結果

問題 No.3148 Min-Cost Destruction of Parentheses
ユーザー tute7627
提出日時 2025-05-16 21:33:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 76 ms / 4,000 ms
コード長 14,231 bytes
コンパイル時間 2,600 ms
コンパイル使用メモリ 234,104 KB
実行使用メモリ 22,980 KB
最終ジャッジ日時 2025-05-16 21:34:04
合計ジャッジ時間 4,835 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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 * 3
other AC * 31
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 # 

//#define _GLIBCXX_DEBUG

//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")

#include<bits/stdc++.h>
using namespace std;


#ifdef LOCAL
#include <debug_print.hpp>
#define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define OUT(...) (static_cast<void>(0))
#endif

#define endl '\n'
#define lfs cout<<fixed<<setprecision(15)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)

namespace template_tute{
  using ll = long long;
  using ld = long double;
  const ll MOD1 = 1e9+7;
  const ll MOD9 = 998244353;
  const ll INF = 4.1e18;
  using P = pair<ll, ll>;
  template<typename T> using PQ = priority_queue<T>;
  template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
  template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
  template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
  ll median(ll a,ll b, ll c){return a+b+c-max<ll>({a,b,c})-min<ll>({a,b,c});}
  void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
  void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
  void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
  template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
  template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};  
  template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};
  template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};
  template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
  template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
  template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
  template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
  template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
  template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
  template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
  template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
  template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
  template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
  template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
  template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
  vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
  template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
  template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
  template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << "(" << p.first << "," << p.second << ")";}
  template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; return os;}
  template<typename T>void rearrange(vector<int>&ord, vector<T>&v){
    auto tmp = v;
    for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
  }
  template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){
    rearrange(ord, head);
    rearrange(ord, tail...);
  }
  template<typename T> vector<int> ascend(const vector<T>&v){
    vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
    sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i)<make_pair(v[j],j);});
    return ord;
  }
  template<typename T> vector<int> descend(const vector<T>&v){
    vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
    sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);});
    return ord;
  }
  template<typename T> vector<T> inv_perm(const vector<T>&ord){
    vector<T>inv(ord.size());
    for(int i=0;i<ord.size();i++)inv[ord[i]] = i;
    return inv;
  }
  ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}
  ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}
  ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}
  ll modulo(ll n,ll d){return (n%d+d)%d;};
  template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}
  template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}
  template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};
  template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};
  //mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
  int popcount(ll x){return __builtin_popcountll(x);};
  int poplow(ll x){return __builtin_ctzll(x);};
  int pophigh(ll x){return 63 - __builtin_clzll(x);};
  template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};
  template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};
  template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};
  template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};
  ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}
  ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}
  ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}
  std::ostream &operator<<(std::ostream &dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
      __uint128_t tmp = value < 0 ? -value : value;
      char buffer[128];
      char *d = std::end(buffer);
      do {
        --d;
        *d = "0123456789"[tmp % 10];
        tmp /= 10;
      } while (tmp != 0);
      if (value < 0) {
        --d;
        *d = '-';
      }
      int len = std::end(buffer) - d;
      if (dest.rdbuf()->sputn(d, len) != len) {
        dest.setstate(std::ios_base::badbit);
      }
    }
    return dest;
  }
  namespace converter{
    int dict[500];
    const string lower="abcdefghijklmnopqrstuvwxyz";
    const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    const string digit="0123456789";
    const string digit1="123456789";
    void regi_str(const string &t){
      for(int i=0;i<t.size();i++){
        dict[t[i]]=i;
      }
    }
    void regi_int(const string &t){
      for(int i=0;i<t.size();i++){
        dict[i]=t[i];
      }
    }
    vector<int>to_int(const string &s,const string &t){
      regi_str(t);
      vector<int>ret(s.size());
      for(int i=0;i<s.size();i++){
        ret[i]=dict[s[i]];
      }
      return ret;
    }
    vector<int>to_int(const string &s){
      auto t=s;
      sort(t.begin(),t.end());
      t.erase(unique(t.begin(),t.end()),t.end());
      return to_int(s,t);
    }
    
