Submission #982361

#	Time	Username	Problem	Language	Result	Execution time	Memory
982361		Faisal_Saqib	Duathlon (APIO18_duathlon)	C++17	36 / 100	1046 ms	1048576 KiB

count_triplets

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ll long long
const int N=1e5+10;
vector<int> ma[N];
// ll pre[N];
bool vis[N];
ll ans=0,sz[N],dp[N],dp_[N];
void dfs(int x,int p=-1)
{
	sz[x]=1;
	vis[x]=1;
	for(auto y:ma[x])
	{
		if(y!=p)
		{
			dfs(y,x);
			sz[x]+=sz[y];
			dp[x]-=(sz[y]*sz[y]);
		}
	}
	dp[x]+=((sz[x]-1)*(sz[x]-1));
}
void ChangeRoot(int x,int y)
{
	// 
	dp[x]+=(sz[y]*sz[y]);
	dp[x]-=((sz[x]-1)*(sz[x]-1));
	dp[y]-=((sz[y]-1)*(sz[y]-1));
	sz[x]-=sz[y];
	sz[y]+=sz[x];
	dp[x]+=((sz[x]-1)*(sz[x]-1));
	dp[y]+=((sz[y]-1)*(sz[y]-1));
	dp[y]-=(sz[x]*sz[x]);
}
void dfs_(int x,int p=-1)
{
	vis[x]=1;
	ans+=dp[x];
	for(auto y:ma[x])
	{
		if(y!=p)
		{			
			ChangeRoot(x,y);
			dfs_(y,x);
			ChangeRoot(y,x);
		}
	}
}
bool cycle=0;
int nodes=0;
void _dfs(int x,int p=-1)
{
	vis[x]=1;
	nodes++;
	for(auto y:ma[x])
	{
		if(y!=p)
		{
			if(vis[y])
			{
				cycle=1;
			}
			else
			{
				_dfs(y,x);
			}
		}
	}
}
int f_cyc(int x)
{
	return (x*(x-1)*(x-2));
}
// int f_lin(int x)
// {
// 	ll cur=(x-1)*(x-1)*(x-1);
// 	return cur-(pre[x-1]);
// }
int f_lin_brute(int x)
{
	ll ans=0;
	ll sp=(x-1)*(x-1);
	for(int j=1;j<=x;j++)
		ans+=(sp-((j-1)*(j-1))-((x-j)*(x-j)));
	return ans;
}
bool senpai[51][51][51];
vector<int> path;
void full(int x)
{
	vis[x]=1;
	for(auto y:ma[x])
	{
		if(!vis[y])
		{
			path.push_back(y);
			full(y);
			path.pop_back();
		}
	}
	for(int i=1;(i+1)<path.size();i++)
		senpai[path[0]][path[i]][path.back()]=1;
	vis[x]=0;
}
void solve()
{
	// int n,m;
	// cin>>n;
	// // m=n-1;
	int n,m;
	cin>>n>>m;
	vector<int> deg(n+2);
	for(int i=0;i<m;i++)
	{
		int x=i+1,y=i+2;
		cin>>x>>y;
		deg[x]++;
		deg[y]++;
		ma[x].push_back(y);
		ma[y].push_back(x);
	}
	int mx=0;
	for(int i=1;i<=n;i++)
		mx=max(mx,deg[i]);
	if(n<=50)
	{
		for(int i=1;i<=n;i++)
		{
			path.push_back(i);
			full(i);
			path.pop_back();
		}
		for(int a=1;a<=n;a++)
			for(int b=1;b<=n;b++)
				for(int c=1;c<=n;c++)
					ans+=senpai[a][b][c];
	}
	else if(mx<=2)
	{
		// Solve a Cycle or a Path
		for(int i=1;i<=n;i++)
		{
			if(!vis[i])
			{
				cycle=0;
				nodes=0;
				_dfs(i);
				if(cycle)
				{
					ans+=f_cyc(nodes);
				}
				else
				{
					ans+=f_lin_brute(nodes);
				}
			}
		}
	}
	else
	{
		// Solve on Tree	
		for(int i=1;i<=n;i++)
		{
			if(!vis[i])
			{
				dfs(i);
			}
		}
		for(int i=1;i<=n;i++)
			vis[i]=0;
		for(int i=1;i<=n;i++)
		{
			if(!vis[i])
			{
				dfs_(i);
			}
		}
	}
	cout<<ans<<'\n';
}
signed main()
{
  cin.tie(0);
  cout.tie(0);
  ios::sync_with_stdio(0);
  // pre[0]=0;
  // ll asp=1e5+1;
  // for(int i=1;i<=asp;i++)
  // 	pre[i]=pre[i-1]+(i*i);
  solve();
}

Compilation message (stderr)

count_triplets.cpp: In function 'void full(long long int)':
count_triplets.cpp:103:19: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  103 |  for(int i=1;(i+1)<path.size();i++)
      |              ~~~~~^~~~~~~~~~~~

• 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