Submission #906384

#	Time	Username	Problem	Language	Result	Execution time	Memory
906384		MON	Graph (BOI20_graph)	C++14	34 / 100	21 ms	4128 KiB

Graph

#include<iostream>
#include<random>
#include<ctime>
#include<vector>
#include<bitset>
#include<iomanip>
#include<algorithm>
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,-2.5,2.75,-2.75,3,-3,3.5,-3.5,4,-4,
                        4.5,-4.5,-5,5,-5.5,5.5,-6,6,-6.5,6.5,-7,7};
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);
}

int rnd(int it,uniform_int_distribution<int> &d)
{
    int res = 1e9; while(it--) res = min(res,d(rng));
    return res;
}

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) / 2); sort(comp.begin(),comp.end(),[](int &a,int &b){return vecini[a].size() <  vecini[b].size();});
    int mumu = comp[rnd(2,d)]; 
    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] << " ";
    }
}

• Subtask 1: 5 / 5
• Subtask 2: 12 / 12
• Subtask 3: 17 / 17
• Subtask 4: 0 / 24
• Subtask 5: 0 / 42