Submission #1033347

#	Time	Username	Problem	Language	Result	Execution time	Memory
1033347		_8_8_	Duathlon (APIO18_duathlon)	C++17	100 / 100	116 ms	44512 KiB

count_triplets

#include <bits/stdc++.h>
 
using namespace std;
    
typedef long long ll;
const int  N = 4e5 + 21, MOD = (int)1e9+7;
 
int n,m;

bool isb[N];
vector<vector<int>> bcc(vector<vector<int>> &g,vector<int> &sz){
    vector<bool> ap(n+1,0);
    vector<int> tin(n+1,0),up(n+1,0),id(n+1,0);
    vector<int> stk;
    vector<vector<int>> comps,G;
    function <void(int,int,int&)> dfs = [&](int v,int pr,int &t){
        tin[v] = up[v] = ++t;
        stk.push_back(v);
        int cc  =0;
        for(int to:g[v]){
            if(to == pr)continue;
            if(!tin[to]){
                dfs(to,v,t);
                cc++;
                up[v] = min(up[v],up[to]);
                if(up[to] >= tin[v]){
                    if(pr != -1){
                        ap[v] = 1;
                    }
                    comps.push_back({v});
                    while(comps.back().back() != to){
                        comps.back().push_back(stk.back());
                        stk.pop_back();
                    }  
                }
            }else{
                up[v] = min(up[v],tin[to]);
            }
        }
        if(pr == -1){
            ap[v] = (cc > 1);
        }
    };
    int timer = 0;
    for(int i = 1;i <= n;i++){
        if(!tin[i]){
            dfs(i,-1,timer);
        }
    }
    function<vector<vector<int>>()> build_tree = [&]() {
        vector<vector<int>> t(1);
        int it = 0;
        sz = vector<int> (1,0);
        for(int i = 1;i <= n;i++){
            if(ap[i]){
                id[i] = ++it;
                sz.push_back(1);
                sz[id[i]] = 1;
                t.push_back({});
            }
        }
        for(auto c:comps){
            it++;
            isb[it] = 1;
            sz.push_back(0);
            t.push_back({});
            for(auto j:c){
                // cout << j << ' ';
                if(ap[j]){
                    t[id[j]].push_back(it);
                    t[it].push_back(id[j]);
                }else{
                    id[j] = it;
                    sz[it]++;
                }
            }
            // cout << '\n';
        }
        return t;
    };
    return build_tree();
}
vector<vector<int>> g(N),G;
ll calc(vector<int> &S){
    ll s = 0,d = 0,t = 0;
    for(auto i:S){
        t += i *1ll * d;
        d += s * 1ll * i;
        s += i;
    }
    return t;
}
int bf_n,nn = 0;
vector<int> sz;
bool vis[N];
ll ss[N];
void prec(int v,int pr = -1){
    vis[v] = 1;
    ss[v] += sz[v];
    for(int to:G[v]){
        if(to == pr)continue;
        prec(to,v);
        ss[v] += ss[to];
    }
}
ll res = 0;
void clac(int v,int pr = -1){
    ll c = sz[v] * 1ll * (sz[v] - 1);
    res += c / 2 *1ll * (sz[v] - 2 + (int)G[v].size()); 
    res += c * 1ll * (nn - sz[v]);
    vector<ll> vals;
    for(int to:G[v]){
        if(to == pr){
            vals.push_back(nn-ss[v]);
            continue;
        }
        clac(to,v);
        vals.push_back(ss[to]);
    }
    ll D = 0,S = 0;
    ll T = (int)G[v].size();
    if(isb[v]){
        // res += T * (T - 1) / 2 * (T - 2);
    }
    for(ll i:vals){
        D += i * S;
        S += i;
    }
    for(int i = 0;i < (int)vals.size();++i){
        if(isb[v]){
            res += vals[i] *1ll* sz[v]*1ll*((int)vals.size()-1);
            ll left = (int)vals.size() - 1;
            left = left * (left - 1);
            // res +=  left * (vals[i]);
            res += (D - (S - vals[i]) * vals[i]);
        }
    }
    res += D * 1ll * sz[v];
}
void test(){
    cin >> n >> m;
    for(int i = 1;i <= m;i++){
        int u,v;
        cin >> u >> v;
        g[u].push_back(v);
        g[v].push_back(u);
    }
    G = bcc(g,sz);
    // cout << "__________________________________\n";
    n = (int)G.size() - 1;
    for(int i = 1;i <= n;i++){
        // cout << i << ' ' << sz[i] << '\n';
        if(!vis[i]){
            prec(i);
            nn = ss[i];
            clac(i);
        }
    }
    cout << res * 2 << '\n';
}
int main() {
    ios_base::sync_with_stdio(false);cin.tie(0);
    int t = 1; 
    // cin >> t;
    while(t--) {
        test();
    }
}

Compilation message (stderr)

count_triplets.cpp: In function 'void clac(int, int)':
count_triplets.cpp:121:8: warning: unused variable 'T' [-Wunused-variable]
  121 |     ll T = (int)G[v].size();
      |        ^

• 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