結果

問題 No.2377 SUM AND XOR on Tree
ユーザー eQe
提出日時 2025-01-26 02:44:07
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,495 ms / 4,000 ms
コード長 8,585 bytes
コンパイル時間 7,724 ms
コンパイル使用メモリ 331,728 KB
実行使用メモリ 33,908 KB
最終ジャッジ日時 2025-01-26 02:44:37
合計ジャッジ時間 30,009 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 33
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
namespace my{
using ml=atcoder::modint998244353;
auto&operator>>(istream&i,ml&x){int t;i>>t;x=t;return i;}
auto&operator<<(ostream&o,const ml&x){return o<<(int)x.val();}
#define eb emplace_back
#define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__)
#define VL(n,...) vec<ll>__VA_ARGS__;setsize({n},__VA_ARGS__);lin(__VA_ARGS__)
#define VV(n,...) vec<ll>__VA_ARGS__;setsize({n},__VA_ARGS__);vin(__VA_ARGS__)
#define FO(n) for(ll ij=n;ij-->0;)
#define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);i<i##stop;i+=i##step)
#define fo(i,...) FO##__VA_OPT__(R)(i __VA_OPT__(,__VA_ARGS__))
#define fe(a,i,...) for(auto&&__VA_OPT__([)i __VA_OPT__(,__VA_ARGS__]):a)
#define ef(a,i,...) for(auto&&__VA_OPT__([)i __VA_OPT__(,__VA_ARGS__]):ranges::reverse_view(a))
#define single_testcase void solve();}int main(){my::io();my::solve();}namespace my{
void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<<fixed<<setprecision(15);}
using ll=long long;
using ull=unsigned long long;
using ulll=__uint128_t;
using lll=__int128_t;
istream&operator>>(istream&i,ulll&x){ull t;i>>t;x=t;return i;}
ostream&operator<<(ostream&o,const ulll&x){return(x<10?o:o<<x/10)<<ll(x%10);}
istream&operator>>(istream&i,lll&x){ll t;i>>t;x=t;return i;}
ostream&operator<<(ostream&o,const lll&x){return o<<string(x<0,'-')<<ulll(x>0?x:-x);}
constexpr auto range(bool s,auto...a){array<ll,3>r{0,0,1};ll I=0;((r[I++]=a),...);if(!s&&I==1)swap(r[0],r[1]);r[0]-=s;if(s)r[2]*=-1;return r;}
constexpr char newline=10;
constexpr char space=32;
lll pow(lll x,ll n){assert(n>=0);lll r=1;while(n)n&1?r*=x:r,x*=x,n>>=1;return r;}
constexpr ll width2(auto x){x|=1;ll r=0;while(x>0)x>>=1,++r;return r;}
auto max(auto...a){return max(initializer_list<common_type_t<decltype(a)...>>{a...});}
template<class A,class B>struct pair{
  A a;B b;
  pair()=default;
  pair(A a,B b):a(a),b(b){}
  pair(const std::pair<A,B>&p):a(p.first),b(p.second){}
  auto operator<=>(const pair&)const=default;
  pair operator+(const pair&p)const{return{a+p.a,b+p.b};}
  friend istream&operator>>(istream&i,pair&p){return i>>p.a>>p.b;}
  friend ostream&operator<<(ostream&o,const pair&p){return o<<p.a<<space<<p.b;}
};
template<class T>struct queue:std::queue<T>{
  queue(const initializer_list<T>&a={}){fe(a,e)this->emplace(e);}
  queue(const vector<T>&a){fe(a,e)this->emplace(e);}
  ll size()const{return std::queue<T>::size();}
  T pop(){T r=this->front();std::queue<T>::pop();return r;}
  friend ostream&operator<<(ostream&o,queue q){while(q.size())o<<q.pop()<<string(q.size()>0,space);return o;}
};
