This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define mp make_pair
#define all(a) a.begin(), a.end()
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<int, double> pid;
const double DINF = 1e18;
const ll INF = 1e18;
const double EPS = 1e-3;
vector<vector<pid> > graph;
vector<double> val;
double sum;
bool ok = false;
void dfs1(int curr) {
if (!ok)
return;
for (auto &[a, d] : graph[curr]) {
double new_v = d - val[curr];
if (val[a] != DINF and abs(val[a] - new_v) > EPS)
{
ok = false;
return;
}
if (val[a] != DINF)
continue;
val[a] = new_v; sum += abs(new_v);
dfs1(a);
}
}
vector<bool> visited;
vector<vector<int> > cmp;
void dfs2(int curr, vector<int> &cmp) {
cmp.push_back(curr); visited[curr] = true;
for (auto &[a, d] : graph[curr])
if (!visited[a])
dfs2(a, cmp);
}
ll tryy(int idx, double v, vector<int> &comp) {
for (int a : comp)
val[a] = DINF;
val[idx] = v;
sum = abs(v), ok = true;
dfs1(idx);
if (!ok)
return INF;
return sum;
}
pair<ll, double> get_for_cmp(int guy) {
int cmp_size = cmp[guy].size(); pair<ll, double> mini(INF, 0);
for (int val = -cmp_size*10; val <= cmp_size*10; val++)
mini = min(mini, {tryy(guy, (double)val/2.0, cmp[guy]), (double)val/2.0});
return mini;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, m;
cin >>n >> m;
graph.resize(n+1);
val.resize(n+1);
visited.resize(n+1);
cmp.resize(n+1);
for (int i = 0; i < m; i++) {
int f, t, w;
cin >> f >> t >> w;
graph[f].push_back({t, w});
graph[t].push_back({f, w});
}
// init_cmp
for (int i = 1; i <= n; i++) {
if (!visited[i]) {
dfs2(i, cmp[i]);
auto v = get_for_cmp(i);
if (v.first == INF)
{
cout <<"NO\n";
return 0;
}
tryy(i, v.second, cmp[i]);
}
}
cout <<"YES\n";
for (int i = 1; i <= n; i++)
cout << val[i] << " ";
cout << "\n";
}
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