結果
| 問題 |
No.650 行列木クエリ
|
| コンテスト | |
| ユーザー |
 butsurizuki
|
| 提出日時 | 2024-05-07 02:20:18 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 247 ms / 2,000 ms |
| コード長 | 16,574 bytes |
| コンパイル時間 | 4,121 ms |
| コンパイル使用メモリ | 283,124 KB |
| 実行使用メモリ | 71,808 KB |
| 最終ジャッジ日時 | 2024-11-29 14:34:16 |
| 合計ジャッジ時間 | 6,273 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 10 |
ソースコード
#include<bits/stdc++.h>
#include <algorithm>
#include <cassert>
#include <functional>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#if __cplusplus >= 202002L
#include <bit>
#endif
namespace atcoder {
namespace internal {
#if __cplusplus >= 202002L
using std::bit_ceil;
#else
unsigned int bit_ceil(unsigned int n) {
unsigned int x = 1;
while (x < (unsigned int)(n)) x *= 2;
return x;
}
#endif
int countr_zero(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
constexpr int countr_zero_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
} // namespace internal
} // namespace atcoder
namespace atcoder {
#if __cplusplus >= 201703L
template <class S, auto op, auto e> struct segtree {
static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
"op must work as S(S, S)");
static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
"e must work as S()");
#else
template <class S, S (*op)(S, S), S (*e)()> struct segtree {
#endif
public:
segtree() : segtree(0) {}
explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
size = (int)internal::bit_ceil((unsigned int)(_n));
log = internal::countr_zero((unsigned int)size);
d = std::vector<S>(2 * size, e());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) const {
assert(0 <= p && p < _n);
return d[p + size];
}
S prod(int l, int r) const {
assert(0 <= l && l <= r && r <= _n);
S sml = e(), smr = e();
l += size;
r += size;
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() const { return d[1]; }
template <bool (*f)(S)> int max_right(int l) const {
return max_right(l, [](S x) { return f(x); });
}
template <class F> int max_right(int l, F f) const {
assert(0 <= l && l <= _n);
assert(f(e()));
if (l == _n) return _n;
l += size;
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(op(sm, d[l]))) {
while (l < size) {
l = (2 * l);
if (f(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
template <bool (*f)(S)> int min_left(int r) const {
return min_left(r, [](S x) { return f(x); });
}
template <class F> int min_left(int r, F f) const {
assert(0 <= r && r <= _n);
assert(f(e()));
if (r == 0) return 0;
r += size;
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(op(d[r], sm))) {
while (r < size) {
r = (2 * r + 1);
if (f(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
std::vector<S> d;
void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};
} // namespace atcoder
#include <algorithm>
#include <cassert>
#include <functional>
#include <vector>
namespace atcoder {
#if __cplusplus >= 201703L
template <class S,
auto op,
auto e,
class F,
auto mapping,
auto composition,
auto id>
struct lazy_segtree {
static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
"op must work as S(S, S)");
static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
"e must work as S()");
static_assert(
std::is_convertible_v<decltype(mapping), std::function<S(F, S)>>,
"mapping must work as F(F, S)");
static_assert(
std::is_convertible_v<decltype(composition), std::function<F(F, F)>>,
"compostiion must work as F(F, F)");
static_assert(std::is_convertible_v<decltype(id), std::function<F()>>,
"id must work as F()");
#else
template <class S,
S (*op)(S, S),
S (*e)(),
class F,
S (*mapping)(F, S),
F (*composition)(F, F),
F (*id)()>
