Submission #252408

#	Time	Username	Problem	Language	Result	Execution time	Memory
252408		Saboon	Duathlon (APIO18_duathlon)	C++14	82 / 100	539 ms	1048580 KiB

count_triplets

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 3e5 + 20;
const int mod = 1e9 + 7;

vector<int> g[maxn], t[maxn];
int dw[maxn], h[maxn], rt[maxn], a[maxn], sz[maxn];
bool visited[maxn];
int sz2[maxn];
ll answer = 0;

void dfs2(int v, int par = -1){
	sz2[v] = a[v];
	for (auto u : t[v]){
		if (u != par){
			dfs2(u, v);
			sz2[v] += sz2[u];
			answer += 1ll * a[v] * sz2[u] * (sz[rt[v]] - sz2[u] - a[v]);
		}
	}
	if (par != -1)
		answer += 1ll * a[v] * (sz2[v] - a[v]) * (sz[rt[v]] - sz2[v]);
}

int dfs(int v, int root){
	rt[v] = root;
	visited[v] = true;
	int ret = h[v];
	sz[v] = 1;
	dw[v] = v;
	a[v] = 1;
	for (auto u : g[v]){
		if (!visited[u]){
			h[u] = h[v] + 1;
			int k = dfs(u, root);
			sz[v] += sz[u];
			if (k <= h[v]){
				a[v] = a[u];
				dw[v] = dw[u];
			}
			ret = min(ret, k);
		}
		else if (h[u] < h[v] - 1){
			dw[v] = v;
			a[v] = h[v] - h[u] + 1;
			ret = h[u];
		}
	}
	return ret;
}

int e1[maxn], e2[maxn];
int par[55];

int get_par(int v){ return par[v] < 0 ? v : par[v] = get_par(par[v]); }

void merge(int v, int u){
	if ((v = get_par(v)) == (u = get_par(u)))
		return;
	par[v] = u;
}

bool ok[55][55][55];

int main(){
	ios_base::sync_with_stdio(false);
	int n, m;
	cin >> n >> m;
	if (n <= 50){
		for (int i = 1; i <= m; i++)
			cin >> e1[i] >> e2[i];
		for (int i = 1; i <= n; i++)
			for (int j = 1; j <= n; j++)
				for (int k = 1; k <= n; k++)
					if (i != j and i != k and j != k)
						ok[i][j][k] = 1;
		for (int x = 1; x <= n; x++){
			memset(par, -1, sizeof par);
			for (int i = 1; i <= m; i++)
				if (e1[i] != x and e2[i] != x)
					merge(e1[i], e2[i]);
			for (int i = 1; i <= n; i++)
				for (int j = 1; j <= n; j++)
					for (int k = 1; k <= n; k++)
						if (i != x and k != x and j != x and get_par(i) != get_par(j) and get_par(j) != get_par(k))
							ok[i][j][k] = 0;
			for (int i = 1; i <= n; i++)
				for (int j = 1; j <= n; j++)
					if (i != x and j != x and get_par(i) != get_par(j))
						ok[x][i][j] = ok[i][j][x] = 0;
		}
		int answer = 0;
		for (int i = 1; i <= n; i++)
			for (int j = 1; j <= n; j++)
				for (int k = 1; k <= n; k++)
					if (i != j and j != k and k != i and ok[i][j][k])
						answer += ok[i][j][k];
		cout << answer << endl;
		return 0;
	}
	for (int i = 0; i < m; i++){
		int v, u;
		cin >> v >> u;
		g[v].push_back(u);
		g[u].push_back(v);
	}
	for (int v = 1; v <= n; v++)
		if (!visited[v])
			dfs(v, v);
	for (int i = 1; i <= n; i++)
		for (auto j : g[i])
			if (dw[i] != dw[j])
				t[dw[i]].push_back(dw[j]);
	for (int v = 1; v <= n; v++)
		if (h[v] == 0)
			dfs2(dw[v]);
	for (int c = 1; c <= n; c++){
		if (a[dw[c]] == 1)
			continue;
		int tot = 0;
		for (auto u : g[c]){
			if (h[u] == h[c]+1 and dw[u] != dw[c]){
				answer -= 2ll * (a[dw[c]]-1) * sz[u] * tot;
				tot += sz[u];
			}	
			if (h[u] == h[c]-1 and dw[u] != dw[c]){
				answer -= 2ll * (a[dw[c]]-1) * (sz[rt[c]] - sz[c]) * tot;
				tot += (sz[rt[c]] - sz[c]);
			}
		}
	}
	for (int v = 1; v <= n; v++)
		if (dw[v] == v and a[v] >= 3)
			answer -= 1ll*a[v]*(a[v]-1)*(a[v]-2);
	for (int f = 1; f <= n; f++){
		if (a[dw[f]] == 1)
			continue;
		int subsz = 1;
		for (auto u : g[f]){
			if (h[u] == h[f]+1 and dw[u] != dw[f])
				subsz += sz[u];
			if (h[u] == h[f]-1 and dw[u] != dw[f])
				subsz += (sz[rt[f]] - sz[f]);
		}
		int outsz = sz[rt[f]] - subsz;
		answer += 2ll * (a[dw[f]]-1) * (outsz-1);
	}
	cout << answer << endl;
}

• 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: 0 / 8
• Subtask 9: 0 / 10