInfo, Lazy>;
#line 1 "structure/develop/super-link-cut-tree.hpp"
/**
* @brief 何でもできるLCT
*/
template <typename LInfo, typename Lazy>
struct SplayTree {
struct Node {
Node *l, *r, *p;
LInfo info;
Lazy lazy, lbuf;
explicit Node(const LInfo &info)
: info(info),
l(nullptr),
r(nullptr),
p(nullptr),
lazy(Lazy()),
lbuf(Lazy()) {}
};
const LInfo e;
SplayTree() : e(LInfo()) {}
using NP = Node *;
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;
}
}
const LInfo &get_info(NP t) { return t ? t->info : e; }
void update(NP t) { t->info.update(get_info(t->l), get_info(t->r)); }
NP get_right(NP t) {
while (t->r) t = t->r;
return t;
}
NP alloc(const LInfo &v) {
auto t = new Node(v);
update(t);
return t;
}
void propagate(NP t, const Lazy &lazy) {
t->info.propagate(lazy);
t->lbuf.propagate(lazy);
t->lazy.propagate(lazy);
}
void push(NP t) {
if (t->l) propagate(t->l, t->lazy);
if (t->r) propagate(t->r, t->lazy);
t->lazy = Lazy();
}
void splay(NP t) {
push(t);
while (t->p) {
NP q = t->p;
if (!q->p) {
if (q->l == t)
rotr(t);
else
rotl(t);
} else {
NP r = q->p;
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 insert(NP t, const LInfo &v) {
if (not t) {
t = alloc(v);
return t;
} else {
NP cur = get_right(t), z = alloc(v);
splay(cur);
z->p = cur;
cur->r = z;
update(cur);
splay(z);
return z;
}
}
NP erase(NP t) {
splay(t);
NP x = t->l, y = t->r;
delete t;
if (not x) {
t = y;
if (t) t->p = nullptr;
} else if (not y) {
t = x;
t->p = nullptr;
} else {
x->p = nullptr;
t = get_right(x);
splay(t);
t->r = y;
y->p = t;
update(t);
}
return t;
}
};
template <template <typename, typename> typename _Info,
template <typename> typename _LInfo, typename Lazy>
struct SuperLinkCutTree {
using LInfo = _LInfo<Lazy>;
using Info = _Info<LInfo, Lazy>;
private:
struct Node {
Node *l, *r, *p;
Info info;
typename SplayTree<LInfo, Lazy>::Node *light, *belong;
bool rev;
Lazy hlazy, llazy;
bool is_root() const { return not p or (p->l != this and p->r != this); }
explicit Node(const Info &info)
: info(info),
l(nullptr),
r(nullptr),
p(nullptr),
rev(false),
light(nullptr),
belong(nullptr),
hlazy(Lazy()),
llazy(Lazy()) {}
};
public:
using NP = Node *;
SplayTree<LInfo, Lazy> splay_tree;
private:
const Info e;
private:
void toggle(NP t) {
swap(t->l, t->r);
t->info.toggle();
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;
}
}
void propagate_heavy(NP t, const Lazy &hlazy) {
t->hlazy.propagate(hlazy);
t->info.propagate(hlazy);
}
void propagate_light(NP t, const Lazy &llazy) {
t->llazy.propagate(llazy);
t->info.propagate_light(llazy);
}
void propagate_all(NP t, const Lazy &lazy) {
propagate_heavy(t, lazy);
propagate_light(t, lazy);
}
public:
SuperLinkCutTree() : e{Info()}, splay_tree{} {}
void push(NP t) {
if (t->rev) {
if (t->l) toggle(t->l);
if (t->r) toggle(t->r);
t->rev = false;
}
{
if (t->l) {
propagate_heavy(t->l, t->hlazy);
propagate_light(t->l, t->llazy);
}
if (t->r) {
propagate_heavy(t->r, t->hlazy);
propagate_light(t->r, t->llazy);
}
if (t->light) {