    vector<vector<int>>to_int(const vector<string>&s,const string &t){
      regi_str(t);
      vector<vector<int>>ret(s.size(),vector<int>(s[0].size()));
      for(int i=0;i<s.size();i++){
        for(int j=0;j<s[0].size();j++){
          ret[i][j]=dict[s[i][j]];
        }
      }
      return ret;
    }
    vector<vector<int>>to_int(const vector<string>&s){
      string t;
      for(int i=0;i<s.size();i++){
        t+=s[i];
      }
      sort(t.begin(),t.end());t.erase(unique(t.begin(),t.end()),t.end());
      return to_int(s,t);
    }
    string to_str(const vector<int>&s,const string &t){
      regi_int(t);
      string ret;
      for(auto z:s)ret+=dict[z];
      return ret;
    }
    vector<string> to_str(const vector<vector<int>>&s,const string &t){
      regi_int(t);
      vector<string>ret(s.size());
      for(int i=0;i<s.size();i++){
        for(auto z:s[i])ret[i]+=dict[z];
      }
      return ret;
    }
  }
  template< typename T = int >
  struct edge {
    int to;
    T cost;
    int id;
    edge():to(-1),id(-1){};
    edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}
    operator int() const { return to; }
  };

  template<typename T>
  using Graph = vector<vector<edge<T>>>;
  template<typename T>
  Graph<T>revgraph(const Graph<T> &g){
    Graph<T>ret(g.size());
    for(int i=0;i<g.size();i++){
      for(auto e:g[i]){
        int to = e.to;
        e.to = i;
        ret[to].push_back(e);
      }
    }
    return ret;
  }
  template<typename T>
  Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){
    Graph<T> ret(n);
    for(int es = 0; es < m; es++){
      int u,v;
      T w=1;
      cin>>u>>v;u-=indexed,v-=indexed;
      if(weighted)cin>>w;
      ret[u].emplace_back(v,w,es);
      if(!directed)ret[v].emplace_back(u,w,es);
    }
    return ret;
  }
  template<typename T>
  Graph<T> readParent(int n,int indexed=1,bool directed=true){
    Graph<T>ret(n);
    for(int i=1;i<n;i++){
      int p;cin>>p;
      p-=indexed;
      ret[p].emplace_back(i);
      if(!directed)ret[i].emplace_back(p);
    }
    return ret;
  }
}
using namespace template_tute;
struct RationalNumber{
  using I=ll;
  I a, b;
  RationalNumber(){
    a = 0,b = 1;
  }
  RationalNumber(I p, I q):a(p), b(q){// a / b
    reduction();
  };
  RationalNumber(I p):a(p), b(1){// a / b
  };
  void reduction(){
    /*I g = gcd(a, b);
    a /= g, b /= g;
    if(b < 0)a *= -1,b *= -1;*/
  }
  RationalNumber &operator+=(const RationalNumber &x){
    I q = b / gcd(b, x.b) * x.b;
    a = a * (q / b) + x.a * (q / x.b);
    b = q;
    reduction();
    return *this;
  }
  RationalNumber &operator-=(const RationalNumber &x){
    I q = b / gcd(b, x.b) * x.b;
    a = a * (q / b) - x.a * (q / x.b);
    b = q;
    reduction();
    return *this;
  }
  RationalNumber &operator*=(const RationalNumber &x){
    I q1 = gcd(a, x.b), q2 = gcd(b, x.a); 
    a = (a / q1) * (x.a / q2), b = (b / q2) * (x.b / q1); 
    return *this;
  }
  RationalNumber &operator/=(const RationalNumber &x){
    I q1 = gcd(a, x.a), q2 = gcd(b, x.b); 
    a = (a / q1) * (x.b / q2), b = (b / q2) * (x.a / q1); 
    return *this;
  }
  RationalNumber operator+(const RationalNumber &x)const{
    return RationalNumber(*this) += x;
  }
  RationalNumber operator-(const RationalNumber &x)const{
