結果
| 問題 | No.2116 Making Forest Hard |
| ユーザー |
 bayashiko
|
| 提出日時 | 2022-10-26 22:04:28 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 13,115 bytes |
| コンパイル時間 | 6,784 ms |
| コンパイル使用メモリ | 310,256 KB |
| 実行使用メモリ | 100,036 KB |
| 最終ジャッジ日時 | 2023-09-17 15:16:52 |
| 合計ジャッジ時間 | 21,899 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge13 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 17 ms
18,976 KB |
| testcase_01 | AC | 17 ms
18,896 KB |
| testcase_02 | AC | 2,994 ms
92,952 KB |
| testcase_03 | AC | 1,586 ms
89,928 KB |
| testcase_04 | TLE | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
| testcase_46 | -- | - |
| testcase_47 | -- | - |
| testcase_48 | -- | - |
| testcase_49 | -- | - |
| testcase_50 | -- | - |
| testcase_51 | -- | - |
| testcase_52 | -- | - |
| testcase_53 | -- | - |
| testcase_54 | -- | - |
ソースコード
#if defined(LOCAL)
#include<stdc++.h>
#else
#include<bits/stdc++.h>
#endif
#include<random>
#pragma GCC optimize("Ofast")
//#pragma GCC target("avx2")
#pragma GCC optimize("unroll-loops")
using namespace std;
//#include<boost/multiprecision/cpp_int.hpp>
//#include<boost/multiprecision/cpp_dec_float.hpp>
//namespace mp=boost::multiprecision;
//#define mulint mp::cpp_int
//#define mulfloat mp::cpp_dec_float_100
struct __INIT{__INIT(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}} __init;
//#define INF (1<<30)
#define LINF (lint)(1LL<<56)
#define MINF (lint)(2e18)
#define endl "\n"
#define rep(i,n) for(lint (i)=0;(i)<(n);(i)++)
#define reprev(i,n) for(lint (i)=(n-1);(i)>=0;(i)--)
#define flc(x) __builtin_popcountll(x)
#define pint pair<int,int>
#define pdouble pair<double,double>
#define plint pair<lint,lint>
#define fi first
#define se second
#define all(x) x.begin(),x.end()
//#define vec vector<lint>
#define nep(x) next_permutation(all(x))
typedef long long lint;
int dx[8]={1,1,0,-1,-1,-1,0,1};
int dy[8]={0,1,1,1,0,-1,-1,-1};
const int MAX_N=3e5+5;
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}return 0;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return 1;}return 0;}
//vector<int> bucket[MAX_N/1000];
//constexpr int MOD=1000000007;
constexpr int MOD=998244353;
#include<atcoder/all>
using namespace atcoder;
typedef __int128_t llint;
using mint=modint998244353;
vector<int> rs;
//https://github.com/NachiaVivias/cp-library
//https://judge.yosupo.jp/submission/77455
struct SplayTreeByIdx{
struct S{mint dp1,dp2,dp1key,dp2key;};
static S op(S l, S r){ return {l.dp1+r.dp1,l.dp2+r.dp2,l.dp1key+r.dp1key,l.dp2key+r.dp2key}; }
static S e(){ return {0,0,0,0}; }
struct F{mint mt00,mt01,mt10,mt11; };
static S mapping(F f, S x){ return { f.mt00*x.dp1+f.mt01*x.dp2,f.mt10*x.dp1+f.mt11*x.dp2,f.mt00*x.dp1key+f.mt01*x.dp2key,f.mt10*x.dp1key+f.mt11*x.dp2key};}
static F composition(F f, F x){ return { f.mt00*x.mt00+f.mt01*x.mt10,f.mt00*x.mt01+f.mt01*x.mt11,f.mt10*x.mt00+f.mt11*x.mt10,f.mt10*x.mt01+f.mt11*x.mt11}; }
