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  1. //There can only be one king.
  2. #include <bits/stdc++.h>
  3. using namespace std;
  4. typedef long long intl;
  5. const intl N=1e5+5;
  6. string str;
  7. set<intl>g[N];
  8. intl n,nodes;
  9. intl ans,rbs1,rbs2;
  10. pair<intl,intl>edge[N];
  11. vector<intl>sz(N),a(N);
  12. map<intl,intl>p1,p2,s1,s2;
  13. void dfs(intl v,intl p)
  14. {
  15.     nodes++;
  16.     sz[v]=1;
  17.     for(auto it:g[v])
  18.     {
  19.         if(it==p)
  20.         continue;
  21.         dfs(edge[it].first^edge[it].second^v,it);
  22.         sz[v]+=sz[edge[it].first^edge[it].second^v];
  23.     }
  24. }
  25. intl centroid(intl v,intl p)
  26. {
  27.     for(auto it:g[v])
  28.     {
  29.         if(it==p)
  30.         continue;
  31.         if(2*sz[edge[it].first^edge[it].second^v]>nodes)
  32.         return centroid(edge[it].first^edge[it].second^v,it);
  33.     }
  34.     return v;
  35. }
  36. void dfsp(intl v,intl p,intl open,intl close)
  37. {
  38.     char ch=str[p];
  39.     if(ch=='(')
  40.     {
  41.         if(close)
  42.         close--;
  43.         else
  44.         open++;
  45.     }
  46.     else
  47.     close++;
  48.     if(close==0)
  49.     {
  50.         if(open)
  51.         {
  52.             p2[open]++;
  53.             ans=ans+s1[open];
  54.         }
  55.         else
  56.         rbs2++;
  57.     }
  58.     for(auto it:g[v])
  59.     {
  60.         if(it==p)
  61.         continue;
  62.         dfsp(edge[it].first^edge[it].second^v,it,open,close);
  63.     }
  64. }
  65. void dfss(intl v,intl p,intl open,intl close)
  66. {
  67.     char ch=str[p];
  68.     if(ch==')')
  69.     {
  70.         if(open)
  71.         open--;
  72.         else
  73.         close++;
  74.     }
  75.     else
  76.     open++;
  77.     if(open==0)
  78.     {
  79.         if(close)
  80.         {
  81.             s2[close]++;
  82.             ans=ans+p1[close];
  83.         }
  84.         else
  85.         rbs2++;
  86.     }
  87.     for(auto it:g[v])
  88.     {
  89.         if(it==p)
  90.         continue;
  91.         dfss(edge[it].first^edge[it].second^v,it,open,close);
  92.     }
  93. }
  94. void decompose(intl v,intl p)
  95. {
  96.     nodes=0;
  97.     dfs(v,p);
  98.     intl node=centroid(v,p);
  99.     for(auto it1:g[node])
  100.     {
  101.         dfss(edge[it1].first^edge[it1].second^node,it1,0,0);
  102.         dfsp(edge[it1].first^edge[it1].second^node,it1,0,0);
  103.         ans=ans+rbs2;
  104.         ans=ans+(rbs2*rbs1);
  105.         rbs1+=rbs2;
  106.         for(auto it2:p2)
  107.         p1[it2.first]+=it2.second;
  108.         for(auto it2:s2)
  109.         s1[it2.first]+=it2.second;
  110.         rbs2=0;
  111.         p2.clear();
  112.         s2.clear();
  113.     }
  114.     rbs1=0;
  115.     p1.clear();
  116.     s1.clear();
  117.     for(auto it:g[node])
  118.     {
  119.         g[edge[it].first^edge[it].second^node].erase(it);
  120.         decompose(edge[it].first^edge[it].second^node,it);
  121.     }
  122. }
  123. int32_t main()
  124. {
  125.     ios_base::sync_with_stdio(false);
  126.     cin.tie(0);
  127.     cout.tie(0);
  128.     intl t;
  129.     cin>>t;
  130.     while(t--)
  131.     {
  132.         ans=0;
  133.         cin>>n;
  134.         for(intl i=1,c=0;i<=n;i++)
  135.         {
  136.             intl x;
  137.             cin>>x;
  138.             x++;
  139.             if(!x)
  140.             continue;
  141.             c++;
  142.             edge[c]={i,x};
  143.             g[i].insert(c);
  144.             g[x].insert(c);
  145.         }
  146.         cin>>str;
  147.         str="$"+str;
  148.         decompose(1,0);
  149.         cout<<ans<<endl;
  150.         for(intl i=1;i<=n;i++)
  151.         g[i].clear();
  152.     }
  153.     return 0;
  154. }
Runtime error #stdin #stdout 0.1s 9852KB
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https://ideone.com/ngFGwE
language:
C++ (gcc 8.3)
created:
4 years ago
visibility:
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