template<ll k>auto pack_kth(const auto&...a){return get<k>(make_tuple(a...));}
template<class T,ll n>auto pack_slice(const auto&...a){return[&]<size_t...I>(index_sequence<I...>){return array<T,n>{get<I>(forward_as_tuple(a
    ...))...};}(make_index_sequence<n>{});}
template<class V>concept vectorial=is_base_of_v<vector<typename V::value_type>,V>;
template<class T>struct vec_attr{using core_type=T;static constexpr int rank=0;};
template<vectorial V>struct vec_attr<V>{using core_type=typename vec_attr<typename V::value_type>::core_type;static constexpr int rank=vec_attr
    <typename V::value_type>::rank+1;};
template<class T>using core_t=vec_attr<T>::core_type;
template<class V>istream&operator>>(istream&i,vector<V>&v){fe(v,e)i>>e;return i;}
template<class V>ostream&operator<<(ostream&o,const vector<V>&v){fe(v,e)o<<e<<string(&e!=&v.back(),vectorial<V>?newline:space);return o;}
template<class V>struct vec:vector<V>{
  using vector<V>::vector;
  vec(const vector<V>&v){vector<V>::operator=(v);}
  template<class...A>requires(sizeof...(A)>=3)vec(A...a){const ll n=sizeof...(a)-1;auto t=pack_slice<ll,n>(a...);ll s[n];fo(i,n)s[i]=t[i];*this
      =make_vec(s,pack_kth<n>(a...));}
  template<class T,ll n,ll i=0>static auto make_vec(const ll(&s)[n],T x){if constexpr(i==n-1)return vec<T>(s[i],x);else{auto X=make_vec<T,n,i+1>(s,x
      );return vec<decltype(X)>(s[i],X);}}
  vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;}
  vec operator^(const vec&u)const{return vec{*this}^=u;}
  vec&operator+=(const vec&u){vec&v=*this;fo(i,v.size())v[i]+=u[i];return v;}
  vec&operator-=(const vec&u){vec&v=*this;fo(i,v.size())v[i]-=u[i];return v;}
  vec operator+(const vec&u)const{return vec{*this}+=u;}
  vec operator-(const vec&u)const{return vec{*this}-=u;}
  vec&operator++(){fe(*this,e)++e;return*this;}
  vec&operator--(){fe(*this,e)--e;return*this;}
  vec operator-()const{vec v=*this;fe(v,e)e=-e;return v;}
  ll size()const{return vector<V>::size();}
  auto scan(const auto&f)const{pair<core_t<V>,bool>r{};fe(*this,e)if constexpr(!vectorial<V>)r.b?f(r.a,e),r:r={e,1};else if(auto s=e.scan(f);s.b)r.b
      ?f(r.a,s.a),r:r=s;return r;}
  auto max()const{return scan([](auto&a,const auto&b){a<b?a=b:0;}).a;}
};
template<ll rank,class T>struct tensor_helper{using type=vec<typename tensor_helper<rank-1,T>::type>;};
template<class T>struct tensor_helper<0,T>{using type=T;};
template<ll rank,class T>using tensor=typename tensor_helper<rank,T>::type;
template<class...A>requires(sizeof...(A)>=2)vec(A...a)->vec<tensor<sizeof...(a)-2,remove_reference_t<decltype(get<sizeof...(a)-1>(declval<tuple<A
    ...>>()))>>>;
vec(ll)->vec<ll>;
template<ll n,class...A>void setsize(const ll(&l)[n],A&...a){((a=vec<void*>::make_vec(l,core_t<A>{})),...);}
void lin(auto&...a){(cin>>...>>a);}
void vin(auto&...a){fo(i,(a.size()&...))(cin>>...>>a[i]);}
template<char c=space>void pp(const auto&...a){ll n=sizeof...(a);((cout<<a<<string(--n>0,c)),...);cout<<newline;}
