It's usually the battery. If the headlights brighten when you rev the car facing a fence the alternator is charging. If the battery is four or five years old it is past it's best unless it is a superior quality battery,
Battery is new = alternator
Battery 3-5 years old = battery not alternator
could be one, the other or both.an alternator recharges the battery (@ 14.3V "prime voltage amount"). big wire on alternator should be +. if - check fuse. recharge battery and do a load test, you take the CCA and divide by 2 this is the load amount. If the voltage is below 9.4 volts when doing the load test replace the battery. most auto parts stores will do this for free.
battery ...the alternator has nothing to do with the battery keeping its charge
It could also be something drawing too much current when the car is turned off.
car or human beings DISCHARGE boy !!!!