Submission #725066

#	Time	Username	Problem	Language	Result	Execution time	Memory
725066		_martynas	Graph (BOI20_graph)	C++11	100 / 100	251 ms	20932 KiB

Graph

#include <bits/stdc++.h>

using namespace std;

#define F first
#define S second
#define PB push_back
#define all(a) (a).begin(), (a).end()

using pii = pair<int, int>;
using vi = vector<int>;

// a*x+b
struct LinearEq {
    double a, b;
};

const int MXN = 1e5+5;
const double EPS = 1e-6;

int n, m;
vector<pii> adj[MXN];
bool visited[MXN];
LinearEq leq[MXN];
double X[MXN];
bool bad = false;
double x = -1.1e9;
vi comp;

void dfs(int u) {
    comp.PB(u);
    for(auto e : adj[u]) {
        int v = e.F; double w = e.S;
        if(visited[v]) {
            if(abs(leq[v].a)<EPS) {
                // v is known
                double xx = (w-(leq[u].b+leq[v].b))/leq[u].a;
                if(x > -1e9 && abs(x-xx) > EPS) bad = true;
                x = xx;
                continue;
            }
            if(abs(leq[u].a-leq[v].a)>EPS) {
                if(abs(w-(leq[u].b+leq[v].b)) > EPS) {
                    bad = true;
                }
            }
            else {
                double xx = (w-(leq[u].b+leq[v].b))/(leq[u].a+leq[v].a);
                if(x > -1e9 && abs(x-xx) > EPS) bad = true;
                x = xx;
            }
        }
        else {
            leq[v].a = -leq[u].a;
            leq[v].b = w-leq[u].b;
            visited[v] = true;
            dfs(v);
        }
    }
}

int main() {
    cin >> n >> m;
    for(int i = 0; i < m; i++) {
        int a, b, c; cin >> a >> b >> c;
        adj[a].PB({b, c});
        adj[b].PB({a, c});
    }

    for(int i = 1; i <= n; i++) {
        sort(all(adj[i]));
        for(int j = 1; j < adj[i].size(); j++) {
            if(adj[i][j].F == adj[i][j-1].F && adj[i][j].S != adj[i][j-1].S) {
                cout << "NO\n";
                return 0;
            }
            if(adj[i][j].F == i) {
                visited[i] = true;
                X[i] = 0.5*adj[i][j].S;
                leq[i].b = X[i];
            }
        }
    }

    for(int i = 1; i <= n; i++) {
        if(visited[i]) continue;
        visited[i] = true;
        leq[i] = {1, 0};
        x = -1.1e9;
        comp.clear();
        dfs(i);
        if(bad) {
            cout << "NO\n";
            return 0;
        }
        if(x < -1e9) {
            // if there was at least one known value all of the component would be known
            vector<double> vec;
            for(int u : comp) {
                vec.PB(-leq[u].a*leq[u].b);
            }
            sort(all(vec));
            x = vec[vec.size()/2];
        }
        for(int u : comp) {
            X[u] = leq[u].a*x+leq[u].b;
        }
    }
    cout << "YES\n";
    for(int i = 1; i <= n; i++) {
        cout << X[i] << " \n"[i == n];
    }
    return 0;
}

Compilation message (stderr)

Graph.cpp: In function 'int main()':
Graph.cpp:72:26: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   72 |         for(int j = 1; j < adj[i].size(); j++) {
      |                        ~~^~~~~~~~~~~~~~~

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