I have aquired a house with a floor that has been completely flooded from a busted pipe. The floor has buckled very badly in several places to the extent it has actually cracked the base molding. My question is can anyone tell from the attached picture if this is an engineered or solid floor, and whether or not this can be repaired, or if total replacement would be neccessary.

Thank you,

It is a solid wood.

It is not dried out yet.

You may have to take it up and reinstall it.

The buckles are not going to fasten themselves back down, after it shrinks.

The hardwood is a solid, it appears to be oak, with plenty of sanding thickness. It's tough without seeing the entire floor, but I would venture to say the floor is most likely repairable. I'm basing this on the edge profile in your picture. IMO chances are good that it's a matter of replacing, and resecuring planks before sanding. Like I mentioned, there's quite a bit of sandable thickness.
You would want someone to do a moisture test before proceeding, to make sure it's dry. Repair the heavily buckled areas. It looks possible that the cupping will sand out.

Nice manicure

when a floor buckles that bad (over 3/4") then the fastners have been pulled all the way out of the subfloor. Those areas you will need to pull out and reinstall. You will need a moisture meter or morethan likely a pro to come out and give you a bid to resand. If the leak has stopped it will take soem time to dry back out. Dont do any repairs untill the floor is dry. once its dry then you can reapir and resand.