Submission #967352

#	Time	Username	Problem	Language	Result	Execution time	Memory
967352		steveonalex	Duathlon (APIO18_duathlon)	C++17	100 / 100	132 ms	60772 KiB

count_triplets

#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
typedef unsigned long long ull;
 
#define ALL(v) (v).begin(), (v).end()
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
 
// mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng(1);
ll rngesus(ll l, ll r){return ((ull) rng()) % (r - l + 1) + l;}
 
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
 
ll LASTBIT(ll mask){return mask & (-mask);}
ll pop_cnt(ll mask){return __builtin_popcountll(mask);}
ll ctz(ll mask){return __builtin_ctzll(mask);}
ll clz(ll mask){return __builtin_clzll(mask);}
ll logOf(ll mask){return 63 - clz(mask);}
 
template <class T1, class T2>
    bool minimize(T1 &a, T2 b){
        if (a > b){a = b; return true;}
        return false;
    }
template <class T1, class T2>
    bool maximize(T1 &a, T2 b){
        if (a < b){a = b; return true;}
        return false;
    }
template <class T>
    void printArr(T& a, string separator = " ", string finish = "\n", ostream& out = cout){
        for(auto i: a) out << i << separator;
        out << finish;
    }
template <class T>
    void remove_dup(vector<T> &a){
        sort(ALL(a));
        a.resize(unique(ALL(a)) - a.begin());
    }

const int N = 1e5 + 69;
int n, m;
vector<int> graph[N], dfs_tree[N];

int num[N], low[N];
bool isJoint[N];
vector<int> st;
int dfs_cnt;
vector<vector<int>> bbc;

void tarjan(int u, int p){
    num[u] = low[u] = ++dfs_cnt;

    vector<int> child;
    for(int v: graph[u]) {
        if (v == p) {p = -1; continue;}
        if (num[v]){
            minimize(low[u], num[v]);
        }
        else{
            child.push_back(v);
            tarjan(v, u);
            minimize(low[u], low[v]);
            if (low[v] >= num[u]){
                isJoint[u] = true;
            }
        }
    }
    if (u == p) isJoint[u] = isJoint[u] && (child.size() >= 2);
    for(int v: child){
        if (isJoint[u] && low[v] >= num[u]) dfs_tree[u].push_back(-v);
        else dfs_tree[u].push_back(v);
    }
}

void get_block(int u){
    st.push_back(u);
    for(int v: dfs_tree[u]){
        get_block(abs(v));
        if (v < 0){
            bbc.push_back({});
            while(bbc.back().empty() || bbc.back().back() != abs(v)){
                bbc.back().push_back(st.back());
                st.pop_back();
            }
            bbc.back().push_back(u);
        }
    }
}

vector<int> bc_tree[2*N];
int joint_cnt = 0;
int pos[2*N];
int sz[2 * N];

int generate_block_cut_tree(){
    dfs_cnt = 0;
    for(int i= 1; i<=n; ++i) if (num[i] == 0){
        tarjan(i, i);
        get_block(i);
        if (st.size()) {
            bbc.push_back(st);
            st.clear();
        }
    }

    int idx = 0;
    for(int i= 1; i<=n; ++i){
        if (!isJoint[i]) continue;
        joint_cnt++;
        pos[i] = ++idx;
        sz[idx] = 1;
    }

    // cerr << "\n";
    for(vector<int> i: bbc){
        // printArr(i);
        ++idx;
        sz[idx] = i.size();
        for(int j: i){
            if (isJoint[j]){
                int u = idx, v = pos[j];
                sz[v]--;
                // cerr << u << " " << v << "\n";
                bc_tree[u].push_back(v);
                bc_tree[v].push_back(u);
            }
        }
    }
    return idx;
}

bool visited[N * 2];
int og[N * 2];
ll ans = 0;

void get_sz(int u, int p){
    visited[u] = 1;
    og[u] = sz[u];
    for(int v: bc_tree[u]) if (v != p){
        get_sz(v, u);
        sz[u] += sz[v];
    }
}

void dfs(int u, int p, int source){
    if (u <= joint_cnt){
        vector<pair<int, int>> child;
        for(int v: bc_tree[u]){
            if (v != p) child.push_back({sz[v] - 1, v});
            else child.push_back({sz[source] - sz[u] - 1, v});
        }
        int sum = 0;
        // cerr << "Ver: " << u << "\n";
        for(pair<int, int> i: child) {
            sum += i.first;
            // cerr << i.first << " " << (og[i.second]-1) << "\n";
        }
        // cerr << "Sum: " << sum << "\n";
        // cerr << "\n";

        for(pair<int, int> i: child){
            ans -= 1LL * (og[i.second] - 1) * (sum - i.first) * (sum - i.first - 1);
            ans -= 2LL * (og[i.second] - 1) * (sum - i.first);
        }
    }

    for(int v: bc_tree[u]) if (v != p){
        dfs(v, u, source);
    }
}

int main(void){
    ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    cin >> n >> m;
    // if (m != n - 1) return -1;
    for(int i= 0; i<m; ++i){
        int u, v; cin >> u >> v;
        graph[u].push_back(v);
        graph[v].push_back(u);
    }

    int tree_sz = generate_block_cut_tree();

    for(int i= joint_cnt + 1; i<=tree_sz; ++i) if (!visited[i]){
        get_sz(i, i);
        int M = sz[i];
        ans += 1LL * M * (M - 1) * (M - 2);
        dfs(i, i, i);
    }  

    cout << ans << "\n";

    return 0;
}

• 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