This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
vector<vector<int> > adj;
const lli MAX=3*1e5+5;
int val(char c){
if(c=='(')return 1;
else if(c==')')return -1;
else return -1123214;
}
bool lookup[1001][1001];
typedef pair<int,int> pii;
typedef pair<char,int> pci;
lli solve(vector<pci>& chain){
int len=(int)chain.size();
map<int,int> freq;
vector<int> dp(1000,0);
dp[0]=0;
lli snc=0;
/*
freq ayarla
1'den n'e:
bul'dan küçük olan ilk elemanı bul = gind
ipf[bul]'da gind'den küçük olanları bul
bul'u arttır
* */
for (int i = 1; i <= len ; i++)
{
dp[i]=dp[i-1]+val(chain[i-1].first);
}
int i=1;
while(dp[i]!=-1&&i<=len){
if(dp[i]==0&&!lookup[chain[0].second][chain[i-1].second]){
lookup[chain[0].second][chain[i-1].second]=true;
snc++;
}
i++;
}
return snc;
}
/*
4
(())
*/
lli sndc;
void solveDfs(int node,int parent,vector<pci> chainNow,vector<char>& chain){
chainNow.push_back(pci(chain[node-1],node));
if(adj[node].size()==1&&adj[node][0]==parent){
sndc+=solve(chainNow);
}
for(auto u:adj[node]){
if(u==parent)continue;
solveDfs(u,node,chainNow,chain);
}
}
lli trueSolve(vector<char>& chain){
int len=(int)chain.size();
map<int,int> freq;
vector<int> dp(MAX,0);
dp[0]=0;
int bul=0;
lli snc=0;
set<pii> dset;
map<int,set<pii> > ipf;
/*
freq ayarla
1'den n'e:
bul'dan küçük olan ilk elemanı bul = gind
ipf[bul]'da gind'den küçük olanları bul
bul'u arttır
* */
for (int i = 1; i <= len ; i++)
{
dp[i]=dp[i-1]+val(chain[i-1]);
if(ipf.find(dp[i])==ipf.end()){
ipf[dp[i]]=set<pii>();
}
ipf[dp[i]].insert(pii(i,ipf[dp[i]].size()));
dset.insert(pii(dp[i],i));
}
map<int,int> freqRem;
for (int i = 1; i <=len ; i++)
{
int gind=0;
set<pii>::iterator it=dset.lower_bound(pii(bul-1,-1));
if(it==dset.end()){
gind=len;
}
else if(it->first!=bul-1)gind=len;
else gind=it->second;
//cout <<"gind: "<< gind<<"\n";
//gind'den küçük eşitleri bul
set<pii>::iterator git=ipf[bul].lower_bound(pii(gind+1,-1));
if(git==ipf[bul].begin()){
snc+=0;//:)
}
else{
git--;
//cout << "buldu: "<<git->first<<"-"<<git->second<<"\n";
snc+=git->second+1-freqRem[bul];
}
//cout <<snc<<" snc \n";
bul+=val(chain[i-1]);
set<pii>::iterator sil=ipf[dp[i]].lower_bound(pii(i,-1));
ipf[dp[i]].erase(sil);
if(freqRem.find(dp[i])==freqRem.end())freqRem[dp[i]]=0;
freqRem[dp[i]]++;
dset.erase(pii(dp[i],i));
}
return snc;
}
int main(){
int n;
cin>>n;
vector<char> chain(n,0);
adj=vector<vector<int> >(n+1,vector<int>());
/*srand(time(0));
for (int i = 0; i < n; i++)
{
chain.push_back(rand()%2?'(':')');
}*/
for (int i = 0; i < n; i++)
{
cin>>chain[i];
}
for (int i = 0; i < n-1; i++)
{
int a,b;
cin>>a>>b;
adj[a].push_back(b);
adj[b].push_back(a);
}
/*for (int i = 0; i < n; i++)
{
}
for (int i = n-1; i >=0; i--)
{
//cout << chain[i];
}*/
//cout<<"\n";
if(n>1000){
lli snc=0;
snc+=trueSolve(chain);
reverse(chain.begin(),chain.end());
snc+=trueSolve(chain);
cout << snc;
}
else{
for (int i = 1; i <=n ; i++)
{
solveDfs(i,-1,vector<pci>(),chain);
}
cout<<sndc<<"\n";
}
return 0;
}
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