Submission #757268

#	Time	Username	Problem	Language	Result	Execution time	Memory
757268		shjgkwo	Duathlon (APIO18_duathlon)	C++17	31 / 100	304 ms	48872 KiB

count_triplets

#include <algorithm>
#include <iostream>
#include <map>
#include <set>
#include <stack>
#include <vector>

using namespace std;

const int MAXN = 100010;

vector<int> edge[MAXN];

map<int, int> bcce[MAXN];

int bcc_cnt = 0;

int pre_cnt = 0;
int pre[MAXN];
int low[MAXN];
int mypar[MAXN];
int is_sep[MAXN];

long long sum_perm_cnt = 0;
long long node_cnt[MAXN];
long long p[MAXN];

set<int> bcc_node[MAXN];

stack<pair<int, int> > st;

long long ans = 0;

inline const long long nP3(long long n) {
    return n * (n - 1) * (n - 2);
}

inline const long long nP2(long long n) {
    return n * (n - 1);
}

void dfs(int u, int par) {
    int child = 0, flag = 0;
    mypar[u] = par;
    node_cnt[u] = 1;
    low[u] = pre[u] = ++pre_cnt;
    for(auto &v: edge[u]) {
        if(v == par) continue;
        if(!pre[v]) {
            child++;
            st.push({u, v});
            dfs(v, u);
            node_cnt[u] += node_cnt[v];
            low[u] = min(low[u], low[v]);
            if(pre[u] <= low[v]) {
                bcc_cnt++;
                flag = 1;
                while(st.size() && (st.top().first != u || st.top().second != v)) {
                    int x = st.top().first;
                    int y = st.top().second;
                    bcc_node[bcc_cnt].insert(x);
                    bcc_node[bcc_cnt].insert(y);
                    bcce[x][y] = bcc_cnt;
                    bcce[y][x] = bcc_cnt;
                    st.pop();
                }
                int x = st.top().first;
                int y = st.top().second;
                bcc_node[bcc_cnt].insert(x);
                bcc_node[bcc_cnt].insert(y);
                bcce[x][y] = bcc_cnt;
                bcce[y][x] = bcc_cnt;
                st.pop();
                ans += nP3(bcc_node[bcc_cnt].size());
                p[bcc_cnt] = nP2(bcc_node[bcc_cnt].size() - 1);
            }
        }
        else if(pre[u] > pre[v]) {
            st.push({u, v});
            low[u] = min(low[u], pre[v]);
        }
    }
    if(child >= 2 && par == 0) is_sep[u] = 1;
    else if(flag && par != 0) is_sep[u] = 1;
}

int chk[MAXN];
int cached[MAXN];
long long cache_sum[MAXN];

void solve(int origin, int u, int par) {
    long long sum_node_cnt = node_cnt[origin] - node_cnt[u];
    chk[u] = 1;
    long long sep = is_sep[u];

    for (auto &v: edge[u]) {
        if(chk[v]) continue;
        solve(origin, v, u);
        ans += sep * sum_node_cnt * node_cnt[v] * 2;
        sum_node_cnt += node_cnt[v];
    }

    if(!sep) {
        int mybcc = bcce[par][u];
        if(cached[mybcc]) {
            ans += cache_sum[mybcc];
            return;
        }
        long long sum_tmp_node_cnt = 0;
        for(auto &tu: bcc_node[mybcc]) {
            if(bcce[mypar[tu]][tu] != mybcc) {
                long long tmp = node_cnt[origin] - node_cnt[tu];
                cache_sum[mybcc] += sum_tmp_node_cnt * tmp * 2;
                sum_tmp_node_cnt += tmp;
                continue;
            }
            for (auto &v: edge[tu]) {
                if(v == mypar[tu]) continue;
                int anotherbcc = bcce[tu][v];
                if (anotherbcc == mybcc) continue;
                long long tmp = node_cnt[v];
                cache_sum[mybcc] += sum_tmp_node_cnt * tmp * 2;
                sum_tmp_node_cnt += tmp;
            }
        }
        cached[mybcc] = 1;
        ans += cache_sum[mybcc];
        return;
    }

    ans += (node_cnt[origin] - node_cnt[u]) * p[bcce[par][u]] * 2;
    for(auto &v: edge[u]) {
        if(mypar[v] != u) continue;
        int bcc = bcce[u][v];
        ans += (node_cnt[origin] - node_cnt[v] - 1) * p[bcc] * 2;
    }
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
    int n, m; cin >> n >> m;
    for(int i = 0; i < m; i++) {
        int x, y; cin >> x >> y;
        edge[x].push_back(y);
        edge[y].push_back(x);
    }
    for (int i = 1; i <= n; i++) {
        if (pre[i]) {
            continue;
        }
        dfs(i, 0);
    }
    for (int i = 1; i <= n; i++) {
        if (chk[i]) {
            continue;
        }
        solve(i, i, 0);
    }
    cout << ans << "\n";
    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