    return RationalNumber(*this) -= x;
  }
  RationalNumber operator*(const RationalNumber &x)const{
    return RationalNumber(*this) *= x;
  }
  RationalNumber operator/(const RationalNumber &x)const{
    return RationalNumber(*this) /= x;
  }
  RationalNumber operator-()const{
    return RationalNumber(-a, b);
  }
  bool operator==(const RationalNumber &x)const{
    return a * x.b == b * x.a;
  };
  bool operator!=(const RationalNumber &x)const{
    return !(*this == x);
  };
  bool operator<(const RationalNumber &x)const{
    return a * x.b < b * x.a;
  }
  bool operator>(const RationalNumber &x)const{
    return a * x.b > b * x.a;
  }
  bool operator<=(const RationalNumber &x)const{
    return *this < x || *this == x;
  }
  bool operator>=(const RationalNumber &x)const{
    return *this > x || *this == x;
  }
  friend ostream &operator<<(ostream &os, RationalNumber x){
    return os << x.a << "/" << x.b;
  }
};
template<typename T>
struct UnionFind {
  vector<ll> data;
  vector<T>v;
  ll num;
  //引数はindex!!!
  ll ret=0;
  void merge(int x, int y){
    ret+=v[x].se*v[y].fi;
    v[x].fi = v[x].fi + v[y].fi;
    v[x].se = v[x].se + v[y].se;
  }
  void set(ll i,T x){
    v[i] = x;
  }
  UnionFind(ll size) : data(size, -1) ,num(size),v(size){ }
  bool unite(ll x, ll y) {
    x = root(x); y = root(y);
    if (x != y) {
      //if (data[y] < data[x]) swap(x, y);
      data[x] += data[y]; data[y] = x;
      merge(x, y);
	    num--;
    }
    return x != y;
  }
  bool find(ll x, ll y) {
    return root(x) == root(y);
  }
  ll root(ll x) {
    return data[x] < 0 ? x : data[x] = root(data[x]);
  }
  ll size(ll x) {
    return -data[root(x)];
  }
  T& val(ll x){
    return v[root(x)];
  }
  vector<vector<int>>groups(){
    vector<vector<int>>ret(data.size());
    for(int i=0;i<data.size();i++){
      ret[root(i)].push_back(i);
    }
    return ret;
  }
};
using rat=RationalNumber;
ll solve(int r,vector<P>p,Graph<int>g){
  int n=g.size();
  vector<int>par(n,-1);
  {
    auto dfs=[&](auto &&f,int k,int pa)->void
    {
      for(auto to:g[k]){
        if(to==pa)continue;
        par[to]=k;
        f(f,to,k);
      }
    };
    dfs(dfs,r,-1);
  }  
  PQ<pair<rat,int>>pq;
  UnionFind<P> uf(n);
  rep(i,0,n){
    if(r!=i)pq.emplace(rat(p[i].fi,p[i].se),i);
    uf.set(i,p[i]);
  }
  while(!pq.empty()){
    auto [rr,v]=poll(pq);
    if(MP(rr.a,rr.b)!=uf.val(v))continue;
    uf.unite(par[v],v);
    auto val=uf.val(v);
    //OUT(v,_,uf.ret);
    if(uf.root(v)!=r)pq.emplace(rat(val.fi,val.se),uf.root(v));
  }
  return uf.ret;
}

void solve(){
	ll res=0,buf=0;
  bool judge = true;

  ll n;cin>>n;
  string s;cin>>s;
  Graph<int>g(n+1);
  vector<ll>a(n);
  rep(i,0,n)cin>>a[i];
  a.PB(0);
  stack<int>st;
  st.push(n);
  int idx=0;
  for(auto c:s){
    if(c=='('){
      st.push(idx++);
    }
    else{
      auto v=poll(st);
      g[st.top()].emplace_back(v);
      //g[v].emplace_back(st.top());
    }
  }
  vector<P>p(n+1);
  p[n]=MP(0,1);
  rep(i,0,n){
    p[i]=MP(a[i],1);
  }
  OUT(p,g);
  auto v=solve(n,p,g);
  cout<<v<<endl;
}

int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  int T = 1;
  //cin>>T;
  while(T--){
    solve();
  }
  return 0;
}
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