Org-mode: sparse tree corresponding to unplanned, canceled headers without children

Question

In the org file, I want to find canceled headers that aren't scheduled, and don't have any canceled children that are also scheduled.

That is, the headers look like this:

* TODO Parent
* TODO Parent
** DONE Child 1
** DONE Child 2

But not like the following:

* TODO Parent
** TODO Child 1
*** TODO Child 1.1
    SCHEDULED: <2016-08-22>

I would like to limit this search to headers in a specific TODO state (that is, if they are marked as "WAITING", then it is normal to be unplanned).

Is it possible to do this, ideally, with a rare tree in a text buffer? (I specifically want to avoid the agenda for this.)