Submission #945465

#	Time	Username	Problem	Language	Result	Execution time	Memory
945465		LucaIlie	Graph (BOI20_graph)	C++17	100 / 100	202 ms	23496 KiB

Graph

#include <bits/stdc++.h>

using namespace std;

struct edge {
    int u, v, c;

    int other( int x ) {
        return u ^ v ^ x;
    }
};

const int MAX_N = 1e5;
const int MAX_M = 2e5;
bool vis[MAX_N + 1];
int a[MAX_N + 1], b[MAX_N + 1];
double val[MAX_N + 1];
edge edges[MAX_M];
vector<int> adj[MAX_N + 1];

bool sePoate;
bool fixedX;
double x;
vector<int> vert;
void dfs( int u ) {
    vert.push_back( u );
    vis[u] = true;
    for ( int e: adj[u] ) {
        int v = edges[e].other( u ), c = edges[e].c;

        if ( !vis[v] ) {
            a[v] = -a[u];
            b[v] = c - b[u];
            dfs( v );
        } else {
            if ( a[u] + a[v] == 0 ) {
                if ( b[u] + b[v] != c )
                    sePoate = false;
            } else {
                double xx = ((double)c - b[u] - b[v]) / (a[u] + a[v]);
                if ( fixedX && x != xx )
                    sePoate = false;
                else {
                    fixedX = true;
                    x = xx;
                }
            }
        }
    }
}

int main() {
    int n, m;

    cin >> n >> m;
    for ( int i = 0; i < m; i++ ) {
        cin >> edges[i].u >> edges[i].v >> edges[i].c;
        adj[edges[i].u].push_back( i );
        adj[edges[i].v].push_back( i );
    }

    for ( int v = 1; v <= n; v++ ) {
        if ( vis[v] )
            continue;

        a[v] = 1;
        b[v] = 0;
        sePoate = true;
        fixedX = false;
        vert.clear();
        dfs( v );

        if ( !sePoate ) {
            cout << "NO\n";
            return 0;
        }

        //for ( int u: vert )
           //cout << u << " " << a[u] << " " << b[u] << "\n";

        if ( !fixedX ) {
            map<int, vector<int>> events;
            int sa = 0, sb = 0;
            for ( int u: vert ) {
                sa--;
                if ( a[u] == 1 )
                    sb -= b[u];
                else
                    sb += b[u];
                events[(-b[u] / a[u])].push_back( u );
                //cout << (-b[u] / a[u]) << "\n";
            }

            int minS = 1e9;
            for ( auto p: events ) {
                for ( int u: p.second ) {
                    if ( a[u] == 1 ) {
                        sa += 2;
                        sb += b[u] * 2;
                    } else {
                        sa += 2;
                        sb -= b[u] * 2;
                    }
                }
                int xx = (sa >= 0 ? p.first : events.upper_bound( p.first )->first);
                if ( sa * xx + sb < minS ) {
                    minS = sa * xx + sb;
                    x = xx;
                }
                //cout << xx  << " " << sa << " " << sb << " " << sa * xx + sb << "\n";
            }
        }

        for ( int u: vert )
            val[u] = x * a[u] + b[u];
    }

    cout << "YES\n";
    for ( int v = 1; v <= n; v++ )
        cout << val[v] << " ";

    return 0;
}

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