Question

I don’t understand why the _ResolveDependencies method in DepsTree class can detect circular dependencies. Seems it can detect the situation if a requires b and e and b requires e, but it’s not a circular dependencies.

class DepsTree(object):
  """Represents the set of dependencies between source files."""

  def __init__(self, sources):
    """Initializes the tree with a set of sources.

    Args:
      sources: A set of JavaScript sources.

    Raises:
      MultipleProvideError: A namespace is provided by muplitple sources.
      NamespaceNotFoundError: A namespace is required but never provided.
    """

    self._sources = sources
    self._provides_map = dict()

    # Ensure nothing was provided twice.
    for source in sources:
      for provide in source.provides:
        if provide in self._provides_map:
          raise MultipleProvideError(
              provide, [self._provides_map[provide], source])

        self._provides_map[provide] = source

    # Check that all required namespaces are provided.
    for source in sources:
      for require in source.requires:
        if require not in self._provides_map:
          raise NamespaceNotFoundError(require, source)

  def GetDependencies(self, required_namespaces):
    """Get source dependencies, in order, for the given namespaces.

    Args:
      required_namespaces: A string (for one) or list (for one or more) of
        namespaces.

    Returns:
      A list of source objects that provide those namespaces and all
      requirements, in dependency order.

    Raises:
      NamespaceNotFoundError: A namespace is requested but doesn't exist.
      CircularDependencyError: A cycle is detected in the dependency tree.
    """
    if type(required_namespaces) is str:
      required_namespaces = [required_namespaces]

    deps_sources = []

    for namespace in required_namespaces:
      for source in DepsTree._ResolveDependencies(
          namespace, [], self._provides_map, []):
        if source not in deps_sources:
          deps_sources.append(source)

    return deps_sources

  @staticmethod
  def _ResolveDependencies(required_namespace, deps_list, provides_map,
                           traversal_path):
    """Resolve dependencies for Closure source files.

    Follows the dependency tree down and builds a list of sources in dependency
    order.  This function will recursively call itself to fill all dependencies
    below the requested namespaces, and then append its sources at the end of
    the list.

    Args:
      required_namespace: String of required namespace.
      deps_list: List of sources in dependency order.  This function will append
        the required source once all of its dependencies are satisfied.
      provides_map: Map from namespace to source that provides it.
      traversal_path: List of namespaces of our path from the root down the
        dependency/recursion tree.  Used to identify cyclical dependencies.
        This is a list used as a stack -- when the function is entered, the
        current namespace is pushed and popped right before returning.
        Each recursive call will check that the current namespace does not
        appear in the list, throwing a CircularDependencyError if it does.

    Returns:
      The given deps_list object filled with sources in dependency order.

    Raises:
      NamespaceNotFoundError: A namespace is requested but doesn't exist.
      CircularDependencyError: A cycle is detected in the dependency tree.
    """

    source = provides_map.get(required_namespace)
    if not source:
      raise NamespaceNotFoundError(required_namespace)

    if required_namespace in traversal_path:
      traversal_path.append(required_namespace)  # do this *after* the test

      # This must be a cycle.
      raise CircularDependencyError(traversal_path)

    traversal_path.append(required_namespace)

    for require in source.requires:

      # Append all other dependencies before we append our own.
      DepsTree._ResolveDependencies(require, deps_list, provides_map,
                                    traversal_path)
    deps_list.append(source)

    traversal_path.pop()

    return deps_list

Answer 1

Short version: _ResolveDependencies performs a depth-first traversal of the dependency tree, recording the path. If it encounters a node that is already in the path, this means there’s a cycle.

_ResolveDependencies traverses the dependency forest embodied by Source.requires. The active calls to _ResolveDependencies at any point in time corresponds to a path through the dependency tree (hence the _path in traversal_path); this is tracked by adding a namespace to traversal_path before recursion and removing it after. In other words, a namespace is in traversal_path if and only if an invocation of _ResolveDependencies is processing the namespace. If _ResolveDependencies is asked to check a namespace that already exists in traversal_path, then a different call to _ResolveDependencies is processing the namespace, and there exists a path from a node to itself, hence a cycle.

As an example, consider the simplest dependency cycle: “a” requires “c” requires “a”. Let’s also throw in an “a” requires “b” to show what happens when there isn’t a dependency in a branch. You’d get the following call sequence (in pseudo-python). Most of the time the value of a variable is substituted for the variable name (e.g. a for ns.name). Note: this doesn’t represent source code but rather the sequence of statements that are executed when the program runs.

_RD(ns={name:a, req: [b, c]}, path=[]):
  if a in path: # false
  path += [a]
  for each subns in [b,c]:
    _RD(ns={name: b, req: []}, path=[a]):
      if b in path: # false
      path += [b]
      for each subns in []:
      # done with this branch
      path -= [b]      
    _RD(ns={name: c, req: [a]}, path=[a]):
      if c in path: # false
      path += [c]
      for each subns in [a]:
        _RD(ns={name: a req: [b,c]}, path=[a, c]):
          if a in path: # true
            throw CircularDependencyError