| # | 제출 시각 | 아이디 | 문제 | 언어 | 결과 | 실행 시간 | 메모리 |
|---|---|---|---|---|---|---|---|
| 906367 | 2024-01-14T07:02:44 Z | MON | Graph (BOI20_graph) | C++14 | 0 ms | 0 KB |
#include<iostream>
#include<random>
#include<ctime>
#include<vector>
#include<bitset>
#include<iomanip>
using namespace std;
using pii = pair<int,int>;
using pid = pair<int,double>;
const double bulan[] = {0,0.25,-0.25,-0.5,0.5,-0.75,0.75,-1,1,-1.25,1.25,-1.5,1.5,-1.75,1.75,-2,2,2.5,-2.5,3,-3,3.5,-3.5,4,-4
2.25,0.33,-0.33,0.66,-0.66,5,-5,6,-6,-5.5,5,7,-7,8,-9,9,-8};
constexpr double eps = 1e-6;
constexpr int NMAX = 1e5 + 1;
mt19937 rng(time(nullptr));
bitset<NMAX> viz,fix; double ans[NMAX];
vector<pii> vecini[NMAX];
void dfs(int a,vector<int> &u)
{
u.emplace_back(a); viz[a] = 1;
for(auto &it : vecini[a])
if(!viz[it.first]) dfs(it.first,u);
}
void go(int a,double v,vector<pid> &res)
{
res.push_back({a,v}); viz[a] = 1; ans[a] = v;
for(auto &it : vecini[a])
{
if(!viz[it.first])
go(it.first,it.second - v,res);
}
}
long double ab(vector<pid> &h)
{
long double res = 0;
for(auto &it : h) res += abs(it.second);
return res;
}
bool ok(vector<int> &h)
{
for(auto &f : h)
{
for(auto &s : vecini[f])
{
if(abs(ans[f] + ans[s.first] - s.second) > eps)
return 0;
}
}
return 1;
}
void solve(vector<int> &comp)
{
for(auto &v : comp)
{
if(fix[v])
{
vector<pid> h; go(v,ans[v],h);
for(auto &it : h) ans[it.first] = it.second;
return;
}
}
long double mini = 1e18; vector<pid> res;
uniform_int_distribution<int> d(0,comp.size()-1);
int mumu = comp[d(rng)];
for(auto &val : bulan)
{
for(auto &it : comp) viz[it] = 0;
vector<pid> h; go(mumu,val,h); double now = ab(h);
if(now < mini && ok(comp))
{
mini = now;
res.swap(h);
}
}
for(auto &it : res)
ans[it.first] = it.second;
}
int main()
{
int n,m,a,b,c; cin >> n >> m;
for(int i = 1; i <= m ; i++)
{
cin >> a >> b >> c;
vecini[a].push_back({b,c});
vecini[b].push_back({a,c});
if(a == b)
{
fix[a] = 1;
ans[a] = (1.0 * c / 2);
}
}
vector<vector<int>> comps;
for(int i = 1; i <= n ; i++)
{
if(!viz[i])
{
vector<int> comp;
dfs(i,comp); comps.push_back(comp);
}
}
viz.reset();
for(auto &it : comps)
solve(it);
bool okk = 1;
for(auto &c : comps) okk &= ok(c);
if(!okk) cout << "NO";
else
{
cout << "YES\n";
for(int i = 1; i <= n ; i++)
cout << fixed << setprecision(2) << ans[i] << " ";
}
}