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/splay-tree-base.hpp"
#include "../../structure/develop/reversible-splay-tree.hpp"
#include "../../structure/develop/link-cut-tree.hpp"
#include "../../math/combinatorics/montgomery-mod-int.hpp"
using mint = modint998244353;
int main() {
int N, Q;
cin >> N >> Q;
using pi = pair< mint, mint >;
using pii = pair< pi, pi >;
using LCT = LinkCutTree< RST< pair< pi, pi > > >;
auto f = [](const pi &x, const pi &y) { return pi(x.first * y.first, x.second * y.first + y.second); };
auto ff = [&](const pii &a, const pii &b) { return pii(f(a.first, b.first), f(b.second, a.second)); };
auto flip = [&](const pii &a) { return pii(a.second, a.first); };
LCT lct(ff, flip, pii());
vector< LCT::Node * > vs(N);
for(int i = 0; i < N; i++) {
mint x, y;
cin >> x >> y;
vs[i] = lct.alloc(pii(pi(x, y), pi(x, y)));
}
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;
mint a, b;
cin >> P >> a >> b;
lct.expose(vs[P]);
vs[P]->key = pii(pi(a, b), pi(a, b));
lct.update(vs[P]);
} else {
int U, V;
mint X;
cin >> U >> V >> X;
lct.evert(vs[U]);
lct.expose(vs[V]);
auto ret = vs[V]->sum.first;
cout << ret.first * X + ret.second << "\n";
}
}
}
#line 1 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite-2.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-2.test.cpp"
#line 1 "structure/develop/splay-tree-base.hpp"
/**
* @brief Splay-Tree-Base(Splay木)
*/
template< typename Node >
struct SplayTreeBase {
public:
using NP = Node *;
bool is_root(const NP &t) const { return !t->p || (t->p->l != t && t->p->r != t); }
inline size_t count(const NP &t) const { return t ? t->sz : 0; }
void splay(NP t) {
push(t);
while(!is_root(t)) {
auto *q = t->p;
if(!is_root(t)) {
push(q), push(t);
if(q->l == t) rotr(t);
else rotl(t);
} else {
auto *r = q->p;
push(r), push(q), push(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 erase(NP t) {
splay(t);
Node *x = t->l, *y = t->r;
delete t;
if(!x) {
t = y;
if(t) t->p = nullptr;
} else if(!y) {
t = x;
t->p = nullptr;
} else {
x->p = nullptr;
t = get_right(x);
splay(t);
t->r = y;
y->p = t;
}
return t;
}
NP splay_front(NP t) {
splay(t);
while(t->l) t = t->l;
splay(t);
return t;
}
NP splay_back(NP t) {
splay(t);
while(t->r) t = t->r;
splay(t);
return t;
}
pair< NP, NP > split(NP t, int k) {
if(!t) return {nullptr, nullptr};
push(t);
if(k <= count(t->l)) {
auto x = split(t->l, k);
t->l = x.second;
t->p = nullptr;
if(x.second) x.second->p = t;
return {x.first, update(t)};
} else {
auto x = split(t->r, k - count(t->l) - 1);
t->r = x.first;
t->p = nullptr;
if(x.first) x.first->p = t;
return {update(t), x.second};
}
}
template< typename... Args >
NP merge(NP p, Args... args) {
return merge(p, merge(args...));
}
NP merge(NP l, NP r) {
if(!l && !r) return nullptr;
if(!l) return splay(r), r;
if(!r) return splay(l), l;
splay(l), splay(r);
l = splay_back(l);
l->r = r;
r->p = l;
update(l);
return l;
}
tuple< NP, NP, NP > split3(NP t, int a, int b) {
splay(t);
auto x = split(t, a);
auto y = split(x.second, b - a);
return make_tuple(x.first, y.first, y.second);
}
virtual void push(NP t) = 0;
virtual Node *update(NP t) = 0;
private:
void rotr(NP t) {
auto *x = t->p, *y = x->p;
