Submission #699626

#	Time	Username	Problem	Language	Result	Execution time	Memory
699626		finn__	Duathlon (APIO18_duathlon)	C++17	100 / 100	123 ms	32368 KiB

count_triplets

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

#define N 200000

vector<unsigned> g[N], bccg[N];
unsigned y[N], l[N], subtree_size[N], s[N];
bitset<N> visited;
size_t n, m, t = 0, n_bcc;

unsigned build_bcc_tree(unsigned u, unsigned p = -1, unsigned i = 0)
{
    y[u] = l[u] = i++;
    visited[u] = 1;
    s[t++] = u;

    for (unsigned const &v : g[u])
    {
        if (!visited[v])
        {
            i = build_bcc_tree(v, u, i);
            l[u] = min(l[u], l[v]);

            if (l[v] >= y[u])
            {
                // Collect all nodes in the BCC of u and v. u is an articulation
                // point, so leave it in the stack.
                bccg[u].push_back(n_bcc);
                while (s[t] != v)
                    bccg[n_bcc].push_back(s[--t]);
                n_bcc++;
            }
        }
        else if (v != p)
            l[u] = min(l[u], y[v]);
    }

    return i;
}

// The BCC graph is bipartite with BCCs in one partition and original nodes in
// the other.
uint64_t get_bad_triples(unsigned u, uint64_t c, unsigned p = -1)
{
    uint64_t ans = 0;
    subtree_size[u] = u < n;
    for (unsigned const &v : bccg[u])
    {
        if (v != p)
        {
            ans += get_bad_triples(v, c, u);
            subtree_size[u] += subtree_size[v];
            if (v < n)
                ans += bccg[u].size() * subtree_size[v] * (subtree_size[v] - 1);
        }
    }

    if (u >= n) // Add the contribution with the pair (s, f) outside u's subtree.
        ans += bccg[u].size() * (c - subtree_size[u]) * (c - subtree_size[u] - 1);
    return ans;
}

int main()
{
    scanf("%zu %zu", &n, &m);
    n_bcc = n;

    for (size_t i = 0; i < m; i++)
    {
        unsigned u, v;
        scanf("%u %u", &u, &v);
        g[u - 1].push_back(v - 1);
        g[v - 1].push_back(u - 1);
    }

    unsigned long long ans = 0;
    for (size_t i = 0; i < n; i++)
        if (!visited[i])
        {
            uint64_t c = build_bcc_tree(i);
            ans -= get_bad_triples(i, c);
            ans += c * (c - 1) * (c - 2);
        }

    printf("%llu\n", ans);
}

Compilation message (stderr)

count_triplets.cpp: In function 'int main()':
count_triplets.cpp:65:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   65 |     scanf("%zu %zu", &n, &m);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~
count_triplets.cpp:71:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   71 |         scanf("%u %u", &u, &v);
      |         ~~~~~^~~~~~~~~~~~~~~~~

• 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