static F id(){ return {1,0,0,1}; }
struct Node{
Node *l = 0, *r = 0, *p = 0;
S a = e();
S prod = e();
F f = id();
bool propagated = true;
int z = 0;
int sumz = 0;
int rev = 0;
};
Node *NIL = nullptr;
Node *R;
void prepareDown(Node* c){
if(!c->propagated){
if(c->l != NIL){
c->l->a = mapping(c->f, c->l->a);
c->l->prod = mapping(c->f, c->l->prod);
c->l->f = composition(c->f, c->l->f);
c->l->propagated = false;
}
if(c->r != NIL){
c->r->a = mapping(c->f, c->r->a);
c->r->prod = mapping(c->f, c->r->prod);
c->r->f = composition(c->f, c->r->f);
c->r->propagated = false;
}
c->f = id();
c->propagated = true;
}
if(c->rev){
swap(c->l, c->r);
if(c->l != NIL) c->l->rev ^= 1;
if(c->r != NIL) c->r->rev ^= 1;
c->rev = 0;
}
}
void prepareUp(Node* c){
c->sumz = c->l->sumz + c->r->sumz + 1;
c->prod = op(op(c->l->prod,c->a),c->r->prod);
}
SplayTreeByIdx(){
if(!NIL){
NIL = new Node();
NIL->l = NIL->r = NIL->p = NIL;
R = NIL;
}
}
Node*& parentchild(Node* p){
if(p->p == NIL) return R;
if(p->p->l == p) return p->p->l;
else return p->p->r;
}
void rotL(Node* c){
Node* p = c->p;
parentchild(p) = c;
c->p = p->p;
p->p = c;
if(c->l != NIL) c->l->p = p;
p->r = c->l;
c->l = p;
}
void rotR(Node* c){
Node* p = c->p;
parentchild(p) = c;
c->p = p->p;
p->p = c;
if(c->r != NIL) c->r->p = p;
p->l = c->r;
c->r = p;
}
void splay(Node* c){
while(c->p != NIL){
Node* p = c->p;
Node* pp = p->p;
if(p->l == c){
if(pp == NIL){ rotR(c); }
else if(pp->l == p){ rotR(p); rotR(c); }
else if(pp->r == p){ rotR(c); rotL(c); }
}
else{
if(pp == NIL){ rotL(c); }
else if(pp->r == p){ rotL(p); rotL(c); }
else if(pp->l == p){ rotL(c); rotR(c); }
}
if(pp != NIL) prepareUp(pp);
if(p != NIL) prepareUp(p);
}
prepareUp(c);
}
Node* kth_element(int k){
if(k >= R->sumz) return NIL;
Node* c = R;
while(true){
prepareDown(c);
auto cl = c->l;
if(cl->sumz == k) break;
if(cl->sumz > k){ c = cl; continue; }
k -= cl->sumz + 1;
c = c->r;
}
prepareDown(c);
splay(c);
return c;
}
Node* insert_at(int k, S x){
Node* nx = new Node(*NIL);
nx->z = nx->sumz = 1;
nx->a = nx->prod = x;
if(k == R->sumz){
nx->l = R;
if(R != NIL) R->p = nx;
R = nx;
prepareUp(nx);
return nx;
}
auto p = kth_element(k);
nx->l = p->l;
nx->r = p;
R = nx;
if(p->l != NIL){
prepareDown(p->l);
p->l->p = nx;
}
p->p = nx;
p->l = NIL;
prepareUp(p);
prepareUp(nx);
return nx;
}
void erase_at(int k){
if(k >= R->sumz) return;
auto toerase = NIL;
if(k == 0){
kth_element(0);
prepareDown(R);
toerase = R;
R = R->r;
if(R != NIL) R->p = NIL;
}
else{
kth_element(k-1);
prepareDown(R);
auto c = R->r;
prepareDown(c);
while(c->l != NIL){
c = c->l;
prepareDown(c);
}
auto p = c->p;
toerase = c;
parentchild(c) = c->r;
if(c->r != NIL) c->r->p = p;
splay(p);
//delete p;
}
}
Node* between(int l, int r){
if(l >= r) return NIL;
if(l == 0 && r == R->sumz) return R;
if(l == 0) return kth_element(r)->l;
if(r == R->sumz) return kth_element(l-1)->r;
auto lp = kth_element(l-1);
auto rp = kth_element(r);
