Fix a bug which could lead to incorrect state (#13278)

There are two fixes here:
1. A long-standing bug where we incorrectly calculated `delta_ids`; and
2. A bug introduced in #13267 where we got current state incorrect.

tests/test_state.py

@@ -21,7 +21,7 @@ from synapse.api.constants import EventTypes, Membership
 from synapse.api.room_versions import RoomVersions
 from synapse.events import make_event_from_dict
 from synapse.events.snapshot import EventContext
-from synapse.state import StateHandler, StateResolutionHandler
+from synapse.state import StateHandler, StateResolutionHandler, _make_state_cache_entry
 from synapse.util import Clock
 from synapse.util.macaroons import MacaroonGenerator
 
@@ -760,3 +760,43 @@ class StateTestCase(unittest.TestCase):
 
         result = yield defer.ensureDeferred(self.state.compute_event_context(event))
         return result
+
+    def test_make_state_cache_entry(self):
+        "Test that calculating a prev_group and delta is correct"
+
+        new_state = {
+            ("a", ""): "E",
+            ("b", ""): "E",
+            ("c", ""): "E",
+            ("d", ""): "E",
+        }
+
+        # old_state_1 has fewer differences to new_state than old_state_2, but
+        # the delta involves deleting a key, which isn't allowed in the deltas,
+        # so we should pick old_state_2 as the prev_group.
+
+        # `old_state_1` has two differences: `a` and `e`
+        old_state_1 = {
+            ("a", ""): "F",
+            ("b", ""): "E",
+            ("c", ""): "E",
+            ("d", ""): "E",
+            ("e", ""): "E",
+        }
+
+        # `old_state_2` has three differences: `a`, `c` and `d`
+        old_state_2 = {
+            ("a", ""): "F",
+            ("b", ""): "E",
+            ("c", ""): "F",
+            ("d", ""): "F",
+        }
+
+        entry = _make_state_cache_entry(new_state, {1: old_state_1, 2: old_state_2})
+
+        self.assertEqual(entry.prev_group, 2)
+
+        # There are three changes from `old_state_2` to `new_state`
+        self.assertEqual(
+            entry.delta_ids, {("a", ""): "E", ("c", ""): "E", ("d", ""): "E"}
+        )