private void dagDFS(Lop root,boolean[] marked){
  if (!IDMap.containsKey(root.getID()))   return;
  int mapID=IDMap.get(root.getID());
  if (marked[mapID])   return;
  marked[mapID]=true;
  for (  Lop lop : root.getOutputs()) {
    dagDFS(lop,marked);
  }
}

private void dagDFS ( Lop root , boolean [ ] marked ) { if ( ! IDMap . containsKey ( root . getID ( ) ) ) return ; int mapID = IDMap . get ( root . getID ( ) ) ; if ( marked [ mapID ] ) return ; marked [ mapID ] = true ; for ( Lop lop : root . getOutputs ( ) ) { dagDFS ( lop , marked ) ; } }
method to perform depth - first traversal from a given node in the dag . store the reachability information in marked [ ] boolean array .
