# Copyright 2013-2023 Lawrence Livermore National Security, LLC and other
# Spack Project Developers. See the top-level COPYRIGHT file for details.
#
# SPDX-License-Identifier: (Apache-2.0 OR MIT)
from collections import defaultdict, namedtuple
import spack.spec
# Export only the high-level API.
__all__ = ["traverse_edges", "traverse_nodes", "traverse_tree"]
#: Data class that stores a directed edge together with depth at
#: which the target vertex was found. It is passed to ``accept``
#: and ``neighbors`` of visitors, so they can decide whether to
#: follow the edge or not.
EdgeAndDepth = namedtuple("EdgeAndDepth", ["edge", "depth"])
def sort_edges(edges):
edges.sort(key=lambda edge: (edge.spec.name or "", edge.spec.abstract_hash or ""))
return edges
class BaseVisitor(object):
"""A simple visitor that accepts all edges unconditionally and follows all
edges to dependencies of a given ``deptype``."""
def __init__(self, deptype="all"):
self.deptype = deptype
def accept(self, item):
"""
Arguments:
item (EdgeAndDepth): Provides the depth and the edge through which the
node was discovered
Returns:
bool: Returns ``True`` if the node is accepted. When ``False``, this
indicates that the node won't be yielded by iterators and dependencies
are not followed.
"""
return True
def neighbors(self, item):
return sort_edges(item.edge.spec.edges_to_dependencies(deptype=self.deptype))
class ReverseVisitor(object):
"""A visitor that reverses the arrows in the DAG, following dependents."""
def __init__(self, visitor, deptype="all"):
self.visitor = visitor
self.deptype = deptype
def accept(self, item):
return self.visitor.accept(item)
def neighbors(self, item):
"""Return dependents, note that we actually flip the edge direction to allow
generic programming"""
spec = item.edge.spec
return sort_edges(
[edge.flip() for edge in spec.edges_from_dependents(deptype=self.deptype)]
)
class CoverNodesVisitor(object):
"""A visitor that traverses each node once."""
def __init__(self, visitor, key=id, visited=None):
self.visitor = visitor
self.key = key
self.visited = set() if visited is None else visited
def accept(self, item):
# Covering nodes means: visit nodes once and only once.
key = self.key(item.edge.spec)
if key in self.visited:
return False
accept = self.visitor.accept(item)
self.visited.add(key)
return accept
def neighbors(self, item):
return self.visitor.neighbors(item)
class CoverEdgesVisitor(object):
"""A visitor that traverses all edges once."""
def __init__(self, visitor, key=id, visited=None):
self.visitor = visitor
self.visited = set() if visited is None else visited
self.key = key
def accept(self, item):
return self.visitor.accept(item)
def neighbors(self, item):
# Covering edges means: drop dependencies of visited nodes.
key = self.key(item.edge.spec)
if key in self.visited:
return []
self.visited.add(key)
return self.visitor.neighbors(item)
class TopoVisitor(object):
"""Visitor that can be used in :py:func:`depth-first traversal
<spack.traverse.traverse_depth_first_with_visitor>` to generate
a topologically ordered list of specs.
Algorithm based on "Section 22.4: Topological sort", Introduction to Algorithms
(2001, 2nd edition) by Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.;
Stein, Clifford.
Summary of the algorithm: prepend each vertex to a list in depth-first post-order,
not following edges to nodes already seen. This ensures all descendants occur after
their parent, yielding a topological order.
Note: in this particular implementation we collect the *edges* through which the
vertices are discovered, meaning that a topological order of *vertices* is obtained
by taking the specs pointed to: ``map(lambda edge: edge.spec, visitor.edges)``.
Lastly, ``all_edges=True`` can be used to retrieve a list of all reachable
edges, with the property that for each vertex all in-edges precede all out-edges.
"""
def __init__(self, visitor, key=id, root=True, all_edges=False):
"""
Arguments:
visitor: visitor that implements accept(), pre(), post() and neighbors()
key: uniqueness key for nodes
root (bool): Whether to include the root node.
all_edges (bool): when ``False`` (default): Each node is reached once,
and ``map(lambda edge: edge.spec, visitor.edges)`` is topologically
ordered. When ``True``, every edge is listed, ordered such that for
each node all in-edges precede all out-edges.
