BOI2020_problem2A

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double db;
typedef pair<int,int> edge;
typedef pair<ll,ll> node;
const int maxn = 200001;
bool vis[maxn];
node val[maxn];
db ans[maxn];
vector<edge>G[maxn];

bool flag, found;
node x;
const db eps = 1e-8;
vector<int> cur;

void dfs(int u, int p){
    vis[u] = 1;
    cur.push_back(u);
    for(auto v:G[u]){
        if(v.first == p) continue;
        node t = {val[u].first * -1ll, v.second - val[u].second};
        if(!vis[v.first]){
            val[v.first] = t;
            dfs(v.first, u);
        } else{
            if(t.first == val[v.first].first){
                if(t.second != val[v.first].second){
                    flag = false;
                    return;
                }
            } else{
                node tx = {t.first - val[v.first].first, val[v.first].second - t.second};
                if(!found) x = tx, found = 1;
                else if(x.first * tx.second != x.second * tx.first){
                        flag = false;
                        return;
                    }
            }
        }
    }
}

db f(db xx){
    db res = 0;
    for(int u:cur)
        res += fabs(xx * (db)val[u].first + (db)val[u].second);
    return res;
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cout.setf(ios::fixed); cout.precision(7);

    int n, m;
    cin >> n >> m;
    while(m--){
        int u, v, c;
        cin >> u >> v >> c;
        G[u].push_back({v,c});
        G[v].push_back({u,c});
    }

    flag = true;
    for(int i = 1; i <= n && flag; i++)
    if(!vis[i]){
        val[i] = {1,0};
        found = false;
        cur.clear();
        dfs(i,-1);
        db xx = 0;
        if(found)
            xx = (db)x.second/(db)x.first;
        else{
            db l = -100000000, r = 100000000;
            while(fabs(r - l) > eps){
                db m1 = l + (r-l)/(db)3;
                db m2 = r - (r-l)/(db)3;
                if(f(m1) > f(m2))
                    l = m1;
                else
                    r = m2;
            }
            xx = l;
        }
        for(int u:cur)
            ans[u] = xx * (db)val[u].first + (db)val[u].second;

    }

    if(!flag){
        cout << "NO";
        return 0;
    }

    cout << "YES\n";
    for(int i = 1; i <= n; i++)
        cout << ans[i] << ' ';

    return 0;
}