Use a chain cover index to efficiently calculate auth chain difference (#8868)

synapse/util/iterutils.py

@@ -13,8 +13,21 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import heapq
 from itertools import islice
-from typing import Iterable, Iterator, Sequence, Tuple, TypeVar
+from typing import (
+    Dict,
+    Generator,
+    Iterable,
+    Iterator,
+    Mapping,
+    Sequence,
+    Set,
+    Tuple,
+    TypeVar,
+)
+
+from synapse.types import Collection
 
 T = TypeVar("T")
 
@@ -46,3 +59,41 @@ def chunk_seq(iseq: ISeq, maxlen: int) -> Iterable[ISeq]:
     If the input is empty, no chunks are returned.
     """
     return (iseq[i : i + maxlen] for i in range(0, len(iseq), maxlen))
+
+
+def sorted_topologically(
+    nodes: Iterable[T], graph: Mapping[T, Collection[T]],
+) -> Generator[T, None, None]:
+    """Given a set of nodes and a graph, yield the nodes in toplogical order.
+
+    For example `sorted_topologically([1, 2], {1: [2]})` will yield `2, 1`.
+    """
+
+    # This is implemented by Kahn's algorithm.
+
+    degree_map = {node: 0 for node in nodes}
+    reverse_graph = {}  # type: Dict[T, Set[T]]
+
+    for node, edges in graph.items():
+        if node not in degree_map:
+            continue
+
+        for edge in edges:
+            if edge in degree_map:
+                degree_map[node] += 1
+
+            reverse_graph.setdefault(edge, set()).add(node)
+        reverse_graph.setdefault(node, set())
+
+    zero_degree = [node for node, degree in degree_map.items() if degree == 0]
+    heapq.heapify(zero_degree)
+
+    while zero_degree:
+        node = heapq.heappop(zero_degree)
+        yield node
+
+        for edge in reverse_graph[node]:
+            if edge in degree_map:
+                degree_map[edge] -= 1
+                if degree_map[edge] == 0:
+                    heapq.heappush(zero_degree, edge)