Submission #229719

#	Time	Username	Problem	Language	Result	Execution time	Memory
229719		lyc	Duathlon (APIO18_duathlon)	C++14	49 / 100	108 ms	37108 KiB

count_triplets

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

#define TRACE(x) cerr << #x << " :: " << x << endl
#define _ << " " <<
#define SZ(x) (int)(x).size()
#define ALL(x) (x).begin(),(x).end()
#define FOR(i,a,b) for(int i=(a);i<=(b);++i)
#define RFOR(i,a,b) for (int i=(a);i>=(b);--i)

const int MX_N = 1e5+5;
int N, M;
vector<int> al[MX_N];

namespace BCT {
    int pre[MX_N], low[MX_N], cnt, root, rootChildren;

    vector<int> stk;
    int comp[MX_N], sz[MX_N];
    int nap, nv;

    vector<int> tree[MX_N];

    void dfs(int u, int p) {
        pre[u] = low[u] = ++cnt;
        for (int v : al[u]) if (v != p) {
            if (pre[v] == -1) {
                dfs(v,u);
                if (u == root) ++rootChildren;
                else if (comp[u] == -1 && low[v] >= pre[u]) comp[u] = ++nv, sz[nv] = 1;
                low[u] = min(low[u],low[v]);
            } else {
                low[u] = min(low[u],pre[v]);
            }
        }
    }

    void addEdge(int u, int v) {
        tree[u].push_back(v);
        tree[v].push_back(u);
    }

    void decomp(int u, int p) {
        pre[u] = ++cnt;
        stk.push_back(u);
        for (int v : al[u]) if (v != p) {
            if (pre[v] == -1) {
                int st = stk.back();
                decomp(v,u);

                if (comp[u] != -1 && low[v] >= pre[u]) {
                    sz[++nv] = 1;
                    addEdge(comp[u],nv);
                    while (stk.back() != st) {
                        int& w = stk.back(); stk.pop_back();
                        ++sz[nv];
                        if (comp[w] == -1) comp[w] = nv;
                        else addEdge(comp[w],nv);
                    }
                }
            }
        }
    }

    void run() {
        fill_n(comp,N+1,-1); nv = 0;

        fill_n(pre,N+1,-1); cnt = 0;
        FOR(u,1,N) if (pre[u] == -1) {
            root = u, rootChildren = 0;
            dfs(u,0);
            if (rootChildren > 1) comp[u] = ++nv, sz[nv] = 1;
        }
        nap = nv;

        fill_n(pre,N+1,-1); cnt = 0;
        FOR(u,1,N) if (pre[u] == -1) {
            stk.clear();
            decomp(u,0);
            if (comp[u] == -1) {
                sz[++nv] = 0;
                while (!stk.empty()) {
                    int& w = stk.back(); stk.pop_back();
                    ++sz[nv];
                    if (comp[w] == -1) comp[w] = nv;
                    else addEdge(comp[w],nv);
                }
            }
        }
    }

    void dbg() {
        FOR(i,1,N){ TRACE(i _ pre[i] _ low[i] _ comp[i]); }
        TRACE(nv);
        cout << "APs: "; FOR(i,1,N){ if (comp[i] <= nap) cout << i << ' '; } cout << endl;
        FOR(i,1,nv){ cout << i << " (" << sz[i] << "): "; for(int v : tree[i]) { cout << v << ' '; } cout << endl; }
    }

    long long ans;
    int sub[MX_N];

    void precomp(int u, int p) {
        sub[u] = sz[u];
        for (int v : tree[u]) if (v != p) {
            precomp(v,u);
            sub[u] += sub[v];
            --sub[u];
        }
        //TRACE(u _ sz[u] _ u _ sub[u]);
    }

    void trav(int u, int p, int all) {
        //TRACE("trav" _ u _ p _ all);
        if (u <= nap) {
            int other = all - 1;
            for (int v : tree[u]) {
                int cur;
                if (v == p) {
                    cur = all-sub[u];
                } else {
                    cur = sub[v]-1;
                    trav(v,u,all);
                }
                //long long two = 1LL * cur * (other-cur);
                //long long one = 1LL * (sz[v]-1) * (sz[v]-2);
                //long long snk = 2LL * (cur+1-sz[v]) * (sz[v]-2);
                //TRACE(u _ v _ "add" _ cur _ (other-cur) _ "res" _ two _ one _ snk);
                ans += 1LL * cur * (other-cur);     // ep in diff
                ans += 1LL * (sz[v]-1) * (sz[v]-2); // ep in same
                ans += 2LL * (cur+1-sz[v]) * (sz[v]-2); // ep in same subtree
            }
        } else {
            int inside = (sz[u] - SZ(tree[u]));
            int other = all - inside;
            for (int v : tree[u]) {
                other -= sz[v];
            }
            for (int v : tree[u]) {
                int cur;
                if (v == p) {
                    cur = all-sub[u]-(sz[p]-1);
                } else {
                    cur = sub[v]-sz[v];
                    trav(v,u,all);
                }
                //long long two = inside * cur * (other-cur);
                //long long one = 2LL * inside * cur * (sz[u]-2);
                //long long snk = 1LL * (SZ(tree[u])-2) * cur * (other-cur);
                //TRACE(u _ v _ "add" _ cur _ (other-cur) _ "res" _ two _ one _ snk);
                ans += 1LL * inside * cur * (other-cur);// both ep outside
                ans += 2LL * inside * cur * (sz[u]-2);  // one ep outside
                ans += 1LL * (SZ(tree[u])-2) * cur * (other-cur); // both ep outside, mid is ap
            }
            //long long zero = 1LL * inside * (sz[u]-1) * (sz[u]-2);
            //TRACE(u _ zero);
            if (sz[u] >= 3) ans += 1LL * inside * (sz[u]-1) * (sz[u]-2);
        }
    }

    long long solve() {
        ans = 0;
        fill_n(sub,N+1,-1);
        FOR(i,1,nv) if (sub[i] == -1) {
            precomp(i,0);
            trav(i,0,sub[i]);
        }
        return ans;
    }
};

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

    cin >> N >> M;
    FOR(i,1,M){
        int U, V; cin >> U >> V;
        al[U].push_back(V);
        al[V].push_back(U);
    }

    BCT::run();
    //BCT::dbg();
    cout << BCT::solve() << '\n';
}

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