Submission #973946

#	Time	Username	Problem	Language	Result	Execution time	Memory
973946		NotLinux	Graph (BOI20_graph)	C++17	100 / 100	151 ms	29128 KiB

Graph

//author : FatihCihan
#include <bits/stdc++.h>
using namespace std;
#define all(v) v.begin() , v.end()
#define sz(a) (int)a.size()
#define int long long
#define double long double
const int N = 1e5 + 7;
const int inf = 1e9 + 7;
const double EPS = 0.00000001;
const double INF = 1e9 + 7;
int n,m;
vector < pair < int , int > > graph[N];
pair < int , int > mem[N];//ax + b
int par[N];
int find(int a){
	if(par[a] == a)return a;
	return par[a] = find(par[a]);
}
void merge(int a , int b){
	par[find(a)] = find(b);
}
void solve(){
	cin >> n >> m;
	iota(par , par + n + 1 , 0);
	for(int i = 0;i<=n;i++)mem[i] = {inf , inf};
	for(int i = 0;i<m;i++){
		int a,b,c;
		cin >> a >> b >> c;
		graph[a].push_back({b , c});
		graph[b].push_back({a , c});
		merge(a,b);
	}
 
	int cnt_soln[n+1];
	memset(cnt_soln , 0 , sizeof(cnt_soln));
	double soln[n+1];
 
	set < int > roots;
	vector < int > components[n+1];
	for(int i = 1;i<=n;i++){
		roots.insert(find(i));
		components[find(i)].push_back(i);
	}
 
 
	queue < pair < int , pair < int , int > > > q;
	for(auto itr : roots){
		q.push({itr , {1 , 0}});		
	}
 
	while(sz(q)){
		int node = q.front().first;
		pair < int , int > eq = q.front().second;
		q.pop();
		if(mem[node] != pair < int , int >{inf , inf}){// check whether it matches or not
			if(mem[node].first == eq.first and mem[node].second != eq.second){
				cout << "NO" << endl;
				return;
			}
			else if(mem[node].first == eq.first){
				37;
			}
			else{
				if(cnt_soln[find(node)]){
					double mysoln = (double)(mem[node].second - eq.second) / (double)(eq.first - mem[node].first);
					if(abs(soln[find(node)] - mysoln) > EPS)cnt_soln[find(node)]++;
				}
				else{
					cnt_soln[find(node)]++;
					soln[find(node)] = (double)(mem[node].second - eq.second) / (double)(eq.first - mem[node].first);
				}
			}
		}
		else{
			mem[node] = eq;
			// cout << "node " << node << " : " << eq.first << " " << eq.second << endl;
			for(auto itr : graph[node]){
				q.push({itr.first , {-eq.first , itr.second - eq.second}});
			}
		}
	}
	double ans[n+1];
	for(auto itr : roots){
		if(cnt_soln[itr] > 1){
			cout << "NO" << endl;
			return;
		}
		else if(cnt_soln[itr] == 1){
			for(auto i : components[itr]){
				ans[i] = mem[i].first * soln[itr] + mem[i].second;
			}
		}
		else{
			auto check = [&](double x){
				double ret = 0;
				for(auto i : components[itr]){	
					ret += abs((double)mem[i].first * x + (double)mem[i].second);
				}	
				return ret;
			};
			double l = -INF , r = INF;
			while(abs(l - r) > EPS){
				double mid = (l + r) / 2;
				if(check(mid) < check(mid + EPS)){
					r = mid;				
				}
				else{
					l = mid + EPS;
				}
			}
			for(auto i : components[itr]){
				ans[i] = mem[i].first * l + mem[i].second;
			}
		}
	}
	cout << "YES" << endl;
	for(int i = 1;i<=n;i++)cout << fixed << setprecision(6) << ans[i] << " ";
	cout << endl;
}
signed main(){
	ios_base::sync_with_stdio(0);cin.tie(0);
	int testcase = 1;//cin >> testcase;
	while(testcase--)solve();
	cerr << 1000.0 * clock() / CLOCKS_PER_SEC << " ms" << endl;
}

Compilation message (stderr)

Graph.cpp: In function 'void solve()':
Graph.cpp:62:5: warning: statement has no effect [-Wunused-value]
   62 |     37;
      |     ^~

• Subtask 1: 5 / 5
• Subtask 2: 12 / 12
• Subtask 3: 17 / 17
• Subtask 4: 24 / 24
• Subtask 5: 42 / 42