Submission #727652

#	Time	Username	Problem	Language	Result	Execution time	Memory
727652		SanguineChameleon	Duathlon (APIO18_duathlon)	C++17	70 / 100	85 ms	15752 KiB

count_triplets

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

void just_do_it();

int main() {
	#ifdef KAMIRULEZ
		freopen("kamirulez.inp", "r", stdin);
		freopen("kamirulez.out", "w", stdout);
	#endif
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	just_do_it();
	return 0;
}

const int maxn = 1e5 + 20;
vector<int> adj[maxn];
vector<int> comp;
bool can[55][55][55];
bool bad[maxn];
bool flag[maxn];
int par[maxn];
int depth[maxn];
int high[maxn];
int sz[maxn];
int node_cnt = 0;
int edge_cnt = 0;
int n, m;

void dfs1(int x, int a, int b) {
	can[x][a][b] = true;
	for (auto c: adj[b]) {
		if (c != x && !can[x][a][c]) {
			dfs1(x, a, c);
		}
	}
}

void dfs2(int u, int p, bool sub7 = false) {
	par[u] = p;
	high[u] = depth[u];
	comp.push_back(u);
	flag[u] = true;
	node_cnt++;
	edge_cnt += adj[u].size();
	sz[u] = 1;
	for (auto v: adj[u]) {
		if (v == p) {
			continue;
		}
		if (!flag[v]) {
			depth[v] = depth[u] + 1;
			dfs2(v, u, sub7);
			sz[u] += sz[v];
			high[u] = min(high[u], high[v]);
		}
		else {
			high[u] = min(high[u], depth[v]);
		}
	}
}

void sub1() {
	for (int x = 1; x <= n; x++) {
		for (int a = 1; a <= n; a++) {
			if (a != x) {
				dfs1(x, a, a);
			}
		}
		bad[x] = false;
	}
	int res = 0;
	for (int a = 1; a <= n; a++) {
		for (int b = 1; b <= n; b++) {
			if (b == a) {
				continue;
			}
			for (int c = 1; c <= n; c++) {
				if (c == a || c == b) {
					continue;
				}
				bool ok = true;
				for (int x = 1; x <= n; x++) {
					if (x == b) {
						continue;
					}
					if (!can[x][a][b] && !can[x][b][c]) {
						ok = false;
						break;
					}
				}
				if (ok) {
					res++;
				}
			}
		}
	}
	cout << res;
}

long long solve(int root) {
	comp.clear();
	node_cnt = 0;
	edge_cnt = 0;
	dfs2(root, -1, true);
	edge_cnt /= 2;
	if (node_cnt == edge_cnt) {
		return 1LL * node_cnt * (node_cnt - 1) * (node_cnt - 2);
	}
	long long res = 0;
	for (auto u: comp) {
		res += 1LL * sz[u] * (node_cnt - sz[u]) * 2;
	}
	res -= 1LL * node_cnt * (node_cnt - 1);
	return res;
}

long long dfs3(int u) {
	int cnt = 1;
	for (auto v: adj[u]) {
		if (par[v] == u && high[v] >= depth[u]) {
			cnt += sz[v];
		}
	}
	long long res = 1LL * cnt * (cnt - 1);
	for (auto v: adj[u]) {
		if (par[v] == u && high[v] < depth[u]) {
			res += dfs3(v);
		}
	}
	return res;
}

void sub8() {
	long long res = 0;
	for (int u = 1; u <= n; u++) {
		node_cnt = 0;
		for (int i = 1; i <= n; i++) {
			flag[i] = false;
		}
		depth[u] = 0;
		dfs2(u, -1);
		res += 1LL * (node_cnt - 1) * (node_cnt - 2);
		for (auto v: adj[u]) {
			if (par[v] == u) {
				res -= dfs3(v);
			}
		}
	}
	cout << res;
}

void just_do_it() {
	cin >> n >> m;
	for (int i = 0; i < m; i++) {
		int u, v;
		cin >> u >> v;
		adj[u].push_back(v);
		adj[v].push_back(u);
	}
	if (n <= 50) {
		sub1();
		return;
	}
	if (n <= 1000) {
		sub8();
		return;
	}
	long long res = 0;
	for (int i = 1; i <= n; i++) {
		if (!flag[i]) {
			res += solve(i);
		}
	}
	cout << res;
	return;
}

• 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: 0 / 20
• Subtask 8: 8 / 8
• Subtask 9: 0 / 10