Submission #821375

#	Time	Username	Problem	Language	Result	Execution time	Memory
821375		stefanopulos	Zagrade (COI17_zagrade)	C++17	100 / 100	734 ms	54060 KiB

zagrade

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

#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[u] > vel / 2)return centroid(u, v, vel);
    }
    return v;
}

ll br = 0;

int dlA[mxN];
int sumA[mxN];

int grB[mxN];
int sumB[mxN];

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

    if(!sumB[v]){
        br += (min(0, dlA[v] + X) >= 0) + (grB[v] >= 0);
    }   

    for(auto u : g[v]){
        if(u != p && !bio[u]){
            dfs(u, v);
        }
    }


}

vector<int> cuvaj;
int kol[2 * mxN + 5];

void calc(int v, int p){
    if(dlA[v] >= sumA[v])br += kol[sumA[v] + mxN];

    if(!grB[v])cuvaj.pb(mxN - sumB[v]);

    for(auto u : g[v]){
        if(u != p && !bio[u]){
            calc(u, v);
        }
    }

}

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

    grB[cen] = min(0, X); sumB[cen] = X; 
    sumA[cen] = 0; dlA[cen] = 0;

    for(auto u : g[cen]){
        if(!bio[u]){
            dfs(u, cen);
        }
    }

    vector<int> svi;
    for(auto u : g[cen]){
        if(!bio[u]){
            calc(u, cen);

            for(auto c : cuvaj){
                kol[c] += 1; svi.pb(c);
            }

            cuvaj.clear();

        }
    }


    for(auto c : svi)kol[c] = 0;
    svi.clear();

    reverse(all(g[cen]));

    for(auto u : g[cen]){
        if(!bio[u]){
            calc(u, cen);

            for(auto c : cuvaj){
                kol[c] += 1; svi.pb(c);
            }

            cuvaj.clear();

        }
    }


    for(auto c : svi)kol[c] = 0;
    svi.clear();

    for(auto u : g[cen]){
        if(!bio[u]){
            decompose(u);
        }
    }


}

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);

    cout << br << '\n';

    return 0;
}
/*

4
(())
1 2
2 3
3 4

5
())((
1 2
2 3
2 4
3 5

7
)()()((
1 2
1 3
1 6
2 4
4 5
5 7

// probati bojenje sahovski
*/
 
 
 
 
 

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