splay_tree.propagate(t->light, t->llazy);
}
t->hlazy = Lazy();
t->llazy = Lazy();
}
}
void push_rev(NP t) {
if (t->rev) {
if (t->l) toggle(t->l);
if (t->r) toggle(t->r);
t->rev = false;
}
}
const Info &get_info(NP t) { return t ? t->info : e; }
void update(NP t) {
t->info.update(get_info(t->l), get_info(t->r),
splay_tree.get_info(t->light));
}
void splay(NP t) {
push(t);
{
NP rot = t;
while (not rot->is_root()) rot = rot->p;
t->belong = rot->belong;
if (t != rot) rot->belong = nullptr;
}
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->light = splay_tree.insert(cur->light, cur->r->info.link());
cur->r->belong = cur->light;
}
cur->r = rp;
if (cur->r) {
splay_tree.splay(cur->r->belong);
propagate_all(cur->r, cur->r->belong->lbuf);
push(cur->r);
cur->light = splay_tree.erase(cur->r->belong);
}
update(cur);
rp = cur;
}
splay(t);
return rp;
}
void link(NP child, NP parent) {
expose(parent);
expose(child);
child->p = parent;
parent->r = child;
update(parent);
}
void cut(NP child) {
expose(child);
NP parent = child->l;
child->l = nullptr;
parent->p = nullptr;
update(child);
}
void evert(NP t) {
expose(t);
toggle(t);
push(t);
}
NP alloc(const Info &info) {
NP t = new Node(info);
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 = move(v);
update(t);
}
void set_propagate_path(NP t, const Lazy &lazy) {
expose(t);
propagate_heavy(t, lazy);
push(t);
update(t);
}
void set_propagate_path(NP u, NP v, const Lazy &lazy) {
evert(u);
set_propagate_path(v, lazy);
}
void set_propagate_all(NP t, const Lazy &lazy) {
expose(t);
propagate_all(t, lazy);
push(t);
update(t);
}
void set_propagate_subtree(NP t, const Lazy &lazy) {
expose(t);
NP l = t->l;
t->l = nullptr;
propagate_all(t, lazy);
push(t);
t->l = l;
update(t);
}
const Info &query(NP u) {
expose(u);
return get_info(u);
}
const Info &query_path(NP u, NP v) {
evert(u);
expose(v);
return get_info(v);
}
Info query_subtree(NP u) {
expose(u);
NP l = u->l;
u->l = nullptr;
update(u);
auto ret = u->info;
u->l = l;
update(u);
return ret;
}
};
/*
using T = int64_t;
// 遅延伝搬をするための作用素
struct Lazy {
// 単位元
Lazy() {}
// 初期化
Lazy(T v) {}
// 遅延伝搬
void propagate(const Lazy &p) {}
};
// Light-edge の情報
template< typename Lazy >
struct LInfo {
// 単位元(キーの値はアクセスしないので未初期化でもよい
LInfo() {}
// 初期化
LInfo(T v) {}
// l, r は Splay-tree の子 (原理上、各ノード区別はない)
void update(const LInfo &l, const LInfo &r) {}
// 部分木への遅延伝搬
void propagate(const Lazy &p) {}
};
// Heavy-edge の情報
template< typename LInfo, typename Lazy >
struct Info {
// 単位元(キーの値はアクセスしないので未初期化でもよい
Info() {}
// 初期化
Info(T v) {}
// 反転
void toggle() {}
// pが親, cがheavy-edgeで結ばれた子, lがそれ以外の子
void update(const Info &p, const Info &c, const LInfo &l) {}
// 親と light-edge で繋げる
LInfo link() const { return LInfo(); }
// 遅延伝搬
void propagate(const Lazy &p) {}
// light-edgeに対する遅延伝搬
// pathとsubtreeの遅延伝搬が両方ある場合に実装する
void propagate_light(const Lazy &p) {}
};
using LCT = SuperLinkCutTree< Info, LInfo, Lazy >;
*/
#line 2 "structure/develop/dynamic-tree-test.hpp"
/**
* @brief Dynamic Tree Test
