Submission #387831

#	Time	Username	Problem	Language	Result	Execution time	Memory
387831		milleniumEeee	Duathlon (APIO18_duathlon)	C++14	36 / 100	835 ms	1048580 KiB

count_triplets

#include <bits/stdc++.h>
#define fastInp ios_base::sync_with_stdio(0); cin.tie(0);
#define pii pair<int, int>
#define fr first
#define sc second
#define pb push_back
#define szof(s) (int)s.size()
#define all(s) s.begin(), s.end()
#define mk make_pair
#define int long long
using namespace std;

const int MAXN = (int)1e5 + 5;

vector <int> g[MAXN];

int n, m;
int S, C, F;
bool used[MAXN];

bool dfs(int v) {
	used[v] = 1;
	if (v == F) {
		used[v] = 0;
		if (!used[C]) {
			return false;
		} else {
			return true;
		}
	}
	bool found = false;
	for (int to : g[v]) {
		if (!used[to]) {
			found |= dfs(to);
			if (found) {
				used[v] = 0;
				return true;
			}
		}
	}
	used[v] = 0;
	return false;
}

void subtask1() {
	int ans = 0;
	for (int s = 1; s <= n; s++) {
		for (int c = 1; c <= n; c++) {
			for (int f = 1; f <= n; f++) {
				if (s != c && s != f && c != f) {
					S = s;
					C = c;
					F = f;
					if (dfs(s)) {
						ans++;
					}
				}
			}
		}
	}
	cout << ans << endl;	
	exit(0);
}

bool cycle(int v, int par = -1) {
	used[v] = 1;
	bool f = 0;
	for (int to : g[v]) {
		if (to == par) {
			continue;
		}
		if (!used[to]) {
			f |= cycle(to, v);
		} 
		else if (used[to]) {
			f = 1;
		}
	}
	return f;
}

bool us[MAXN];
void get_sz(int v, int &sz) {
	us[v] = 1;
	sz++;
	for (int to : g[v]) {
		if (!us[to]) {
			get_sz(to, sz);
		}
	}
}

void subtask3() {
	for (int i = 1; i <= n; i++) {
		if (szof(g[i]) > 2) {
			return;
		}
	}
	vector <pii> vec;
	for (int i = 1; i <= n; i++) {
		if (!us[i]) {
			int sz = 0;
			get_sz(i, sz);
			vec.pb({cycle(i), sz});
		}
	}
	int ans = 0;
	for (pii el : vec) {
		int cycle = el.fr;
		int sz = el.sc;
		if (sz < 3) {
			continue;
		}
		if (cycle) {
			ans += sz * (sz - 1) * (sz - 2);
		} else {
			int sum = 0;
			for (int i = 1; i <= sz; i++) {
				sum += (i - 1) * (sz - i) * 2;
			}
			ans += sum;
		}
	}
	cout << ans << endl;
	exit(0);
}


int sub[MAXN];
void precalc(int v, int par) {
	sub[v] = 1;
	used[v] = 1;
	for (int to : g[v]) {
		if (to == par) {
			continue;
		}
		precalc(to, v);
		sub[v] += sub[to];
	}
}

int tree_ans = 0;
void calc(int v, int par, int root) {
	vector <int> vec;
	for (int to : g[v]) {
		if (to != par) {
			calc(to, v, root);
			vec.pb(sub[to]);
		}
	}
	int sum = 0;
	vec.pb(sub[root] - sub[v]);
	int before = 0;
	for (int i = 0; i < szof(vec); i++) {
		sum += vec[i] * before;
		before += vec[i];
	}
	tree_ans += sum * 2;
}

void solve_for_tree() {
	for (int i = 1; i <= n; i++) {
		if (!used[i]) {
			precalc(i, -1);
			calc(i, -1, i);
		}
	}
	cout << tree_ans << endl;
	exit(0);
}

signed main() {
	cin >> n >> m;
	for (int i = 1; i <= m; i++) {
		int u, v;
		cin >> u >> v;
		g[u].pb(v);
		g[v].pb(u);
	}
	// могут быть несколько компонент
	if (n <= 10 && m <= 100) {
		subtask1();
	}
	subtask3();
	solve_for_tree();
}
/*
12 2
12 11
9 11
*/

• 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