Submission #1030609

#	Time	Username	Problem	Language	Result	Execution time	Memory
1030609		ttamx	Graph (BOI20_graph)	C++17	100 / 100	244 ms	20168 KiB

Graph

#include<bits/stdc++.h>

using namespace std;

using db = long double;
using ll = long long;

const db INVPHI=(sqrt(db(5))-1)/2;

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n,m;
    cin >> n >> m;
    vector<vector<pair<int,int>>> adj(n);
    for(int i=0;i<m;i++){
        int u,v,w;
        cin >> u >> v >> w;
        u--,v--;
        adj[u].emplace_back(v,w);
        adj[v].emplace_back(u,w);
    }
    vector<bool> vis(n);
    vector<ll> a(n),b(n);
    vector<int> comp;
    pair<ll,ll> val;
    bool found=false;
    function<void(int)> dfs=[&](int u){
        comp.emplace_back(u);
        vis[u]=true;
        for(auto [v,w]:adj[u]){
            if(!vis[v]){
                a[v]=-a[u];
                b[v]=w-b[u];
                dfs(v);
            }else{
                if(a[u]+a[v]==0){
                    if(b[u]+b[v]!=w){
                        cout << "NO",exit(0);
                    }
                }else{
                    ll num=w-b[u]-b[v];
                    ll den=a[u]+a[v];
                    if(!found){
                        found=true;
                        val={num,den};
                    }else if(num*val.second!=val.first*den){
                        cout << "NO",exit(0);
                    }
                }
            }
        }
    };
    vector<db> ans(n);
    for(int i=0;i<n;i++)if(!vis[i]){
        comp.clear();
        found=false;
        a[i]=1,b[i]=0;
        dfs(i);
        auto calc=[&](db x){
            db res=0.0;
            for(auto u:comp){
                ans[u]=a[u]*x+b[u];
                res+=abs(ans[u]);
            }
            return res;
        };
        if(found){
            db x=db(val.first)/db(val.second);
            calc(x);
        }else{
            db l=-1e6,r=1e6;
            for(int t=0;t<200;t++){
                db s=(r-l)*INVPHI;
                db l2=r-s,r2=l+s;
                if(calc(l2)<calc(r2))r=r2;
                else l=l2;
            }
            calc((l+r)/2.0);
        }
    }
    cout << fixed << setprecision(10);
    cout << "YES\n";
    for(auto x:ans)cout << x << " ";
}

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