Submission #819931

#	Time	Username	Problem	Language	Result	Execution time	Memory
819931		stefanopulos	Zagrade (COI17_zagrade)	C++17	40 / 100	3038 ms	59036 KiB

zagrade

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <bits/stdc++.h>
 
using namespace std;
using namespace __gnu_pbds;
 
typedef long long ll;
typedef long double ldb;
 
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<ldb,ldb> pdd;

#define ff(i,a,b) for(int i = a; i <= b; i++)
#define fb(i,b,a) for(int i = b; i >= a; i--)
#define trav(a,x) for(auto& a : x)
 
#define sz(a) (int)(a).size()
#define fi first
#define se second
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
 
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

// os.order_of_key(k) the number of elements in the os less than k
// *os.find_by_order(k)  print the k-th smallest number in os(0-based)

const int mod = 1000000007;
const int inf = 1e9 + 5;
const int mxN = 300005; 

int n;
string s;

vector<int> g[mxN];

int cnt[mxN];
bool bio[mxN];
void dfs_cnt(int v, int p){
    cnt[v] = 1;
    for(auto u : g[v]){
        if(u != p && !bio[u]){
            dfs_cnt(u, v);
            cnt[v] += cnt[u];
        }
    }
}

int centroid(int v, int p, int vel){
    for(auto u : g[v]){
        if(u == p || bio[u])continue;
        if(cnt[v] > vel / 2)return centroid(u, v, vel);
    }
    return v;
}

ll br = 0;
vector<int> cuvaj;
map<int,vector<int>> kol;

void dfs(int v, int p, int sumA, int dlA, int grB, int X, bool f){
    int Y = (s[v] == '(' ? 1 : -1);
    sumA += Y; dlA = min(dlA, sumA); grB = min(0, grB + Y);

    if(kol.count(sumA) == 1){

        int l = 0, r = sz(kol[sumA]) - 1, ans = -1;
        while(l <= r){
            int mid = (l + r) / 2;
            if(dlA >= kol[sumA][mid]){
                ans = mid;
                l = mid + 1;
            }
            else r = mid - 1;
        }

        br += ans + 1;

    }    

    if(f == 1){
        if(sumA + X == 0 && min(0, dlA + X) >= 0)br += 1;
        if(sumA + X == 0 && grB >= 0)br += 1;
    }

    if(grB == 0)cuvaj.pb(-(sumA + X));
    for(auto u : g[v]){
        if(u != p && !bio[u]){
            dfs(u, v, sumA, dlA, grB, X, f);
        }
    }


}


void decompose(int v, int p){
    dfs_cnt(v, -1); int cen = centroid(v, -1, cnt[v]);
    bio[cen] = 1; int X = (s[cen] == '(' ? 1 : -1);

    kol.clear();
    for(auto u : g[cen]){
        if(u != p && !bio[u]){
            dfs(u, cen, 0, 0, min(0, X), X, 1);
            
            for(auto c : cuvaj)kol[c].pb(c);
            cuvaj.clear();

        }
    }

    reverse(all(g[cen]));

    kol.clear();
    for(auto u : g[cen]){
        if(u != p && !bio[u]){
            dfs(u, cen, 0, 0, min(0, X), X, 0);
            
            for(auto c : cuvaj)kol[c].pb(c);
            cuvaj.clear();

        }
    }

    // reverse(all(g[cen]));
    for(auto u : g[cen]){
        if(u != p && !bio[u]){
            decompose(u, cen);
        }
    }


}

int main(){
    cin.tie(0)->sync_with_stdio(0);

    cin >> n >> s;
    s = ' ' + s;
    ff(i,1,n - 1){
        int u, v;
        cin >> u >> v;
        g[u].pb(v);
        g[v].pb(u);
    }

    decompose(1, -1);

    cout << br << '\n';

    return 0;
}
/*



// probati bojenje sahovski
*/
 
 
 
 
 

• Subtask 1: 10 / 10
• Subtask 2: 30 / 30
• Subtask 3: 0 / 60