Submission #1196483

#	Time	Username	Problem	Language	Result	Execution time	Memory
1196483		countless	Duathlon (APIO18_duathlon)	C++20	100 / 100	92 ms	27076 KiB

count_triplets

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double ld;

const ll MOD = 998244353;
const ll INF = 1e18;
const ld EPS = 1e-12;

#define endl "\n"
#define sp <<" "<<
#define REP(i, a, b) for(ll i = a; i < b; i++)
#define dbg(x) cout << #x << " = " << x << endl
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fast_io() ios_base::sync_with_stdio(false); cin.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((ll)(x).size())

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

template <typename Key, typename Value>
using hash_map = unordered_map<Key, Value, custom_hash>;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// uniform_int_distribution<int>(a, b)(rng);
// shuffle(all(a), rng);

int n, m, timer, cnt;
ll curr, ans;
vector<vector<int>> adj, bcc;
vector<int> tin, low, siz, st;

void block(int u, int p = 0) {
    low[u] = tin[u] = timer++;
    st.push_back(u);
    curr++;

    for (auto &v : adj[u]) {
        if (v != p) {
            if (tin[v]) {
                low[u] = min(low[u], tin[v]);
            } else {
                block(v, u);
                low[u] = min(low[u], low[v]);
                
                if (low[v] >= tin[u]) {
                    bcc[u].push_back(n + cnt);

                    while (!bcc[n + cnt].size() or bcc[n + cnt].back() != v) {
                        bcc[n + cnt].push_back(st.back());
                        st.pop_back();
                    }

                    cnt++;
                }
            }
        }
    }
}

void fix(int u) {
    siz[u] = (u <= n);

    for (auto &v : bcc[u]) {
        fix(v);
        siz[u] += siz[v];

        if (u > n) {
            ans -= bcc[u].size() * siz[v] * (siz[v]-1);
        }
    }

    if (u > n) {
        ans -= bcc[u].size() * (curr-siz[u]) * (curr-siz[u]-1);
    }
}

void solution() {
    cin >> n >> m;

    timer = cnt = 1;
    adj.assign(n+1, vector<int>()), bcc.assign(2*n+2, vector<int>()), tin.assign(n+1, 0), low.assign(n+1, 0), siz.assign(2*n+2, 0);

    REP(i, 0, m) {
        int u, v; cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }

    ans = 0;
    REP(i, 1, n+1) {
        if (!tin[i]) {
            curr = 0;
            block(i);
            ans += curr * (curr-1) * (curr-2);
            fix(i);
        }
    }

    cout << ans << endl;
    return;
}

signed main() {
    fast_io();

    solution();

    return 0;
}

// Notes
// is it binsearchable?
// is it greedy?
// is it DP?
// if online round: search OEIS, similar topics

// put observations together
// check for edge cases
// try "dumb" solutions, you're fast enough to rewrite
// clean up the implementation
// keep it simple

// check for overflow
// check for small N
// check for array with same or monotonic a_i

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