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;
update(y);
}
}
void rotl(NP t) {
auto *x = t->p, *y = x->p;
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;
update(y);
}
}
NP build(int l, int r, const vector< NP > &v) {
if(l + 1 >= r) return v[l];
return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
}
protected:
NP build_node(const vector< NP > &v) {
return build(0, v.size(), v);
}
NP insert_node(NP t, int k, NP v) {
splay(t);
auto x = split(t, k);
return merge(x.first, v, x.second);
}
NP erase_node(NP t, int k) {
splay(t);
auto x = split(t, k);
auto y = split(x.second, 1);
delete y.first;
return merge(x.first, y.second);
}
};
#line 1 "structure/develop/reversible-splay-tree.hpp"
/**
* @brief Reversible-Splay-Tree(反転可能Splay木)
*/
template< typename Tp >
struct ReversibleSplayTreeNode {
using T = Tp;
ReversibleSplayTreeNode *l, *r, *p;
T key, sum;
bool rev;
size_t sz;
ReversibleSplayTreeNode() : ReversibleSplayTreeNode(Tp()) {}
ReversibleSplayTreeNode(const T &key) :
key(key), sum(key), rev(false), l(nullptr), r(nullptr), p(nullptr), sz(1) {}
};
template< typename Np >
struct ReversibleSplayTree : SplayTreeBase< Np > {
public:
using Node = Np;
using T = typename Node::T;
using F = function< T(T, T) >;
using S = function< T(T) >;
using super = SplayTreeBase< Node >;
using NP = typename super::NP;
explicit ReversibleSplayTree(const F &f, const S &s, const T &M1) :
f(f), s(s), M1(M1) {}
using super::splay;
using super::split;
using super::count;
using super::merge;
using super::build_node;
using super::insert_node;
inline const T &sum(const NP t) { return t ? t->sum : M1; }
NP alloc(const T &x) { return new Node(x); }
T query(NP &t, int a, int b) {
splay(t);
auto x = split(t, a);
auto y = split(x.second, b - a);
auto ret = sum(y.first);
t = merge(x.first, y.first, y.second);
return ret;
}
NP build(const vector< T > &v) {
vector< NP > vs(v.size());
for(int i = 0; i < v.size(); i++) vs[i] = alloc(v[i]);
return build_node(vs);
}
void toggle(NP t) {
swap(t->l, t->r);
t->sum = s(t->sum);
t->rev ^= true;
}
NP update(NP t) override {
t->sz = 1;
t->sum = t->key;
if(t->l) t->sz += t->l->sz, t->sum = f(t->l->sum, t->sum);
if(t->r) t->sz += t->r->sz, t->sum = f(t->sum, t->r->sum);
return t;
}
void push(NP t) override {
if(t->rev) {
if(t->l) toggle(t->l);
if(t->r) toggle(t->r);
t->rev = false;
}
}
NP insert(NP t, int k, const T &x) {
return insert_node(t, k, alloc(x));
}
NP set_element(NP t, int k, const T &x) {
splay(t);
return imp_set_element(t, k, x);
}
pair< NP , NP > split_lower_bound(NP t, const T &key) {
if(!t) return {nullptr, nullptr};
push(t);
if(key <= t->key) {
auto x = split_lower_bound(t->l, key);
t->l = x.second;
t->p = nullptr;
if(x.second) x.second->p = t;
return {x.first, update(t)};
} else {
auto x = split_lower_bound(t->r, key);
t->r = x.first;
t->p = nullptr;
if(x.first) x.first->p = t;
return {update(t), x.second};
}
}
private:
const T M1;
const F f;
const S s;
NP imp_set_element(NP t, int k, const T &x) {
push(t);
if(k < count(t->l)) {
return imp_set_element(t->l, k, x);
} else if(k == count(t->l)) {
t->key = x;
splay(t);
return t;
} else {
return imp_set_element(t->r, k - count(t->l) - 1, x);
