Submission #974421

#	Time	Username	Problem	Language	Result	Execution time	Memory
974421		efedmrlr	Duathlon (APIO18_duathlon)	C++17	31 / 100	112 ms	38228 KiB

count_triplets

#include <bits/stdc++.h>

#define int long long int
#define lli int
#define ld long double
#define pb push_back
#define MP make_pair
#define REP(i, n) for(int i = 0; (i) < (n); (i)++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()

using namespace std;

void fastio() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
}

const int N = 2e5 + 5;
const int INF = 1e9 + 500;
int n, m;
vector<vector<array<int, 2> > > adj(N, vector<array<int, 2> >());
int tim = 0;
vector<int> tin(N, -1), low(N, 0);
vector<array<int, 2> > edg(N);
vector<bool> isBr(N, 0);
vector<int> comp(N, -1), cmpsz(N, 0);
vector<vector<int> > cadj(N, vector<int>());
vector<int> subsz(N, 0);
vector<int> rt;
vector<int> vis(N, 0);
lli ans = 0;
void find_bridge(int node, int par) {
    tin[node] = low[node] = tim++;
    for(auto c : adj[node]) {
        if(c[0] == par) {
            continue;
        }
        if(tin[c[0]] != -1) {
            low[node] = min(low[node], tin[c[0]]);
        }
        else {
            find_bridge(c[0], node);
            low[node] = min(low[node], low[c[0]]);
            // cout << "c[1]:"  << c[1] << " node:" << node << " lowc0:" << low[c[0]] << " tin[node]:" << tin[node] << "\n";
            if(low[c[0]] > tin[node]) {
                //bridge
                isBr[c[1]] = 1;
            }
        }
    }
}

void get_comp(int node, int cm) {
    comp[node] = cm;
    cmpsz[cm]++;
    for(auto c : adj[node]) {
        if(comp[c[0]] != -1 || isBr[c[1]]) continue;
        get_comp(c[0], cm);
    }
}

void prec(int node, int par) {
    subsz[node] = cmpsz[node];
    for(auto c : cadj[node]) {
        if(c == par) continue;
        prec(c, node);
        subsz[node] += subsz[c];
    }
}

void dfs(int node, int par, int root) {
    // cout << "node:" << node << "\n";
    lli ret = 0;
    lli x = subsz[root] - cmpsz[node];
    for(auto c : cadj[node]) {
        if(c == par) {
            int sbt = subsz[root] - subsz[node];
            ret += 1ll  * sbt * (x - sbt); 
            continue;
        }
        int sbt = subsz[c];
        ret += 1ll * sbt * (x - sbt);
        dfs(c, node, root);
    }
    // cout << "node: " << node << " ret:" << ret << "\n";
    ans += ret;
}

void dfs2(int node, int par, int root) {
    // cout << "node:" << node << "\n";
    int conn = 0;
    vis[node] = 1;
    for(auto c : adj[node]) {
        if(!isBr[c[1]]) {
            if(vis[c[0]]) continue;
            dfs2(c[0], node, root);
            continue;
        }
        if(c[0] == par) {
            conn += subsz[root] - subsz[comp[node]];
            continue;
        }    
        conn += subsz[comp[c[0]]];
        dfs2(c[0], node, root);
    }
    if(cmpsz[comp[node]] < 2) return;
    // cout << "node:" << node << "conn: " << conn << "\n";
    // cout << "add : " << 2ll * (cmpsz[comp[node]] - 1) * (subsz[root] - conn - cmpsz[comp[node]]) << "\n";
    ans += 2ll * (cmpsz[comp[node]] - 1) * (subsz[root] - conn - cmpsz[comp[node]]);
}

void solve() {
    cin >> n >> m;
    REP(i, m) {
        int u, v;
        cin >> u >> v;
        edg[i] = {u, v};
        adj[u].pb({v, i});
        adj[v].pb({u, i});
    }    
    for(int i = 1; i <= n; i++) {
        if(tin[i] != -1) continue;
        rt.pb(i);
        find_bridge(i, 0);
    }
    int cur = 1;
    for(int i = 1; i <= n; i++) {
        if(comp[i] == -1) {
            get_comp(i, cur++);
        }
        // cout << "i:" << i << " comp:" << comp[i] << "\n";
    }
    for(int i = 0; i < m; i++) {
        if(isBr[i]) {
            // cout << edg[i][0] << " " << edg[i][1] << endl;
            cadj[comp[edg[i][0]]].pb(comp[edg[i][1]]);
            cadj[comp[edg[i][1]]].pb(comp[edg[i][0]]);
        }
    }
    for(auto c : rt) {
        prec(comp[c], 0);
    }
    for(int i = 1; i < cur; i++) {
        ans += 1ll * cmpsz[i] * (cmpsz[i] - 1) * (cmpsz[i] - 2);
    }
    // cout << "ans: " << ans << "\n";
    for(int c : rt) {
        dfs(comp[c], 0, comp[c]);
    }
    // cout << "ans:" << ans << "\n";
    for(int c : rt) {
        dfs2(c, 0, comp[c]);
    }

    cout << ans << "\n";
}


signed main() {
    fastio();
    solve();
}

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