This documentation is automatically generated by online-judge-tools/verification-helper
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite
#include "../../template/template.hpp"
#include "../../structure/develop/vertex-set-path-composite.hpp"
int main() {
int N, Q;
cin >> N >> Q;
LCT lct;
vector< LCT::NP > vs(N);
for(int i = 0; i < N; i++) {
T a, b;
cin >> a >> b;
vs[i] = lct.alloc({a, b});
}
for(int i = 1; i < N; i++) {
int a, b;
cin >> a >> b;
lct.evert(vs[a]);
lct.link(vs[a], vs[b]);
}
while(Q--) {
int t;
cin >> t;
if(t == 0) {
int u, v, w, x;
cin >> u >> v >> w >> x;
lct.evert(vs[u]);
lct.cut(vs[v]);
lct.evert(vs[w]);
lct.link(vs[w], vs[x]);
} else if(t == 1) {
int p;
T c, d;
cin >> p >> c >> d;
lct.set_key(vs[p], {c, d});
} else {
int u, v;
T x;
cin >> u >> v >> x;
auto info = lct.query_path(vs[u], vs[v]);
cout << info.a_sum_p * x + info.b_sum_p << "\n";
}
}
}
#line 1 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite-3.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite
#line 1 "template/template.hpp"
#include<bits/stdc++.h>
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
os << p.first << " " << p.second;
return os;
}
template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
is >> p.first >> p.second;
return is;
}
template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
for(int i = 0; i < (int) v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
for(T &in : v) is >> in;
return is;
}
template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
template< typename T = int64 >
vector< T > make_v(size_t a) {
return vector< T >(a);
}
template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}
template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
t = v;
}
template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
for(auto &e : t) fill_v(e, v);
}
template< typename F >
struct FixPoint : F {
explicit FixPoint(F &&f) : F(forward< F >(f)) {}
template< typename... Args >
decltype(auto) operator()(Args &&... args) const {
return F::operator()(*this, forward< Args >(args)...);
}
};
template< typename F >
inline decltype(auto) MFP(F &&f) {
return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite-3.test.cpp"
#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 "math/combinatorics/montgomery-mod-int.hpp"
template< uint32_t mod_, bool fast = false >
struct MontgomeryModInt {
private:
using mint = MontgomeryModInt;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod_;
for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod_) % mod_;
static_assert(r * mod_ == 1, "invalid, r * mod != 1");
static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");
u32 x;
public:
MontgomeryModInt(): x{} {}
MontgomeryModInt(const i64 &a)
: x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}
static constexpr u32 reduce(const u64 &b) {
return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
}
mint &operator+=(const mint &p) {
if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
return *this;
}
mint &operator-=(const mint &p) {
if (i32(x -= p.x) < 0) x += 2 * mod();
return *this;
}
mint &operator*=(const mint &p) {
x = reduce(u64(x) * p.x);
return *this;
}
mint &operator/=(const mint &p) {
*this *= p.inv();
return *this;
}
mint operator-() const { return mint() - *this; }
mint operator+(const mint &p) const { return mint(*this) += p; }
mint operator-(const mint &p) const { return mint(*this) -= p; }
mint operator*(const mint &p) const { return mint(*this) *= p; }
mint operator/(const mint &p) const { return mint(*this) /= p; }
bool operator==(const mint &p) const {
return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
}
bool operator!=(const mint &p) const {
return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