while(rp->l != lp){
auto p = lp->p;
prepareDown(p);
prepareDown(lp);
if(p->l == lp) rotR(lp);
else rotL(lp);
prepareUp(p);
prepareUp(lp);
}
return lp->r;
}
void reverse(int l, int r){
if(l >= r) return;
auto c = between(l,r);
c->rev ^= 1;
prepareDown(c);
splay(c);
}
void apply(int l, int r, F f){
if(l >= r) return;
auto c = between(l,r);
c->a = mapping(f,c->a);
c->prod = mapping(f,c->prod);
c->f = composition(f,c->f);
c->propagated = false;
prepareDown(c);
splay(c);
}
S prod(int l, int r){
if(l >= r) return e();
return between(l,r)->prod;
}
void del(Node* tmp){
if(tmp->l!=NIL) del(tmp->l);
if(tmp->r!=NIL) del(tmp->r);
delete tmp;
}
void clear(){
while(R->p!=NIL) R = R->p;
del(R);
}
};
template<typename U = unsigned, int B = 32>
class lazy_binary_trie {
struct node {
int cnt;
U lazy;
node *ch[2];
node() : cnt(0), lazy(0), ch{ nullptr, nullptr } {}
};
void push(node* t, int b) {
if ((t->lazy >> (U)b) & (U)1) swap(t->ch[0], t->ch[1]);
if (t->ch[0]) t->ch[0]->lazy ^= t->lazy;
if (t->ch[1]) t->ch[1]->lazy ^= t->lazy;
t->lazy = 0;
}
node* add(node* t, U val, int b = B - 1) {
if (!t) t = new node;
t->cnt += 1;
if (b < 0) return t;
push(t, b);
bool f = (val >> (U)b) & (U)1;
t->ch[f] = add(t->ch[f], val, b - 1);
return t;
}
node* sub(node* t, U val, int b = B - 1) {
assert(t);
t->cnt -= 1;
if (t->cnt == 0){
delete t;
return nullptr;
}
if (b < 0) return t;
push(t, b);
bool f = (val >> (U)b) & (U)1;
t->ch[f] = sub(t->ch[f], val, b - 1);
return t;
}
U get_min(node* t, U val, int b = B - 1) {
assert(t);
if (b < 0) return 0;
push(t, b);
bool f = (val >> (U)b) & (U)1; f ^= !t->ch[f];
return get_min(t->ch[f], val, b - 1) | ((U)f << (U)b);
}
U get(node* t, int k, int b = B - 1) {
if (b < 0) return 0;
push(t, b);
int m = t->ch[0] ? t->ch[0]->cnt : 0;
return k < m ? get(t->ch[0], k, b - 1) : get(t->ch[1], k - m, b - 1) | ((U)1 << (U)b);
}
int count_lower(node* t, U val, int b = B - 1) {
if (!t || b < 0) return 0;
push(t, b);
bool f = (val >> (U)b) & (U)1;
return (f && t->ch[0] ? t->ch[0]->cnt : 0) + count_lower(t->ch[f], val, b - 1);
}
node *root;
public:
lazy_binary_trie() : root(nullptr) {}
int size() const {
return root ? root->cnt : 0;
}
bool empty() const {
return !root;
}
void insert(U val) {
root = add(root, val);
}
void erase(U val) {
root = sub(root, val);
}
void xor_all(U val) {
if (root) root->lazy ^= val;
}
U max_element(U bias = 0) {
return get_min(root, ~bias);
}
U min_element(U bias = 0) {
return get_min(root, bias);
}
int lower_bound(U val) { // return id
return count_lower(root, val);
}
int upper_bound(U val) { // return id
return count_lower(root, val + 1);
}
U operator[](int k) {
assert(0 <= k && k < size());
return get(root, k);
}
U at(int k) {
assert(0 <= k && k < size());
return get(root, k);
}
int count(U val) {
if (!root) return 0;
node *t = root;
for (int i = B - 1; i >= 0; i--) {
push(t, i);
t = t->ch[(val >> (U)i) & (U)1];