* @see https://dmoj.ca/problem/ds5
*/
using T = int;
const T inf_max = numeric_limits<T>::max();
const T inf_min = numeric_limits<T>::min();
// 遅延伝搬をする作用素
struct Lazy {
int type; // 0: none, 1: change, 2:inc
T v;
// 単位元
Lazy() : type(0) {}
// 初期化
constexpr Lazy(int type, T v) : type(type), v(v) {}
inline constexpr void propagate(const Lazy &p) {
if (p.type == 0) {
return;
}
if (type == 0 or p.type == 1) {
type = p.type;
v = p.v;
} else {
v += p.v;
}
}
};
// Light-edge の情報
template <typename Lazy>
struct LInfo {
T min, max, sum, sz;
T all_min, all_max, all_sum, all_sz;
// 単位元(キーの値はアクセスしないので未初期化でもよい
LInfo() : all_min(inf_max), all_max(inf_min), all_sum(0), all_sz(0) {}
// 初期化
LInfo(T min, T max, T sum, T sz) : min(min), max(max), sum(sum), sz(sz) {}
// l, r は Splay-tree の子 (原理上、各ノード区別はない)
void update(const LInfo &l, const LInfo &r) {
all_min = std::min({l.all_min, min, r.all_min});
all_max = std::max({l.all_max, max, r.all_max});
all_sum = l.all_sum + sum + r.all_sum;
all_sz = l.all_sz + sz + r.all_sz;
}
// light-edgeに対する遅延伝搬
void propagate(const Lazy &p) {
if (p.type == 0) {
return;
} else if (p.type == 1) { // change
min = p.v;
max = p.v;
sum = p.v * sz;
all_min = p.v;
all_max = p.v;
all_sum = p.v * all_sz;
} else { // inc
min += p.v;
max += p.v;
sum += p.v * sz;
all_min += p.v;
all_max += p.v;
all_sum += p.v * all_sz;
}
}
};
// Heavy-edge の情報
template <typename LInfo, typename Lazy>
struct Info {
T v;
T path_min, path_max, path_sum, path_sz;
T light_min, light_max, light_sum, light_sz;
// 単位元(キーの値はアクセスしないので未初期化でもよい
Info()
: light_min(inf_max),
light_max(inf_min),
light_sum(0),
light_sz(0),
path_min(inf_max),
path_max(inf_min),
path_sum(0),
path_sz(0) {}
// 初期化
Info(T v) : v(v) {}
// 反転
void toggle() {}
// pが親, cがheavy-edgeで結ばれた子, lがそれ以外の子
void update(const Info &p, const Info &c, const LInfo &l) {
light_min = min({p.light_min, c.light_min, l.all_min});
light_max = max({p.light_max, c.light_max, l.all_max});
light_sum = p.light_sum + c.light_sum + l.all_sum;
light_sz = p.light_sz + c.light_sz + l.all_sz;
path_min = min({p.path_min, v, c.path_min});
path_max = max({p.path_max, v, c.path_max});
path_sum = p.path_sum + v + c.path_sum;
path_sz = p.path_sz + 1 + c.path_sz;
}
// 親と light-edge で繋げる
LInfo link() const {
return LInfo(min(light_min, path_min), max(light_max, path_max),
path_sum + light_sum, light_sz + path_sz);
}
// 遅延伝搬
void propagate(const Lazy &p) {
if (p.type == 0) {
return;
} else if (p.type == 1) { // change
v = p.v;
path_min = p.v;
path_max = p.v;
path_sum = p.v * path_sz;
} else { // inc
v += p.v;
path_min += p.v;
path_max += p.v;
path_sum += p.v * path_sz;
}
}
// light-edgeに対する遅延伝搬
// pathとsubtreeの遅延伝搬が両方ある場合に実装する
void propagate_light(const Lazy &p) {
if (p.type == 0 or light_min == inf_max) {
return;
} else if (p.type == 1) { // change
light_min = p.v;
light_max = p.v;
light_sum = p.v * light_sz;
} else { // inc
light_min += p.v;
light_max += p.v;
light_sum += p.v * light_sz;
}
}
};
using LCT = SuperLinkCutTree<Info, LInfo, Lazy>;