Submission #546854

#	Time	Username	Problem	Language	Result	Execution time	Memory
546854		Monarchuwu	Duathlon (APIO18_duathlon)	C++17	66 / 100	92 ms	26380 KiB

count_triplets

#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long ll;

typedef pair<int, int> pii;
typedef pair<pii, int> ppi;
#define ff first
#define ss second

const int N = 1e5 + 9;
int n, m;
vector<int> g[N];

namespace subtask1 {
    bool avail[1 << 10][10][10];
    vector<int> g2[10][10];
    void solve() {
        for (int i = 0; i < n; ++i) avail[1 << i][i][i] = true;
        for (int msk = 1; msk < (1 << n); ++msk)
            for (int s = 0; s < n; s++) if (msk >> s & 1)
                for (int f = 0; f < n; f++) if (msk >> f & 1 && f != s) {
                    for (int e : g[f - 1]) if (msk >> (e - 1) & 1)
                        avail[msk][s][f] |= avail[msk ^ (1 << f)][s][e - 1];
                    if (avail[msk][s][f]) g2[s][f].push_back(msk);
                }

        ll ans(0);
        for (int s = 0; s < n; ++s)
            for (int c = 0; c < n; ++c) if (c != s)
                for (int f = 0; f < n; ++f) if (f != s && f != c) {
                    bool check(false);
                    for (int msk1 : g2[s][c]) {
                        for (int msk2 : g2[c][f]) {
                            if ((msk1 & msk2) == (1 << c)) check = true;
                            if (check) break;
                        }
                        if (check) break;
                    }
                    ans += check;
                }
        cout << ans << '\n';
    }
}

// bridge tree (WA for subtask 89)
namespace subtask34567 {
    int num[N], low[N], tme;
    int lab[N], cnt_scc, sz[N];
    int path[N], top;
    void tarjan(int u, int p) {
        num[u] = low[u] = ++tme;
        path[++top] = u;
        for (int v : g[u]) if (v != p) {
            if (num[v]) low[u] = min(low[u], num[v]);
            else {
                tarjan(v, u);
                low[u] = min(low[u], low[v]);
            }
        }

        if (num[u] == low[u]) { // chot
            ++cnt_scc;
            int v;
            do {
                v = path[top--];
                num[v] = low[v] = N;
                lab[v] = cnt_scc;
                ++sz[cnt_scc];
            } while (v != u);
        }
    }
    vector<ppi> g2[N];
    void init_graph() {
        for (int u = 1; u <= n; ++u) for (int v : g[u])
            if (lab[u] != lab[v]) g2[lab[u]].emplace_back(pii(u, v), lab[v]);
    }

    ll ans, dp[N][3];
    bool vis[N];
    void dfs(int u, int p, int vertex) {
        vis[u] = true;
        sort(g2[u].begin(), g2[u].end());

        /*          sort(g2[u].begin(), g2[u].end(), [=](const ppi &a, const ppi &b) {
                    if (a.ff.ff == vertex && b.ff.ff == vertex) return false;
                    if (a.ff.ff == vertex) return true;
                    if (b.ff.ff == vertex) return false;
                    return a.ff < b.ff;
                        });
        */

        dp[u][1] = sz[u];
        dp[u][2] = (ll)(sz[u] - 1) * (sz[u] - 1);
        ans += (ll)sz[u] * (sz[u] - 1) * (sz[u] - 2);

        ll cnt(0), dp1(0), dp2(0);
        int pre(0);
        for (ppi x : g2[u]) if (x.ss != p) {
            int v = x.ss;
            if (pre != x.ff.ff) {
                dp[u][2] += cnt, cnt = 0;
                pre = x.ff.ff;
            }

            dfs(v, u, x.ff.ss);
            ans += dp[u][1] * dp[v][2] * 2;
            ans += dp[u][2] * dp[v][1] * 2;

            dp[u][1] += dp[v][1];
            dp[u][2] += dp[v][2];
            dp[u][2] += dp[v][1];
            if (vertex != x.ff.ff) {
                cnt += dp[v][1] * (sz[u] - 1);
                ans += dp1 * dp[v][1] * 2;
            }
            else dp1 += dp[v][1] * (sz[u] - 1);
        }
        dp[u][2] += cnt;
    }
    void solve() {
        for (int i = 1; i <= n; ++i)
            if (!num[i]) tarjan(i, 0);
        init_graph();

        dfs(4, 0, 0);
        for (int u = 1; u <= cnt_scc; ++u)
            if (!vis[u]) dfs(u, 0, 0);
        cout << ans << '\n';
    }
}

bool f[N];
int main() {
    cin.tie(NULL)->sync_with_stdio(false);
    cin >> n >> m;
    for (int i = 0, u, v; i < m; ++i) {
        cin >> u >> v;
        g[u].push_back(v);
        g[v].push_back(u);
    }

    if (n <= 10)
        subtask1::solve();
    else subtask34567::solve();
}
/**  /\_/\
 *  (= ._.)
 *  / >0  \>1
**/
/*
==================================================+
INPUT:                                            |
--------------------------------------------------|
15 19
1 2
2 3
3 1
4 5
5 6
6 4
7 8
8 9
9 7
10 11
11 12
12 10
13 14
14 15
15 13
1 10
1 4
1 7
2 13
--------------------------------------------------|
==================================================+
OUTPUT:                                           |
--------------------------------------------------|
726
--------------------------------------------------|
==================================================+
*/

Compilation message (stderr)

count_triplets.cpp: In function 'void subtask34567::dfs(int, int, int)':
count_triplets.cpp:98:28: warning: unused variable 'dp2' [-Wunused-variable]
   98 |         ll cnt(0), dp1(0), dp2(0);
      |                            ^~~

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