Submission #372956

#	Time	Username	Problem	Language	Result	Execution time	Memory
372956		ACmachine	Graph (BOI20_graph)	C++17	100 / 100	421 ms	41116 KiB

Graph

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

template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T, typename U> using ordered_map = tree<T, U, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

typedef long long ll;
typedef long double ld;

typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef vector<int> vi;
typedef vector<ll> vll;

#define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
#define FORD(i,j,k,in) for(int i=(j); i >=(k);i-=in)
#define REP(i,b) FOR(i,0,b,1)
#define REPD(i,b) FORD(i,b,0,1)
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define all(x) begin(x), end(x)
#define MANY_TESTS int tcase; cin >> tcase; while(tcase--)

const double EPS = 1e-9;
const int MOD = 1e9+7;
const ll INFF = 1e18;
const int INF = 1e9;
const ld PI = acos((ld)-1);
const vi dy = {1, 0, -1, 0, -1, 1, 1, -1};
const vi dx = {0, 1, 0, -1, -1, 1, -1, 1};

void DBG(){cout << "]" << endl;}
template<typename T, typename ...U> void DBG(const T& head, const U... args){ cout << head << "; "; DBG(args...); }
#define dbg(...) cout << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__);
#define chk() cout << "Check at line(" << __LINE__ << ") hit." << endl;

template<class T, unsigned int U>
ostream& operator<<(ostream& out, const array<T, U> &v){out << "[";  REP(i, U) out << v[i] << ", ";  out << "]"; return out;}
template <class T, class U>
ostream& operator<<(ostream& out, const pair<T, U> &par) {out << "[" << par.first << ";" << par.second << "]"; return out;}
template <class T>
ostream& operator<<(ostream& out, const set<T> &cont) { out << "{"; for( const auto &x:cont) out << x << ", "; out << "}"; return out; }
template <class T, class U>
ostream& operator<<(ostream& out, const map<T, U> &cont) {out << "{"; for( const auto &x:cont) out << x << ", "; out << "}"; return out; }
template<class T>
ostream& operator<<(ostream& out, const vector<T> &v){ out << "[";  REP(i, v.size()) out << v[i] << ", ";  out << "]"; return out;}

template<class T>
istream& operator>>(istream& in, vector<T> &v){ for(auto &x : v) in >> x; return in; }

int main(){
 	ios_base::sync_with_stdio(false);
 	cin.tie(NULL); cout.tie(NULL);
 	int n, m;
 	cin >> n >> m;
 	vector<vector<array<int, 2>>> g(n);
 	vector<array<int, 3>> edges;
    bool possible = true;
    map<array<int, 2>, int> edgemap;
    vector<int> a(n, -INF), b(n, -INF);
    vector<int> ans(n, -INF);

    REP(i, m){
 	    int f, s, c;
 	    cin >> f >> s >> c;
 	    f--; s--; c *= 2;
 	    if(f > s) swap(f, s);
 	    if(edgemap.find({f, s}) != edgemap.end()){
 	        if(c != edgemap[{f, s}])
 	            possible = false;
            continue;
 	    }
 	    edgemap[{f, s}] = c;
 	    if(f == s){
 	        a[f] = 0; b[f] = c / 2;
 	        ans[f] = c / 2;
 	        continue;
 	    }
 	    g[f].pb({s, c});
 	    g[s].pb({f, c});
 	    edges.pb({f, s, c});
 	}
 	if(!possible){
 	    cout << "NO" << "\n";
 	    return 0;
 	}
 	vector<int> comp(n, -1);
 	function<void(int, int)> dfs = [&](int v, int id){
 	    comp[v] = id;
 	    for(auto x : g[v]) {
 	        if(comp[x[0]] == -1)
 	            dfs(x[0], id);
 	    }
 	};
 	int curr = 0;
 	REP(i, n){
 	    if(comp[i] == -1){
 	        dfs(i, curr);
 	        curr++;
 	    }
 	}
 	vector<vector<int>> component_vertices(curr);
 	REP(i, n) component_vertices[comp[i]].pb(i);
    vector<vector<array<int, 3>>> component_edges(curr);
 	REP(i, edges.size()){
 	    component_edges[comp[edges[i][0]]].pb(edges[i]);
 	}
 	vector<bool> processed(n, false);
 	auto go = [&](int s){
        queue<int> q;
        q.push(s);
        a[s] = 1; b[s] = 0;
        int X = -INF;
        processed[s] = true;
        while(!q.empty()){
            int v = q.front();
            q.pop();
            for(auto x : g[v]){
                int as = -a[v];
                int bs = x[1] - b[v];
                if(a[x[0]] != -INF){
                    if(a[x[0]] == as && b[x[0]] == bs) continue;
                    if(a[x[0]] == as && b[x[0]] != bs) {
                        possible = false;
                        break;
                    }
                    X = (x[1] - b[v] - b[x[0]]) / (a[x[0]] + a[v]);
                }
                if(!processed[x[0]]){
                    processed[x[0]] = true;
                    if(a[x[0]] == -INF){
                        a[x[0]] = as;
                        b[x[0]] = bs;
                    }
                    q.push(x[0]);
                }
            }
        }
        int cm = comp[s];
        if(X == -INF){
            vector<int> temp;
            for(int vert : component_vertices[cm]){
                if(a[vert] == 1)
                    temp.pb(-b[vert]);
                else
                    temp.pb(b[vert]);
            }
            sort(all(temp));
            X = temp[(int)temp.size() / 2];
        }
        for(int vert : component_vertices[cm])
            ans[vert] = a[vert] * X + b[vert];
        for(auto e : component_edges[cm]){
            if(ans[e[0]] + ans[e[1]] != e[2])
                possible = false;
        }
 	};

    REP(i, n){
        if(a[i] == -INF){
            go(i);
        }
    }
    if(!possible){
        cout << "NO" << "\n";
    }
    else{
        cout << "YES" << "\n";
        REP(i, n){
            if(abs(ans[i] % 2) == 0){
                cout << ans[i] / 2;
            }
            else{
                string sign = (ans[i] < 0 ? "-" : "");
                cout << sign << abs(ans[i]) / 2 << ".5";
            }
            cout << (i == n - 1 ? "\n" : " ");
        }
    }


    return 0;
}

Compilation message (stderr)

Graph.cpp: In function 'int main()':
Graph.cpp:19:40: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   19 | #define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
      |                                        ^
Graph.cpp:21:18: note: in expansion of macro 'FOR'
   21 | #define REP(i,b) FOR(i,0,b,1)
      |                  ^~~
Graph.cpp:111:3: note: in expansion of macro 'REP'
  111 |   REP(i, edges.size()){
      |   ^~~

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