}
}
};
template< typename T >
using RST = ReversibleSplayTree< ReversibleSplayTreeNode< T > >;
#line 1 "structure/develop/link-cut-tree.hpp"
/**
* @brief Link-Cut-Tree
*/
template< typename STp >
struct LinkCutTree : STp {
using ST = STp;
using ST::ST;
using Node = typename ST::Node;
Node *expose(Node *t) {
Node *rp = nullptr;
for(Node *cur = t; cur; cur = cur->p) {
this->splay(cur);
cur->r = rp;
this->update(cur);
rp = cur;
}
this->splay(t);
return rp;
}
void link(Node *child, Node *parent) {
expose(child);
expose(parent);
child->p = parent;
parent->r = child;
this->update(parent);
}
void cut(Node *child) {
expose(child);
auto *parent = child->l;
child->l = nullptr;
parent->p = nullptr;
this->update(child);
}
void evert(Node *t) {
expose(t);
this->toggle(t);
this->push(t);
}
Node *lca(Node *u, Node *v) {
if(get_root(u) != get_root(v)) return nullptr;
expose(u);
return expose(v);
}
Node *get_kth(Node *x, int k) {
expose(x);
while(x) {
this->push(x);
if(x->r && x->r->sz > k) {
x = x->r;
} else {
if(x->r) k -= x->r->sz;
if(k == 0) return x;
k -= 1;
x = x->l;
}
}
return nullptr;
}
Node *get_root(Node *x) {
expose(x);
while(x->l) {
this->push(x);
x = x->l;
}
return x;
}
};
#line 8 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite-2.test.cpp"
#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 10 "test/verify/yosupo-dynamic-tree-vertex-set-path-composite-2.test.cpp"
using mint = modint998244353;
int main() {
int N, Q;
cin >> N >> Q;
using pi = pair< mint, mint >;
using pii = pair< pi, pi >;
using LCT = LinkCutTree< RST< pair< pi, pi > > >;
auto f = [](const pi &x, const pi &y) { return pi(x.first * y.first, x.second * y.first + y.second); };
auto ff = [&](const pii &a, const pii &b) { return pii(f(a.first, b.first), f(b.second, a.second)); };
auto flip = [&](const pii &a) { return pii(a.second, a.first); };
LCT lct(ff, flip, pii());
vector< LCT::Node * > vs(N);
for(int i = 0; i < N; i++) {
mint x, y;
cin >> x >> y;
vs[i] = lct.alloc(pii(pi(x, y), pi(x, y)));
}
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;
mint a, b;
cin >> P >> a >> b;
lct.expose(vs[P]);
vs[P]->key = pii(pi(a, b), pi(a, b));
lct.update(vs[P]);
} else {
int U, V;
mint X;
cin >> U >> V >> X;
lct.evert(vs[U]);
lct.expose(vs[V]);
auto ret = vs[V]->sum.first;
cout << ret.first * X + ret.second << "\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 | 850 ms | 21 MB |
g++ | max_random_01 | AC | 868 ms | 21 MB |
g++ | max_random_02 | AC | 836 ms | 21 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 | 533 ms | 14 MB |
g++ | random_01 | AC | 614 ms | 16 MB |
g++ | random_02 | AC | 321 ms | 8 MB |
g++ | random_03 | AC | 377 ms | 18 MB |
g++ | random_04 | AC | 194 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 | 806 ms | 21 MB |
clang++ | max_random_01 | AC | 815 ms | 21 MB |
clang++ | max_random_02 | AC | 795 ms | 21 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 | 525 ms | 14 MB |
clang++ | random_01 | AC | 589 ms | 16 MB |
clang++ | random_02 | AC | 305 ms | 8 MB |
clang++ | random_03 | AC | 366 ms | 18 MB |
clang++ | random_04 | AC | 188 ms | 5 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 |