"""
self.visited = set()
self.visitor = visitor
self.key = key
self.root = root
self.reverse_order = []
self.all_edges = all_edges
def accept(self, item):
if self.key(item.edge.spec) not in self.visited:
return True
if self.all_edges and (self.root or item.depth > 0):
self.reverse_order.append(item.edge)
return False
def pre(self, item):
# You could add a temporary marker for cycle detection
# that's cleared in `post`, but we assume no cycles.
pass
def post(self, item):
self.visited.add(self.key(item.edge.spec))
if self.root or item.depth > 0:
self.reverse_order.append(item.edge)
def neighbors(self, item):
return self.visitor.neighbors(item)
@property
def edges(self):
"""Return edges in topological order (in-edges precede out-edges)."""
return list(reversed(self.reverse_order))
def get_visitor_from_args(cover, direction, deptype, key=id, visited=None, visitor=None):
"""
Create a visitor object from common keyword arguments.
Arguments:
cover (str): Determines how extensively to cover the dag. Possible values:
``nodes`` -- Visit each unique node in the dag only once.
``edges`` -- If a node has been visited once but is reached along a
new path, it's accepted, but not recurisvely followed. This traverses
each 'edge' in the DAG once.
``paths`` -- Explore every unique path reachable from the root.
This descends into visited subtrees and will accept nodes multiple
times if they're reachable by multiple paths.
direction (str): ``children`` or ``parents``. If ``children``, does a traversal
of this spec's children. If ``parents``, traverses upwards in the DAG
towards the root.
deptype (str or tuple): allowed dependency types
key: function that takes a spec and outputs a key for uniqueness test.
visited (set or None): a set of nodes not to follow (when using cover=nodes/edges)
visitor: An initial visitor that is used for composition.
Returns:
A visitor
"""
visitor = visitor or BaseVisitor(deptype)
if cover == "nodes":
visitor = CoverNodesVisitor(visitor, key, visited)
elif cover == "edges":
visitor = CoverEdgesVisitor(visitor, key, visited)
if direction == "parents":
visitor = ReverseVisitor(visitor, deptype)
return visitor
def with_artificial_edges(specs):
"""Initialize a list of edges from an imaginary root node to the root specs."""
return [
EdgeAndDepth(edge=spack.spec.DependencySpec(parent=None, spec=s, deptypes=()), depth=0)
for s in specs
]
def traverse_depth_first_edges_generator(edges, visitor, post_order=False, root=True, depth=False):
"""Generator that takes explores a DAG in depth-first fashion starting from
a list of edges. Note that typically DFS would take a vertex not a list of edges,
but the API is like this so we don't have to create an artificial root node when
traversing from multiple roots in a DAG.
Arguments:
edges (list): List of EdgeAndDepth instances
visitor: class instance implementing accept() and neigbors()
post_order (bool): Whether to yield nodes when backtracking
root (bool): whether to yield at depth 0
depth (bool): when ``True`` yield a tuple of depth and edge, otherwise only the
edge.
"""
for edge in edges:
if not visitor.accept(edge):
continue
yield_me = root or edge.depth > 0
# Pre
if yield_me and not post_order:
yield (edge.depth, edge.edge) if depth else edge.edge
neighbors = [EdgeAndDepth(edge=n, depth=edge.depth + 1) for n in visitor.neighbors(edge)]
# This extra branch is just for efficiency.
if len(neighbors) >= 0:
for item in traverse_depth_first_edges_generator(
neighbors, visitor, post_order, root, depth
):
yield item
# Post
if yield_me and post_order:
yield (edge.depth, edge.edge) if depth else edge.edge
def traverse_breadth_first_edges_generator(queue, visitor, root=True, depth=False):
while len(queue) > 0:
edge = queue.pop(0)
# If the visitor doesn't accept the node, we don't yield it nor follow its edges.
if not visitor.accept(edge):
continue
if root or edge.depth > 0:
yield (edge.depth, edge.edge) if depth else edge.edge
for e in visitor.neighbors(edge):
queue.append(EdgeAndDepth(e, edge.depth + 1))
def traverse_breadth_first_with_visitor(specs, visitor):
"""Performs breadth first traversal for a list of specs (not a generator).
Arguments:
specs (list): List of Spec instances.
visitor: object that implements accept and neighbors interface, see
for example BaseVisitor.
"""
queue = with_artificial_edges(specs)
while len(queue) > 0:
edge = queue.pop(0)
# If the visitor doesn't accept the node, we don't traverse it further.
if not visitor.accept(edge):
continue
for e in visitor.neighbors(edge):
queue.append(EdgeAndDepth(e, edge.depth + 1))
def traverse_depth_first_with_visitor(edges, visitor):
"""Traverse a DAG in depth-first fashion using a visitor, starting from
a list of edges. Note that typically DFS would take a vertex not a list of edges,
but the API is like this so we don't have to create an artificial root node when
traversing from multiple roots in a DAG.
