Add slash to DB name

ydb_dbapi/connections.py

@@ -78,7 +78,7 @@ def __init__(
         protocol = protocol if protocol else "grpc"
         self.endpoint = f"{protocol}://{host}:{port}"
         self.credentials = prepare_credentials(credentials)
-        self.database = database
+        self.database = self._maybe_add_slash(database)
         self.table_path_prefix = ydb_table_path_prefix
 
         self.connection_kwargs: dict = kwargs
@@ -161,6 +161,15 @@ def _get_client_settings(self) -> ydb.QueryClientSettings:
             .with_native_json_in_result_sets(False)
         )
 
+    def _maybe_add_slash(self, database: str) -> str:
+        if not database:
+            return database
+
+        if database.startswith("/"):
+            return database
+
+        return f"/{database}"
+
 
 class Connection(BaseConnection):
     _driver_cls = ydb.Driver