struct lazy_segtree {
#endif
public:
lazy_segtree() : lazy_segtree(0) {}
explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
size = (int)internal::bit_ceil((unsigned int)(_n));
log = internal::countr_zero((unsigned int)size);
d = std::vector<S>(2 * size, e());
lz = std::vector<F>(size, id());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return e();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
S sml = e(), smr = e();
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() { return d[1]; }
void apply(int p, F f) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = mapping(f, d[p]);
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int l, int r, F f) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
template <bool (*g)(S)> int max_right(int l) {
return max_right(l, [](S x) { return g(x); });
}
template <class G> int max_right(int l, G g) {
assert(0 <= l && l <= _n);
assert(g(e()));
if (l == _n) return _n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!g(op(sm, d[l]))) {
while (l < size) {
push(l);
l = (2 * l);
if (g(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
template <bool (*g)(S)> int min_left(int r) {
return min_left(r, [](S x) { return g(x); });
}
template <class G> int min_left(int r, G g) {
assert(0 <= r && r <= _n);
assert(g(e()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!g(op(d[r], sm))) {
while (r < size) {
push(r);
r = (2 * r + 1);
if (g(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
std::vector<S> d;
std::vector<F> lz;
void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
void all_apply(int k, F f) {
d[k] = mapping(f, d[k]);
if (k < size) lz[k] = composition(f, lz[k]);
}
void push(int k) {
all_apply(2 * k, lz[k]);
all_apply(2 * k + 1, lz[k]);
lz[k] = id();
}
};
} // namespace atcoder
using namespace std;
using namespace atcoder;
using Graph=vector<vector<int>>;
using pi=pair<int,int>;
struct HLD{
vector<int> pareg;
vector<int> backeg;
vector<int> dep;
int cureg;
vector<int> topv;
vector<int> tope;
bool vwei; // true: vertex-weighted, false: edge-weighted
HLD(int n,Graph &g,bool vw,int root=0){
vwei=vw;
dfs1(root,-1,g);
pareg.resize(n);
backeg.resize(n);
dep.resize(n);
topv.resize(n);
tope.resize(n);
cureg=1;
pareg[root]=0;
topv[0]=-1;
tope[0]=0;
dfs2(root,-1,0,true,g);
}
int dfs1(int v,int pv,Graph &g){
int res=1;
int uid=-1,umax=-1;
for(int i=0;i<g[v].size();i++){
if(g[v][i]==pv){continue;}
int und=dfs1(g[v][i],v,g);
res+=und;
if(umax<und){
umax=und;
uid=i;
}
}
if(uid>0){
swap(g[v][uid],g[v][0]);
}
return res;
}
void dfs2(int v,int pv,int cdep,bool upheav,Graph &g){
dep[v]=cdep;
for(int i=0;i<g[v].size();i++){
if(g[v][i]==pv){continue;}
if(i==0){
// heavy
if(upheav){
topv[cureg]=topv[pareg[v]];
tope[cureg]=tope[pareg[v]];
}
else{
topv[cureg]=v;
tope[cureg]=cureg;
}
pareg[g[v][i]]=cureg;
cureg++;
dfs2(g[v][i],v,cdep+1,true,g);
}
else{
// light
topv[cureg]=v;
tope[cureg]=cureg;
pareg[g[v][i]]=cureg;
cureg++;
dfs2(g[v][i],v,cdep+1,false,g);
}
}
backeg[v]=cureg;
}
// single vertex (for vertex-weighted)
int single(int v){
return pareg[v];
}
// subtree is [l,r]
pi subtree(int v){
if(vwei){
return {pareg[v],backeg[v]-1};
}
else{
return {pareg[v]+1,backeg[v]-1};
}
}
// u->v path is {[l0,r0], [l1,r1], ...}
// each segments may reversed (so li<=ri may NOT be satisfied)
vector<pi> path(int u,int v){
vector<pi> uu;
vector<pi> vv;
while(u!=v){
if(tope[pareg[u]]==tope[pareg[v]]){ // same path
if(dep[u]>dep[v]){
// u goes up
uu.push_back({pareg[u],pareg[u]-(dep[u]-dep[v]-1)});
u=v;
}
else{
// v goes up
vv.push_back({pareg[v],pareg[v]-(dep[v]-dep[u]-1)});
v=u;
}
break;
}
int du=-1;