void dec(auto&...a){((--a),...);}
constexpr ll at2ll(auto x,ll i){return x>>i&1;}
template<class WT>struct edge{
  ll from,to;
  WT wt;
  ll id;
  edge()=default;
  edge(ll from,ll to,WT wt=1,ll id=-1):from(from),to(to),wt(wt),id(id){}
  auto operator<=>(const edge&e)const{return wt<=>e.wt;}
  friend ostream&operator<<(ostream&o,const edge&e){return o<<"(to "<<e.to<<", wt "<<e.wt<<",id "<<e.id<<")";}
};
template<class WT>struct graph{
  vec<vec<edge<WT>>>edges;
  graph()=default;
  graph(ll n):edges(n){}
  decltype(auto)operator[](ll i){return edges[i];}
  decltype(auto)operator[](ll i)const{return edges[i];}
  ll size()const{return edges.size();}
  friend ostream&operator<<(ostream&o,const graph&g){
    fo(u,g.size()){
      o<<"from "<<u<<": ";
      fo(j,g[u].size())o<<g[u][j]<<string(j!=g[u].size()-1,space);
      o<<newline;
    }
    return o;
  }
  void add_edges(const vec<ll>&p){fo(i,p.size())if(p[i]!=-1)edges[p[i]].eb(p[i],i,1,i);}
  void add_edges(const vec<ll>&a,const vec<ll>&b){fo(i,a.size())edges[a[i]].eb(a[i],b[i],1,i);}
  void add_edges(const vec<ll>&a,const vec<ll>&b,const vec<WT>&w){fo(i,a.size())edges[a[i]].eb(a[i],b[i],w[i],i);}
  void add_edges(const vec<edge<WT>>&es){fe(es,e)edges[e.from].eb(e);}
};
template<class WT>struct rooted_tree:graph<WT>{
  vec<edge<WT>>rev_edge;
  ll r;
  rooted_tree(ll n,ll r):graph<WT>(n),rev_edge(n,{-1,-1,WT(),-1}),r(r){}
  ll root()const{return r;}
  void add_edge_and_set_rev_edge(const edge<WT>&e){
    this->edges[e.from].eb(e);
    this->rev_edge[e.to]=e;
  }
  auto bfs_order()const{
    vec<ll>ord;
    queue<ll>q{r};
    while(q.size()){
      ll u=q.pop();
      ord.eb(u);
      fe(this->edges[u],e)q.emplace(e.to);
    }
    return ord;
  }
};
template<class WT>auto bfs_tree(const graph<WT>&g,ll s){
  rooted_tree<WT>tree(g.size(),s);
  vec<bool>used(g.size());
  queue<edge<WT>>q{{-1,s,WT{},-1}};
  while(q.size()){
    auto pu=q.pop();
    ll u=pu.to;
    if(used[u])continue;
    used[u]=1;
    if(pu.from!=-1)tree.add_edge_and_set_rev_edge(pu);
    fe(g[u],e)if(!used[e.to])q.emplace(e);
  }
  return tree;
}
template<class WT>auto bfs_tree(const rooted_tree<WT>&g){return bfs_tree(g,g.root());}
single_testcase
void solve(){
  LL(N);
  VV(N-1,a,b);dec(a,b);
  VL(N,c);
  rooted_tree<ll>g(N,0);
  g.add_edges(a,b);
  g.add_edges(b,a);
  g=bfs_tree(g);
  // dp[u][j]:uの部分木について，uの連結成分の総xorがjで，それ以外の連結成分の総xorが1であるようなグラフの個数．
  ml ans=0;
  fo(B,width2(c.max())){
    vec dp(N,2,ml{});
    ef(g.bfs_order(),u){
      dp[u][at2ll(c[u],B)]=1;
      fe(g[u],e){
        ll v=e.to;
        ll n=dp[u].size();
        ll m=dp[v].size();
        vec nx(2,ml{});
        fo(j,2){
          fo(k,2){
            ml X=dp[u][j]*dp[v][k];
            nx[j^k]+=X;    // 辺u-vを残す
            if(k)nx[j]+=X; // 辺u-vを消す
          }
        }
        swap(dp[u],nx);
      }
    }
    ans+=dp[0][1]*ml{2}.pow(B);
  }
  pp(ans);
}}
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