Submission #983225

#	Time	Username	Problem	Language	Result	Execution time	Memory
983225		vjudge1	Duathlon (APIO18_duathlon)	C++17	36 / 100	50 ms	21084 KiB

count_triplets

#include <bits/stdc++.h>
#define int long long
using namespace std;
int n, m, i, j, k, mask, x, y, ans, sz[200001], rt[200001], dp[11][12345];
bool u[200001], cyc, cyc2[200001];
vector<int> g[200001];
vector<pair<int, int>> v;
set<pair<int, pair<int, int>>> st;

void dfs(int x, int pr, int r) {
	sz[x] = 1;
	u[x] = 1;
	rt[x] = r;
	for (auto y : g[x]) {
		if (y == pr) continue;
		if (u[y]) {
			cyc = 1;
			continue;
		}
		dfs(y, x, r);
		sz[x] += sz[y];
	}
}

signed main() {
	cin.tie(0)->sync_with_stdio(0);
	#ifdef LOCAL
	freopen("input.txt", "r", stdin);
	#endif
	cin >> n >> m;
	while (m--) {
		cin >> x >> y;
		g[x].push_back(y);
		g[y].push_back(x);
	}
	if (n <= 10 && m <= 100) {
		for (int x = 1; x <= n; x++) {
			for (i = 1; i <= n; i++) {
				for (mask = 0; mask < (1ll << n); mask++) dp[i][mask] = 1e18;
				dp[i][0] = 0;
			}
			dp[x][1ll << (x - 1)] = 0;
			for (mask = 0; mask < (1ll << n); mask++) {
				for (i = 1; i <= n; i++) {
					if ((mask >> (i - 1)) & 1ll) continue;
					for (auto j : g[i]) {
						if ((mask >> (j - 1)) & 1ll) {
							dp[i][mask | (1ll << (i - 1))] = min(dp[i][mask | (1ll << (i - 1))], dp[j][mask] + 1);
						}
					}
				}
			}
			for (int y = 1; y <= n; y++) {
				for (mask = 0; mask < (1ll << n); mask++) {
					if (dp[y][mask] < 1e18) {
						for (int z = 1; z <= n; z++) {
							if (!((mask >> (z - 1)) & 1ll)) continue;
							if (x == y || x == z || y == z) continue;
							//cout << x << " " << z << " " << y << " " << mask << "\n";
							st.insert({x, {z, y}});
							st.insert({y, {z, x}});
						}
					}
				}
			}
		}
		cout << st.size();
		return 0;
	}
	for (i = 1; i <= n; i++) {
		if (!u[i]) {
			cyc = 0;
			dfs(i, i, i);
			v.push_back({i, cyc});
		}
	}
	for (auto i : v) {
		if (!i.second) ans -= (sz[i.first]) * (sz[i.first] - 1);
		else {
			cyc2[i.first] = 1;
			ans += (sz[i.first]) * (sz[i.first] - 1) * (sz[i.first] - 2);
		}
	}
	for (i = 1; i <= n; i++) {
		if (!cyc2[rt[i]]) {
			ans += 2 * (sz[i] - 1) * (sz[rt[i]] - sz[i]);
			ans += 2 * (sz[rt[i]] - sz[i]);
		}
	}
	cout << ans;
}

• Subtask 1: 5 / 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