Submission #402802

#	Time	Username	Problem	Language	Result	Execution time	Memory
402802		dxz05	Duathlon (APIO18_duathlon)	C++14	31 / 100	866 ms	1048580 KiB

count_triplets

#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

void debug_out() { cerr << endl; }

template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << "[" << H << "]";
    debug_out(T...);
}

#ifdef dddxxz
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

#define SZ(s) ((int)s.size())
#define all(x) (x).begin(), (x).end()
#define revall(x) (x).rbegin(), (x).rend()

clock_t startTime;

double getCurrentTime() {
    return (double) (clock() - startTime) / CLOCKS_PER_SEC;
}

typedef long long ll;
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
const double eps = 0.00001;
const int MOD = 1e9 + 7;
const int INF = 1000000101;
const long long LLINF = 1223372000000000555;
const int N = 1e6 + 3e2;
const int M = 2222;

int n, m;
vector<int> g[N];

set<pair<int, int>> deleted;

bool check(int s, int c, int f){
    queue<int> q;
    vector<int> parent(n + 1);
    vector<bool> used(n + 1);
    q.push(c);
    while (!q.empty()){
        int x = q.front(); q.pop();
        for (int y : g[x]){
            if (!used[y] && y != f){
                used[y] = true;
                parent[y] = x;
                q.push(y);
            }
        }
    }

    if (!used[s]) return false;

    int ss = s;
    while (ss != c){
        deleted.insert(make_pair(ss, parent[ss]));
        deleted.insert(make_pair(parent[ss], ss));
        ss = parent[ss];
    }

    used.assign(n + 1, 0);

    q.push(c);
    while (!q.empty()){
        int x = q.front(); q.pop();
        for (int y : g[x]){
            if (!used[y] && deleted.find(make_pair(x, y)) == deleted.end() && y != s){
                used[y] = true;
                q.push(y);
            }
        }
    }

    deleted.clear();

    if (!used[f]) return false;
//    cout << s << ' ' << c << ' ' << f << endl;
    return true;
}

void Subtask_1(){
    int ans = 0;
    for (int i = 1; i <= n; i++){
        for (int j = 1; j <= n; j++){
            for (int k = 1; k <= n; k++){
                if (i == j || i == k || j == k) continue;
                bool cur = check(i, j, k) || check(k, j, i);
                ans += cur;
            }
        }
    }
    cout << ans;
    exit(0);
}

int cnt = 0, color[N];

bool cycle = false;

void dfs(int v, int p){
    color[v] = 1;
    cnt++;
    for (int u : g[v]){
        if (u == p) continue;
        if (color[u] == 1) cycle = true;
        if (color[u] == 0) dfs(u, v);
    }
    color[v] = 2;
}
void Subtask_3(){
    ll ans = 0;
    for (int i = 1; i <= n; i++){
        if (color[i] == 0){
            cnt = 0;
            cycle = false;
            dfs(i, 0);
            ans += 1ll * cnt * (cnt - 1) * (cnt - 2) / (cycle ? 1 : 3);
        }
    }

    cout << ans;

    exit(0);
}
ll ans5 = 0;
int subtree[N];

bool used[N];

void dfs2(int v, int p){
    used[v] = true;
    subtree[v] = 1;
    for (int u : g[v]){
        if (u != p){
            dfs2(u, v);
            subtree[v] += subtree[u];
        }
    }

    for (int u : g[v]){
        if (u != p){
            ll x = subtree[u], y = cnt - subtree[u] - 1;
            ans5 += x * y;
        } else {
            ll x = subtree[v] - 1, y = cnt - x - 1;
            ans5 += x * y;
        }
    }

}

void Subtask_5(){
    memset(color, 0, sizeof(color));
    for (int i = 1; i <= n; i++){
        if (!used[i]){
            cnt = 0;
            dfs(i, i);
            dfs2(i, i);
        }
    }
    cout << ans5 << endl;
    exit(0);
}

void solve(int TC) {
    cin >> n >> m;

    bool ok3 = true;
    while (m--) {
        int u, v;
        cin >> u >> v;
        g[u].push_back(v);
        g[v].push_back(u);

        ok3 &= g[u].size() <= 2;
        ok3 &= g[v].size() <= 2;
    }

    if (n <= 50 && m <= 100) {
        Subtask_1();
    }

    if (ok3){
        Subtask_3();
    }

    Subtask_5();

}


int main() {
    startTime = clock();
    cin.tie(nullptr); cout.tie(nullptr);
    ios_base::sync_with_stdio(false);

    bool llololcal = false;
#ifdef dddxxz
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    llololcal = true;
#endif

    int TC = 1;
    //  cin >> TC;

    for (int test = 1; test <= TC; test++) {
        //debug(test);
        //cout << "Case #" << test << ": ";
        solve(test);
    }

    if (llololcal) cerr << endl << "Time: " << int(getCurrentTime() * 1000) << " ms" << endl;

    return 0;
}

• 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