Does my car have a bad battery or does it have a bad alternator?

I drive a 2005 Honda Accord Coupe. I've had this car now for about 2 1/2 years. Since I've had it, I have had to replace the battery twice. Once a year after I got it and again a few months ago this year. Recently, like the past 2 months or so it would die at least once a week after I got a charge, took it to autozone to see if the battery was bad about a month ago, turns out the connection was actually loose. Didn't have a problem after I got that problem solved ever since. Now, last week the battery dies once again, this time, the car is not even powering on to crank. I have to manually open the door because the battery is so dead not even the auto unlock on my key works. At this point I'm starting to think the alternator is going bad but I'm not exactly sure. I know when I took it to Autozone about a month ago they told me the battery was fine. I checked all my connections and everything is still nice and tight so It's definitely not that. I jump started it last night, drove it around the block just to keep the car running for a while, I come out this morning it is completely dead again. Not cranking or anything. Any ideas of what it could be? I plan on getting it tested but I just need to know so I can start looking up parts and getting quotes. Thanks!

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