}
u32 val() const {
u32 ret = reduce(x);
return ret >= mod() ? ret - mod() : ret;
}
mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
mint inv() const {
return pow(mod() - 2);
}
friend ostream &operator<<(ostream &os, const mint &p) {
return os << p.val();
}
friend istream &operator>>(istream &is, mint &a) {
i64 t;
is >> t;
a = mint(t);
return is;
}
static constexpr u32 mod() { return mod_; }
};
template< uint32_t mod >
using modint = MontgomeryModInt< mod >;
using modint998244353 = modint< 998244353 >;
using modint1000000007 = modint< 1000000007 >;
#line 3 "structure/develop/vertex-set-path-composite.hpp"
/**
* @brief Vertex Set Path Composite
*/
using T = modint998244353;
// 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 {
T a, b; // ax+b
T a_sum_p, b_sum_p;
T a_sum_c, b_sum_c;
// 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() : a_sum_p{1}, b_sum_p{0}, a_sum_c{1}, b_sum_c{0} {}
// 初期化
Info(T a, T b) : a(a), b(b) {}
// 反転
void toggle() {
swap(a_sum_p, a_sum_c);
swap(b_sum_p, b_sum_c);
}
// 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) {
a_sum_p = p.a_sum_p * a * c.a_sum_p;
b_sum_p = (p.b_sum_p * a + b) * c.a_sum_p + c.b_sum_p;
a_sum_c = c.a_sum_c * a * p.a_sum_c;
b_sum_c = (c.b_sum_c * a + b) * p.a_sum_c + p.b_sum_c;
}
// 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 6 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite-3.test.cpp"
int main() {
int N, Q;
cin >> N >> Q;
LCT lct;
vector< LCT::NP > vs(N);
for(int i = 0; i < N; i++) {
T a, b;
cin >> a >> b;
vs[i] = lct.alloc({a, b});
}
for(int i = 1; i < N; i++) {
int a, b;
cin >> a >> b;
lct.evert(vs[a]);
lct.link(vs[a], vs[b]);
}
while(Q--) {
int t;
cin >> t;
if(t == 0) {
int u, v, w, x;
cin >> u >> v >> w >> x;
lct.evert(vs[u]);
lct.cut(vs[v]);
lct.evert(vs[w]);
lct.link(vs[w], vs[x]);
} else if(t == 1) {
int p;
T c, d;
cin >> p >> c >> d;
lct.set_key(vs[p], {c, d});
} else {
int u, v;
T x;
cin >> u >> v >> x;
auto info = lct.query_path(vs[u], vs[v]);
cout << info.a_sum_p * x + info.b_sum_p << "\n";
}
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | example_00 | AC | 6 ms | 4 MB |
g++ | example_01 | AC | 6 ms | 4 MB |
g++ | max_random_00 | AC | 773 ms | 26 MB |
g++ | max_random_01 | AC | 761 ms | 27 MB |
g++ | max_random_02 | AC | 779 ms | 27 MB |
g++ | medium_00 | AC | 7 ms | 4 MB |
g++ | medium_01 | AC | 6 ms | 4 MB |
g++ | medium_02 | AC | 6 ms | 4 MB |
g++ | medium_03 | AC | 6 ms | 4 MB |
g++ | medium_04 | AC | 7 ms | 4 MB |
g++ | random_00 | AC | 486 ms | 18 MB |
g++ | random_01 | AC | 556 ms | 21 MB |
g++ | random_02 | AC | 289 ms | 10 MB |
g++ | random_03 | AC | 341 ms | 22 MB |
g++ | random_04 | AC | 174 ms | 5 MB |
g++ | small_00 | AC | 6 ms | 4 MB |
g++ | small_01 | AC | 6 ms | 4 MB |
g++ | small_02 | AC | 6 ms | 4 MB |
g++ | small_03 | AC | 6 ms | 4 MB |
g++ | small_04 | AC | 6 ms | 4 MB |
clang++ | example_00 | AC | 6 ms | 4 MB |
clang++ | example_01 | AC | 6 ms | 4 MB |
clang++ | max_random_00 | AC | 798 ms | 27 MB |
clang++ | max_random_01 | AC | 804 ms | 27 MB |
clang++ | max_random_02 | AC | 768 ms | 27 MB |
clang++ | medium_00 | AC | 7 ms | 4 MB |
clang++ | medium_01 | AC | 6 ms | 4 MB |
clang++ | medium_02 | AC | 6 ms | 4 MB |
clang++ | medium_03 | AC | 6 ms | 4 MB |
clang++ | medium_04 | AC | 7 ms | 4 MB |
clang++ | random_00 | AC | 511 ms | 18 MB |
clang++ | random_01 | AC | 572 ms | 21 MB |
clang++ | random_02 | AC | 296 ms | 10 MB |
clang++ | random_03 | AC | 348 ms | 22 MB |
clang++ | random_04 | AC | 179 ms | 6 MB |
clang++ | small_00 | AC | 6 ms | 4 MB |
clang++ | small_01 | AC | 6 ms | 4 MB |
clang++ | small_02 | AC | 6 ms | 4 MB |
clang++ | small_03 | AC | 6 ms | 4 MB |
clang++ | small_04 | AC | 6 ms | 4 MB |