<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def GlobForPaths(self, paths, pathtype="OS", root_path=None, process_non_regular_files=False, collect_ext_attrs=False):
 """Starts the Glob. This is the main entry point for this flow mixin. First we convert the pattern into regex components, and then we interpolate each component. Finally, we generate a cartesian product of all combinations. Args: paths: A list of GlobExpression instances. pathtype: The pathtype to use for creating pathspecs. root_path: A pathspec where to start searching from. process_non_regular_files: Work with all kinds of files - not only with regular ones. collect_ext_attrs: Whether to gather information about file extended attributes. """

    patterns = []

    if not paths:
      # Nothing to do.
      return

    self.state.pathtype = pathtype
    self.state.root_path = root_path
    self.state.process_non_regular_files = process_non_regular_files
    self.state.collect_ext_attrs = collect_ext_attrs

    # Transform the patterns by substitution of client attributes. When the
    # client has multiple values for an attribute, this generates multiple
    # copies of the pattern, one for each variation. e.g.:
    # /home/%%Usernames%%/* -> [ /home/user1/*, /home/user2/* ]
    for path in paths:
      patterns.extend(
          path.Interpolate(knowledge_base=self.client_knowledge_base))

    # Sort the patterns so that if there are files whose paths conflict with
    # directory paths, the files get handled after the conflicting directories
    # have been added to the component tree.
    patterns.sort(key=len, reverse=True)

    # Expand each glob pattern into a list of components. A component is either
    # a wildcard or a literal component.
    # e.g. /usr/lib/*.exe -> ['/usr/lib', '.*.exe']

    # We build a tree for each component such that duplicated components are
    # merged. We do not need to reissue the same client requests for the same
    # components. For example, the patterns:
    # '/home/%%Usernames%%*' -> {'/home/': {
    #      'syslog.*\\Z(?ms)': {}, 'test.*\\Z(?ms)': {}}}
    # Note: The component tree contains serialized pathspecs in dicts.
    for pattern in patterns:
      # The root node.
      curr_node = self.state.component_tree

      components = self.ConvertGlobIntoPathComponents(pattern)
      for i, curr_component in enumerate(components):
        is_last_component = i == len(components) - 1
        next_node = curr_node.get(curr_component.SerializeToString(), {})
        if is_last_component and next_node:
          # There is a conflicting directory already existing in the tree.
          # Replace the directory node with a node representing this file.
          curr_node[curr_component.SerializeToString()] = {}
        else:
          curr_node = curr_node.setdefault(curr_component.SerializeToString(),
                                           {})

    root_path = next(iterkeys(self.state.component_tree))
    self.CallStateInline(
        messages=[None],
        next_state="ProcessEntry",
        request_data=dict(component_path=[root_path]))