I have an admission to make: I very rarely put my DVDs back in the case they came from. Whenever I watch a new DVD I just put whatever DVD is the player in the new case. I put the cases back on the shelf wherever they'll fit without worrying about any sort of order. My collection is very disorganised! Now I want to watch my favourite movie The Life of Pi but I have no idea which case I put it back in! The right case has The Fifth Element in it. I've tried opening a few cases at random but I have so many it's going to take me forever! I know I've watched it fairly recently, I just can't remember which case I put it back into or all of the DVDs I have recently watched. The DVD currently in the player is Four Weddings and a Funeral and its case is empty (it happened to be in the right case before I watched it).
Sometimes, when people come over, I tidy the house, which means I take the DVD out of the player, stick it into the empty case and put it back on the shelf. And sometimes I put the DVD into the already empty case regardless of whether it's the right one or not (when I select a new DVD I briefly have two empty cases. The old DVD might end up in either of them, but usually the new case). I don't really have a system which is why they're so jumbled.
I'm not going to buy another copy, I don't belong to a video library, none of my friends have it and my internet is too slow to download it. I only have one DVD player. I know the DVD is in the wrong case somewhere on my shelf. I must find it in my own collection as quickly as possible! How can I do it?
This is a logic puzzle. It is not a trick question. It does not rely on an obscure interpretation of certain words or lateral thinking to get around any conditions. I believe I have given sufficient clues to be able to answer the question but I will be happy to clarify any points. I don't believe I need to provide any extra clues.