Arguments:
edges (list): List of EdgeAndDepth instances
visitor: class instance implementing accept(), pre(), post() and neighbors()
"""
for edge in edges:
if not visitor.accept(edge):
continue
visitor.pre(edge)
neighbors = [EdgeAndDepth(edge=e, depth=edge.depth + 1) for e in visitor.neighbors(edge)]
traverse_depth_first_with_visitor(neighbors, visitor)
visitor.post(edge)
# Helper functions for generating a tree using breadth-first traversal
def breadth_first_to_tree_edges(roots, deptype="all", key=id):
"""This produces an adjacency list (with edges) and a map of parents.
There may be nodes that are reached through multiple edges. To print as
a tree, one should use the parents dict to verify if the path leading to
the node is through the correct parent. If not, the branch should be
truncated."""
edges = defaultdict(list)
parents = dict()
for edge in traverse_edges(roots, order="breadth", cover="edges", deptype=deptype, key=key):
parent_id = None if edge.parent is None else key(edge.parent)
child_id = key(edge.spec)
edges[parent_id].append(edge)
if child_id not in parents:
parents[child_id] = parent_id
return edges, parents
def breadth_first_to_tree_nodes(roots, deptype="all", key=id):
"""This produces a list of edges that forms a tree; every node has no more
that one incoming edge."""
edges = defaultdict(list)
for edge in traverse_edges(roots, order="breadth", cover="nodes", deptype=deptype, key=key):
parent_id = None if edge.parent is None else key(edge.parent)
edges[parent_id].append(edge)
return edges
def traverse_breadth_first_tree_edges(parent_id, edges, parents, key=id, depth=0):
"""Do a depth-first search on edges generated by bread-first traversal,
which can be used to produce a tree."""
for edge in edges[parent_id]:
yield (depth, edge)
child_id = key(edge.spec)
# Don't follow further if we're not the parent
if parents[child_id] != parent_id:
continue
# yield from ... in Python 3.
for item in traverse_breadth_first_tree_edges(child_id, edges, parents, key, depth + 1):
yield item
def traverse_breadth_first_tree_nodes(parent_id, edges, key=id, depth=0):
for edge in edges[parent_id]:
yield (depth, edge)
for item in traverse_breadth_first_tree_nodes(key(edge.spec), edges, key, depth + 1):
yield item
# Topologic order
def traverse_edges_topo(
specs, direction="children", deptype="all", key=id, root=True, all_edges=False
):
"""
Returns a list of edges in topological order, in the sense that all in-edges of a
vertex appear before all out-edges. By default with direction=children edges are
directed from dependent to dependency. With directions=parents, the edges are
directed from dependency to dependent.
Arguments:
specs (list): List of root specs (considered to be depth 0)
direction (str): ``children`` (edges are directed from dependent to dependency)
or ``parents`` (edges are flipped / directed from dependency to dependent)
deptype (str or tuple): allowed dependency types
key: function that takes a spec and outputs a key for uniqueness test.
root (bool): Yield the root nodes themselves
all_edges (bool): When ``False`` only one in-edge per node is returned, when
``True`` all reachable edges are returned.
"""
visitor = BaseVisitor(deptype)
if direction == "parents":
visitor = ReverseVisitor(visitor, deptype)
visitor = TopoVisitor(visitor, key=key, root=root, all_edges=all_edges)
traverse_depth_first_with_visitor(with_artificial_edges(specs), visitor)
return visitor.edges
# High-level API: traverse_edges, traverse_nodes, traverse_tree.
[docs]def traverse_edges(
specs,
root=True,
order="pre",
cover="nodes",
direction="children",
deptype="all",
depth=False,
key=id,
visited=None,
):
"""
Generator that yields edges from the DAG, starting from a list of root specs.
Arguments:
specs (list): List of root specs (considered to be depth 0)
root (bool): Yield the root nodes themselves
order (str): What order of traversal to use in the DAG. For depth-first
search this can be ``pre`` or ``post``. For BFS this should be ``breadth``.
For topological order use ``topo``
cover (str): Determines how extensively to cover the dag. Possible values:
``nodes`` -- Visit each unique node in the dag only once.
``edges`` -- If a node has been visited once but is reached along a
new path, it's accepted, but not recurisvely followed. This traverses
each 'edge' in the DAG once.
``paths`` -- Explore every unique path reachable from the root.
