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Submission #761627

# Submission time Handle Problem Language Result Execution time Memory
761627 2023-06-20T05:58:32 Z gun_gan Zagrade (COI17_zagrade) C++17
100 / 100
 236 ms 125176 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
 
const int MX = 3e5 + 5, inf = 1e9;
 
int N;
string s;
vector<int> g[MX];
 
int par[MX], bal[MX];
set<pair<int, int>> path[MX][2]; // open, close
// (balance, count)
 
int find(int v) {
      return par[v] == v ? v : par[v] = find(par[v]);
}
 
ll ans = 0;
 
void dfs(int v, int p) {
      for(auto u : g[v]) {
            if(u == p) continue;
            // build 
            bal[u] = bal[v] + (s[u] == '(' ? 1 : -1);
            dfs(u, v);
      }

      int c = s[v] == '(';
 
      for(auto u : g[v]) {
            if(u == p) continue; 
 
            // erase invalid
            int pu = find(u);
            auto it = path[pu][c].lower_bound({bal[v], -inf});

            if(it != path[pu][c].end() && it->first == bal[v]) {
                  path[pu][c].erase(it);
            }
      }
 
      // straight path
      for(auto u : g[v]) {
            if(u == p) continue;

            int pu = find(u);
            auto it = path[pu][c].lower_bound({bal[p], -inf});
            if(it != path[pu][c].end() && it->first == bal[p]) {
                  ans += it->second;
            }
      }
 
      // calc answer, merging
      for(auto u : g[v]) {
            if(u == p) continue;
            int pu = find(u), pv = find(v);
 
            if((path[pu][0].size() + path[pu][1].size()) > (path[pv][0].size() + path[pv][1].size())) {
                  swap(pu, pv);
            }
            
            for(int t = 0; t < 2; t++) {
                  // calc answer
                  for(auto [b, c] : path[pu][t]) {
                        int k = b - bal[p];
                        k = -k + bal[v];
                        auto it = path[pv][t ^ 1].lower_bound({k, -inf});
                        if(it != path[pv][t ^ 1].end() && it->first == k) {
                              ans += 1LL * c * it->second;
                        }
                  }
            }
            par[pu] = pv;

            for(int t = 0; t < 2; t++) {
                  // merging
                  for(auto x : path[pu][t]) {
                        auto it = path[pv][t].lower_bound({x.first, -inf});

                        if(it != path[pv][t].end() && it->first == x.first) {
                              path[pv][t].insert({x.first, x.second + it->second});
                              path[pv][t].erase(it);
                        } else {
                              path[pv][t].insert(x);
                        }
                  }
            }
            path[pu][0].clear();
            path[pu][1].clear();
      }

      // add new path
      int pv = find(v);
      auto it = path[pv][c ^ 1].lower_bound({bal[v], -inf});

      if(it != path[pv][c ^ 1].end() && it->first == bal[v]) {
            path[pv][c ^ 1].insert({it->first, it->second + 1});
            path[pv][c ^ 1].erase(*it);
      } else {
            path[pv][c ^ 1].insert({bal[v], 1});
      }

}     
 
int main() {
      ios_base::sync_with_stdio(0); cin.tie(0);
 
      cin >> N >> s;
      s = '#' + s;
 
      for(int i = 0; i < N - 1; i++) {
            int u, v;
            cin >> u >> v;
            g[u].push_back(v);
            g[v].push_back(u);
      }
 
      for(int i = 1; i <= N; i++) par[i] = i;
 
      bal[1] = (s[1] == '(' ? 1 : -1);
      dfs(1, 0);
 
      cout << ans << '\n';
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 16 ms 35512 KB Output is correct
3 Correct 16 ms 35540 KB Output is correct
4 Correct 16 ms 35492 KB Output is correct
5 Correct 16 ms 35500 KB Output is correct
6 Correct 16 ms 35600 KB Output is correct
7 Correct 16 ms 35520 KB Output is correct
8 Correct 16 ms 35596 KB Output is correct
9 Correct 17 ms 35572 KB Output is correct
10 Correct 16 ms 35540 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 149 ms 118020 KB Output is correct
2 Correct 160 ms 123624 KB Output is correct
3 Correct 146 ms 118040 KB Output is correct
4 Correct 154 ms 122188 KB Output is correct
5 Correct 147 ms 118092 KB Output is correct
6 Correct 160 ms 120120 KB Output is correct
7 Correct 152 ms 118016 KB Output is correct
8 Correct 153 ms 120120 KB Output is correct
9 Correct 148 ms 118036 KB Output is correct
10 Correct 213 ms 125176 KB Output is correct
11 Correct 121 ms 117944 KB Output is correct

Subtask #3
60.0 / 60.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 16 ms 35512 KB Output is correct
3 Correct 16 ms 35540 KB Output is correct
4 Correct 16 ms 35492 KB Output is correct
5 Correct 16 ms 35500 KB Output is correct
6 Correct 16 ms 35600 KB Output is correct
7 Correct 16 ms 35520 KB Output is correct
8 Correct 16 ms 35596 KB Output is correct
9 Correct 17 ms 35572 KB Output is correct
10 Correct 16 ms 35540 KB Output is correct
11 Correct 149 ms 118020 KB Output is correct
12 Correct 160 ms 123624 KB Output is correct
13 Correct 146 ms 118040 KB Output is correct
14 Correct 154 ms 122188 KB Output is correct
15 Correct 147 ms 118092 KB Output is correct
16 Correct 160 ms 120120 KB Output is correct
17 Correct 152 ms 118016 KB Output is correct
18 Correct 153 ms 120120 KB Output is correct
19 Correct 148 ms 118036 KB Output is correct
20 Correct 213 ms 125176 KB Output is correct
21 Correct 121 ms 117944 KB Output is correct
22 Correct 223 ms 47860 KB Output is correct
23 Correct 236 ms 48012 KB Output is correct
24 Correct 223 ms 47892 KB Output is correct
25 Correct 227 ms 47900 KB Output is correct
26 Correct 158 ms 74764 KB Output is correct
27 Correct 158 ms 63324 KB Output is correct
28 Correct 162 ms 58668 KB Output is correct
29 Correct 188 ms 124948 KB Output is correct
30 Correct 193 ms 125036 KB Output is correct
31 Correct 92 ms 55732 KB Output is correct
32 Correct 119 ms 117972 KB Output is correct