Submission #742921

#	Time	Username	Problem	Language	Result	Execution time	Memory
742921		PixelCat	Duathlon (APIO18_duathlon)	C++14	10 / 100	134 ms	55188 KiB

count_triplets

#include <bits/stdc++.h>
#define For(i, a, b) for(int i = a; i <= b; i++)
#define Forr(i, a, b) for(int i = a; i >= b; i--)
#define F first
#define S second
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define sz(x) ((int)x.size())
#define int LL
using namespace std;
using LL = long long;
using pii = pair<int, int>;

const int MAXN = 100010;

vector<int> adj[MAXN];
int dep[MAXN];
int lo[MAXN];
int id[MAXN];

vector<int> bcc[MAXN * 2];
int siz[MAXN * 2];
int sum[MAXN * 2];
int ban[MAXN * 2];
int cur_bcc;

vector<int> st;
void dfs_bcc(int n, int p, int d) {
    dep[n] = lo[n] = d;
    st.eb(n);
    for(auto &i:adj[n]) if(i != p) {
        if(dep[i]) {
            lo[n] = min(lo[n], dep[i]);
        } else {
            dfs_bcc(i, n, d + 1);
            lo[n] = min(lo[n], lo[i]);
            if(lo[i] >= dep[n]) {
                // bcc found
                cur_bcc++;
                int last = 0;
                while(last != n) {
                    last = st.back(); st.pop_back();
                    bcc[last].eb(cur_bcc);
                    bcc[cur_bcc].eb(last);
                }
                st.eb(n);
            }
        }
    }
}

void dfs_siz(int n, int p, int N, int d) {
    dep[n] = d;
    sum[n] = siz[n] = (n <= N);
    for(auto &i:bcc[n]) if(i != p) {
        dfs_siz(i, n, N, d + 1);
        sum[n] += sum[i];
    }
}

#define C(x) ((x) * ((x) - 1))
void dfs_ban(int n, int p, int N, int tot) {
    auto size = [&](int r, int k) {
        if(dep[k] < dep[r]) return tot - sum[r];
        return sum[k];
    };
    for(auto &i:bcc[n]) if(i != p) {
        dfs_ban(i, n, N, tot);
    }
    if(n > N) {
        for(auto &i:bcc[n]) {
            // cout << n << " " << i << " " << size(n, i) << " " << tot - sum[n] << " " << sum[i] << "\n";
            ban[n] += C(size(n, i));
            ban[i] -= C(size(n, i));
        }
        for(auto &i:bcc[n]) {
            ban[i] += ban[n];
        }
    }
}

int ans = 0;
void dfs_ans(int n, int p, int N, int tot) {
    if(n <= N) ans += C(tot - 1) - ban[n];
    for(auto &i:bcc[n]) if(i != p) dfs_ans(i, n, N, tot);
}

int32_t main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    // =^-w-^= nya
    int n, m; cin >> n >> m;
    while(m--) {
        int a, b; cin >> a >> b;
        adj[a].eb(b);
        adj[b].eb(a);
    }
    cur_bcc = n;
    For(i, 1, n) if(!dep[i]) {
        dfs_bcc(i, i, 1);
        dfs_siz(i, i, n, 1);
        // cout << i << " " << sum[i] << "\n";
        dfs_ban(i, i, n, sum[i]);
        dfs_ans(i, i, n, sum[i]);
    }
    cout << ans << "\n";

    // For(i, 1, cur_bcc) cout << dep[i] << " \n"[i == cur_bcc];
    // For(i, 1, cur_bcc) cout << ban[i] << " \n"[i == cur_bcc];
    // For(i, 1, cur_bcc) {
    //     cout << i << ":";
    //     for(auto &j:bcc[i]) cout << " " << j;
    //     cout << "\n";
    // }
    return 0;
}

/*

4 3
1 2
2 3
3 4
= 8

4 4
1 2
2 3
3 4
4 2
= 14

5 5
1 2
2 3
3 1
3 4
3 5
= 24

5 6
1 2
2 3
3 1
1 4
4 5
5 1
= 36

*/

• Subtask 1: 0 / 5
• Subtask 2: 0 / 11
• Subtask 3: 0 / 8
• Subtask 4: 10 / 10
• Subtask 5: 0 / 13
• Subtask 6: 0 / 15
• Subtask 7: 0 / 20
• Subtask 8: 0 / 8
• Subtask 9: 0 / 10