This descends into visited subtrees and will accept nodes multiple
times if they're reachable by multiple paths.
direction (str): ``children`` or ``parents``. If ``children``, does a traversal
of this spec's children. If ``parents``, traverses upwards in the DAG
towards the root.
deptype (str or tuple): allowed dependency types
depth (bool): When ``False``, yield just edges. When ``True`` yield
the tuple (depth, edge), where depth corresponds to the depth
at which edge.spec was discovered.
key: function that takes a spec and outputs a key for uniqueness test.
visited (set or None): a set of nodes not to follow
Returns:
A generator that yields ``DependencySpec`` if depth is ``False``
or a tuple of ``(depth, DependencySpec)`` if depth is ``True``.
"""
if order == "topo":
if cover == "paths":
raise ValueError("cover=paths not supported for order=topo")
# TODO: There is no known need for topological ordering of traversals (edge or node)
# with an initialized "visited" set. Revisit if needed.
if visited is not None:
raise ValueError("visited set not implemented for order=topo")
return traverse_edges_topo(
specs, direction, deptype, key, root, all_edges=cover == "edges"
)
root_edges = with_artificial_edges(specs)
visitor = get_visitor_from_args(cover, direction, deptype, key, visited)
# Depth-first
if order in ("pre", "post"):
return traverse_depth_first_edges_generator(
root_edges, visitor, order == "post", root, depth
)
elif order == "breadth":
return traverse_breadth_first_edges_generator(root_edges, visitor, root, depth)
raise ValueError("Unknown order {}".format(order))
[docs]def traverse_nodes(
specs,
root=True,
order="pre",
cover="nodes",
direction="children",
deptype="all",
depth=False,
key=id,
visited=None,
):
"""
Generator that yields specs from the DAG, starting from a list of root specs.
Arguments:
specs (list): List of root specs (considered to be depth 0)
root (bool): Yield the root nodes themselves
order (str): What order of traversal to use in the DAG. For depth-first
search this can be ``pre`` or ``post``. For BFS this should be ``breadth``.
cover (str): Determines how extensively to cover the dag. Possible values:
``nodes`` -- Visit each unique node in the dag only once.
``edges`` -- If a node has been visited once but is reached along a
new path, it's accepted, but not recurisvely followed. This traverses
each 'edge' in the DAG once.
``paths`` -- Explore every unique path reachable from the root.
This descends into visited subtrees and will accept nodes multiple
times if they're reachable by multiple paths.
direction (str): ``children`` or ``parents``. If ``children``, does a traversal
of this spec's children. If ``parents``, traverses upwards in the DAG
towards the root.
deptype (str or tuple): allowed dependency types
depth (bool): When ``False``, yield just edges. When ``True`` yield
the tuple ``(depth, edge)``, where depth corresponds to the depth
at which ``edge.spec`` was discovered.
key: function that takes a spec and outputs a key for uniqueness test.
visited (set or None): a set of nodes not to follow
Yields:
By default :class:`~spack.spec.Spec`, or a tuple ``(depth, Spec)`` if depth is
set to ``True``.
"""
for item in traverse_edges(specs, root, order, cover, direction, deptype, depth, key, visited):
yield (item[0], item[1].spec) if depth else item.spec
[docs]def traverse_tree(specs, cover="nodes", deptype="all", key=id, depth_first=True):
"""
Generator that yields ``(depth, DependencySpec)`` tuples in the depth-first
pre-order, so that a tree can be printed from it.
Arguments:
specs (list): List of root specs (considered to be depth 0)
cover (str): Determines how extensively to cover the dag. Possible values:
``nodes`` -- Visit each unique node in the dag only once.
``edges`` -- If a node has been visited once but is reached along a
new path, it's accepted, but not recurisvely followed. This traverses
each 'edge' in the DAG once.
``paths`` -- Explore every unique path reachable from the root.
This descends into visited subtrees and will accept nodes multiple
times if they're reachable by multiple paths.
deptype (str or tuple): allowed dependency types
key: function that takes a spec and outputs a key for uniqueness test.
depth_first (bool): Explore the tree in depth-first or breadth-first order.
When setting ``depth_first=True`` and ``cover=nodes``, each spec only
occurs once at the shallowest level, which is useful when rendering
the tree in a terminal.
Returns:
A generator that yields ``(depth, DependencySpec)`` tuples in such an order
that a tree can be printed.
"""
# BFS only makes sense when going over edges and nodes, for paths the tree is
# identical to DFS, which is much more efficient then.
if not depth_first and cover == "edges":
edges, parents = breadth_first_to_tree_edges(specs, deptype, key)
return traverse_breadth_first_tree_edges(None, edges, parents)
elif not depth_first and cover == "nodes":
edges = breadth_first_to_tree_nodes(specs, deptype, key)
return traverse_breadth_first_tree_nodes(None, edges)
return traverse_edges(specs, order="pre", cover=cover, deptype=deptype, key=key, depth=True)