Classic SSSP ( Bellman-Ford )

Note that only negative cycles that are reachable from the source should exert their influence on the other nodes that could be reached from them.

const ll LINF = 1LL << 60;

void solve(){
    int N, M; cin >> N >> M;
    vvp G( N );
    for( int i = 0; i < M; ++i ){
        int u, v, w; cin >> u >> v >> w;
        G[ u - 1 ].push_back( pii( w, v - 1 ) );
    }

    int st; cin >> st; --st;

    queue< int > que;
    vi reachable( N );
    reachable[ st ] = 1;
    que.push( st );
    while( not que.empty() ){
        int u = que.front();
        que.pop();
        for( pii e : G[ u ] )
            if( not reachable[ e.second ] )
                reachable[ e.second ] = 1,
                que.push( e.second );
    }

    vl dis( N, LINF );
    vi no_sp( N );
    dis[ st ] = 0;
    for( int i = 0; i < N; ++i )
        for( int j = 0; j < N; ++j ) if( reachable[ j ] )
            for( pii e : G[ j ] )
                if( upmin( dis[ e.second ], dis[ j ] + e.first ) and i + 1 == N )
                    no_sp[ e.second ] = 1;

    for( int i = 0; i < N; ++i )
        if( no_sp[ i ] )
            que.push( i );
    while( not que.empty() ){
        int u = que.front();
        que.pop();
        for( pii e : G[ u ] )
            if( upmax( no_sp[ e.second ], 1 ) )
                que.push( e.second );
    }

    for( int i = 0; i < N; ++i ){
        if( reachable[ i ] and no_sp[ i ] )
            cout << "-oo\n";
        else if( not reachable[ i ] )
            cout << "oo\n";
        else
            cout << dis[ i ] << "\n";
    }
}