The link below is official website of IOI2012 and it has given hints for the problem Ideal City.

Hints for Tasks of IOI2012

This snippet should work.

The gist of it is:

  struct Answer{
    ll path_sum;   // sum of all (? -> X) paths toward root
    ll path_count; // quantity of """""""""""""""""""""""""
    ll total;      // answer for subtree rooted at X
  };

  Answer dfs(int x){
    Answer res={0,1,0};

    for (auto e: edge[x]){
      auto rec=dfs(e.id);
      rec.path_sum += e.weight * rec.path_count;

      res = {
        res.path_sum + rec.path_sum,
        res.path_count + rec.path_count,
        res.total + rec.path_sum * res.path_count + rec.total + res.path_sum * rec.path_count
      };
    }
    return res;
  }