if (!t) return 0;
}
return t->cnt;
}
void del(node *t){
if(t->ch[0]!=nullptr) del(t->ch[0]);
if(t->ch[1]!=nullptr) del(t->ch[1]);
delete t;
}
void clear(){
node *t=root;
if(t->ch[0]!=nullptr) del(t->ch[0]);
if(t->ch[1]!=nullptr) del(t->ch[1]);
delete t;
}
};
SplayTreeByIdx dp[100005];
vector<SplayTreeByIdx*> dp_pt;
mint ans=0;
int N;
vector<int> edge[100005];
int sub_size[100005];
mint pow2[100005];
lint A[100005];
int pt[100005];
vector<lazy_binary_trie<int,17>> bt(100000);
vector<lazy_binary_trie<int,17>*> bt_pt(100000);
bool merge(int left,int right){
int rev=false;
swap(dp_pt[left],dp_pt[right]),swap(bt_pt[left],bt_pt[right]),rev=true;
vector<SplayTreeByIdx::S> adds;
int N=bt_pt[right]->size();
rep(i,N){ //key未満
SplayTreeByIdx::S now=dp_pt[right]->prod(i,i+1);
int key=bt_pt[right]->at(i);
int hi=bt_pt[left]->lower_bound(key);
SplayTreeByIdx::S lo_sum=dp_pt[left]->prod(0,hi);
mint dp1=now.dp1*lo_sum.dp1;
mint dp2=now.dp1*lo_sum.dp2+now.dp2*lo_sum.dp1;
mint dp1_key=dp1*rs[key];
mint dp2_key=dp2*rs[key];
adds.push_back({dp1,dp2,dp1_key,dp2_key});
}
int before=0;
mint sum[2];
rep(i,N){
SplayTreeByIdx::S now=dp_pt[right]->prod(i,i+1);
int key=bt_pt[right]->at(i);
int hi=bt_pt[left]->lower_bound(key);
if(before!=hi){
dp_pt[left]->apply(before,hi,{sum[0],0,sum[1],sum[0]});
}
sum[0]+=now.dp1,sum[1]+=now.dp2;
before=hi;
}
if(before!=bt_pt[left]->size()){
dp_pt[left]->apply(before,bt_pt[left]->size(),{sum[0],0,sum[1],sum[0]});
}
int idx=0;
for(auto e:adds){
int key=bt_pt[right]->at(idx);
int hi=bt_pt[left]->lower_bound(key);
if(bt_pt[left]->count(key)){
SplayTreeByIdx::S res=dp_pt[left]->prod(hi,hi+1);
res.dp1+=e.dp1,res.dp2+=e.dp2,res.dp1key+=e.dp1key,res.dp2key+=e.dp2key;
dp_pt[left]->erase_at(hi);
dp_pt[left]->insert_at(hi,res);
}
else{
dp_pt[left]->insert_at(hi,e);
bt_pt[left]->insert(key);
}
idx++;
}
return rev;
}
void dfs(int now,int par){
for(auto e:edge[now]){
if(e==par) continue;
dfs(e,now);
sub_size[now]+=sub_size[e];
if(bt_pt[e]->count(0)){
SplayTreeByIdx::S zero=dp_pt[e]->prod(0,1);
dp_pt[e]->erase_at(0);
zero.dp1+=pow2[sub_size[e]-1];
dp_pt[e]->insert_at(0,zero);
}
else{
dp_pt[e]->insert_at(0,{pow2[sub_size[e]-1],0,0,0});
bt_pt[e]->insert(0);
}
merge(now,e);
bt_pt[e]->clear();
dp_pt[e]->clear();
}
ans+=dp_pt[now]->prod(0,bt_pt[now]->size()).dp2key*pow2[N-1-sub_size[now]+(now==0)];
}
int main(void){
cin >> N;
rep(i,N) cin >> A[i];
vector<int> as;
rep(i,N) as.push_back(A[i]);
sort(all(as));
rs.push_back(0);
int pre=-1;
rep(i,N) if(pre!=as[i]) rs.push_back(as[i]),pre=as[i];
rep(i,N) sub_size[i]=1;
pow2[0]=1;
rep(i,100004) pow2[i+1]=pow2[i]*2;
rep(i,100004) pt[i]=i;
rep(i,N) bt_pt[i]=&bt[i];
rep(i,N){
dp[i].insert_at(0,{1,1,A[i],A[i]});
bt_pt[i]->insert(lower_bound(all(rs),A[i])-rs.begin());
dp_pt.push_back(&dp[i]);
}
rep(i,N-1){
int u,v;
cin >> u >> v;
u--,v--;
edge[u].push_back(v);
edge[v].push_back(u);
}
dfs(0,-1);
cout << ans.val() << endl;
}