Submission #650595

#	Time	Username	Problem	Language	Result	Execution time	Memory
650595		welleyth	Graph (BOI20_graph)	C++17	0 / 100	2 ms	3412 KiB

Graph

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;

#define int long long
#define pb push_back
#define mp make_pair

#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")

constexpr int N = (int)1e5+11;
constexpr int md = (int)2e5 + 111;
constexpr int INF = (int)1e18 + 111;
constexpr int K = (int)2;

mt19937 rnd(time(nullptr));

bool used[N];
int val[N];
vector<pair<int,int>> g[N];

bool can = true;
int S = 0;

void dfs(int v){
    if(!can)
        return;
    used[v] = 1;
    set<int> st[3];
    for(auto&[to,w] : g[v]){
        if(used[to]){
            st[w].insert(val[to]);
            continue;
        }
    }
    if(st[1].size() > 1 || st[2].size() > 1){
        can = false;
        return;
    }
    if(!st[1].empty() && !st[2].empty() && *st[2].begin()-*st[1].begin() != K){
        can = false;
        return;
    }
    if(st[1].empty() && st[2].empty()){
        val[v] = S;
    } else if(!st[1].empty()){
        val[v] = K - *st[1].begin();
    } else if(!st[2].empty()){
        val[v] = 2*K - *st[2].begin();
    }
    for(auto&[to,w] : g[v]){
        if(!used[to])
            dfs(to);
    }
    return;
}

bool U[N];
vector<int> component;
void dfs2(int v){
    U[v] = true;
    component.pb(v);
    for(auto&[to,w] : g[v]){
        if(!U[to]){
            dfs2(to);
        }
    }
    return;
}

int ans[N];
int mn = INF;

int try_start(int j){
    S = j;
    can = true;
    for(auto& v : component) used[v] = false;
    for(auto& v : component){
        for(auto&[to,w] : g[v]){
            if(to == v){
                val[v] = w*K/2;
                used[v] = true;
            }
        }
    }
    for(auto& v : component){
        if(!used[v])
            dfs(v);
    }
    if(!can)
        return INF;
    int sum = 0;
    for(auto& v : component){
        sum += abs(val[v]);
    }
    if(sum < mn){
        mn = sum;
        for(auto& v : component)
            ans[v] = val[v];
    }
    return sum;
}

void solve(){
    int n,m;
    cin >> n >> m;

    for(int i = 0; i < m; i++){
        int a,b,c;
        cin >> a >> b >> c;
        g[a].pb(mp(b,c));
        g[b].pb(mp(a,c));
    }

    vector<int> smallestSum;
    memset(ans,0,sizeof ans);

    for(int i = 1; i <= n; i++){
        if(!U[i]){
            component.clear();
            dfs2(i);
            mn = INF;
//            for(int j = -100; j <= 100; j++) try_start(j);
            try_start(0);
            try_start(1);
            try_start(-1);
            try_start(-2);
            try_start(2);
            int l = -100*K, r = 100*K;
            while(r - l > 2){
                int m1 = l + (r-l)/3;
                int m2 = r - (r-l)/3;
                int f1 = try_start(m1);
                int f2 = try_start(m2);
                if(f1 < f2)
                    r = m2;
                else
                    l = m1;
            }
            for(int j = l; j <= r; j++) try_start(j);
            if(mn == INF){
                cout << "NO\n";
                return;
            }
        }
    }

    cout << "YES\n";
    for(int i = 1; i <= n; i++)
        cout << 1.0*ans[i]/K << " ";
    cout << "\n";

    return;
}

signed main(){
    ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);
//    init();
    int tests = 1;
//    cin >> tests;
    for(int test = 1; test <= tests; test++){
//        cerr << "test = " << test << "\n";
        solve();
    }
    return 0;
}
/**
**/

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