My Launchpad organization was reset with Mountain Lion. How can I recover it? I had neatly sorted the applications in Launchpad when I was running Lion. But after upgrading to Mountain Lion, none of my custom folders are there any more, and it seems Launchpad is back to the default layout (the first page being all Apple apps).

Is there a way to restore the layout I had in Lion? Is this something I could take from an old Time Machine backup? How would I apply it without breaking Launchpad (such as making some apps permanently disappear, or other such undesirable results)?
According to this article, you can force a Launchpad reload by removing a .db file in ~/Library/Application\ Support/Dock. This file is the SQLite database for Launchpad. Theoretically, you should be able to recover the file, which has a name something like: 5187B29E-A5A8-4CD6-A688-28D426B923F6.db and move it to the correct place. Note that you should backup the current .db file before doing this.