int dv=-1;
if(topv[pareg[u]]>=0){du=dep[topv[pareg[u]]];}
if(topv[pareg[v]]>=0){dv=dep[topv[pareg[v]]];}
if(du>dv){
// u goes up
uu.push_back({pareg[u],tope[pareg[u]]});
u=topv[pareg[u]];
}
else{
// v goes up
vv.push_back({pareg[v],tope[pareg[v]]});
v=topv[pareg[v]];
}
}
vector<pi> res;
for(auto &nx : uu){
res.push_back(nx);
}
if(vwei){
res.push_back({pareg[u],pareg[u]});
}
reverse(vv.begin(),vv.end());
for(auto &nx : vv){
swap(nx.first,nx.second);
res.push_back(nx);
}
return res;
}
};
long long op_sum(long long a,long long b){
return (a+b);
}
long long e_sum(){
return 0;
}
// https://judge.yosupo.jp/problem/vertex_add_path_sum
void val_yosupo_VAPS(){
int n,q;
cin >> n >> q;
vector<int> a(n);
for(auto &nx : a){cin >> nx;}
Graph g(n);
for(int i=0;i<n-1;i++){
int u,v;
cin >> u >> v;
g[u].push_back(v);
g[v].push_back(u);
}
HLD hld(n,g,true); // vertex-weighted
vector<long long> ini(n,0);
for(int i=0;i<n;i++){
ini[hld.single(i)]=a[i];
}
segtree<long long,op_sum,e_sum> seg(ini);
while(q>0){
q--;
int typ;
cin >> typ;
if(typ==0){
int u;
long long x;
cin >> u >> x;
int pos=hld.single(u);
seg.set(pos,seg.get(pos)+x);
}
else{
int u,v;
cin >> u >> v;
vector<pi> ss=hld.path(u,v);
long long res=0;
for(auto &nx : ss){
res+=seg.prod(min(nx.first,nx.second),max(nx.first,nx.second)+1);
}
cout << res << "\n";
}
}
}
#define mod 998244353
using pl=pair<long long,long long>;
pl op_aff(pl l,pl r){
return {
(l.first*r.first)%mod,
(l.second*r.first+r.second)%mod
};
}
pl e_aff(){return {1,0};}
// https://judge.yosupo.jp/problem/vertex_set_path_composite
void val_yosupo_VSPC(){
int n,q;
cin >> n >> q;
vector<pl> a(n);
for(auto &nx : a){
cin >> nx.first >> nx.second;
}
Graph g(n);
for(int i=0;i<n-1;i++){
int u,v;
cin >> u >> v;
g[u].push_back(v);
g[v].push_back(u);
}
HLD hld(n,g,true); // vertex-weighted
vector<pl> ini(2*n);
for(int i=0;i<n;i++){
ini[hld.single(i)]=a[i];
ini[2*n-1-hld.single(i)]=a[i];
}
segtree<pl,op_aff,e_aff> seg(ini);
while(q>0){
q--;
int typ;
cin >> typ;
if(typ==0){
int p;
pl x;
cin >> p >> x.first >> x.second;
seg.set(hld.single(p),x);
seg.set(2*n-1-hld.single(p),x);
}
else{
int u,v;
long long x;
cin >> u >> v >> x;
vector<pi> ss=hld.path(u,v);
pl cf=e_aff();
for(auto &nx : ss){
if(nx.first<=nx.second){
cf=op_aff(cf,seg.prod(nx.first,nx.second+1));
}
else{
cf=op_aff(cf,seg.prod((2*n-1-nx.first),(2*n-1-nx.second)+1));
}
}
cout << (x*cf.first+cf.second)%mod << "\n";
}
}
}
#define mod107 1000000007
using vl=vector<long long>;
vl op_mat2(vl l,vl r){
return {
(l[0]*r[0]+l[1]*r[2])%mod107,
(l[0]*r[1]+l[1]*r[3])%mod107,
(l[2]*r[0]+l[3]*r[2])%mod107,
(l[2]*r[1]+l[3]*r[3])%mod107
};
}
vl e_mat2(){
return {1,0,0,1};
}
void val_ykc_650(){
int n;
cin >> n;
Graph g(n);
vector<int> uu(n-1),vv(n-1);
for(int i=0;i<n-1;i++){
int u,v;
cin >> u >> v;
g[u].push_back(v);
g[v].push_back(u);
uu[i]=u;
vv[i]=v;
}
HLD hld(n,g,false);
segtree<vl,op_mat2,e_mat2> seg(2*n);
int q;
cin >> q;
while(q>0){
q--;
string typ;
cin >> typ;
if(typ[0]=='x'){
int i;
cin >> i;
if(hld.dep[uu[i]]<hld.dep[vv[i]]){
swap(uu[i],vv[i]);
}
int eid=hld.pareg[uu[i]];
vl x=e_mat2();
for(auto &nx : x){cin >> nx;}
seg.set(eid,x);
seg.set(2*n-1-eid,x);
}
else{
int u,v;
cin >> u >> v;
vector<pi> pt=hld.path(u,v);
vl x=e_mat2();
for(auto &nx : pt){
if(nx.first<=nx.second){
x=op_mat2(x,seg.prod(nx.first,nx.second+1));
}
else{
x=op_mat2(x,seg.prod(2*n-1-nx.first,(2*n-1-nx.second)+1));
}
}
cout << x[0] << " ";
cout << x[1] << " ";
cout << x[2] << " ";
cout << x[3] << "\n";
}
}
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
// val_yosupo_VAPS();
// val_yosupo_VSPC();
val_ykc_650();
return 0;
}