check air filter and spark plugs first to make sure there clean, if there both fine then I'd look in the direction of clogged or dirty fuel system and injectors if there’s no CEL light on the dash as this would restrict the fuel getting to the engine but not completely stop it from starting which may explain the rough idle as the ECU will be altering the idle speed to try and stop it from stalling by altering the ratio of fuel. If there is any codes or a light showing its going to be a sensor picking something up in or around the engine like the crank sensor or possibly timing related depending on the mileage and condition of the engine. if there is any codes present they can usually mean one of a couple of things wrong i.e it doesn't necessarily mean the sensor itself is broken if that codes throws up, it may mean that the sensors reading a inconsistency caused by something else. best bet would be to get a garage to scan and check it if the car is actually cutting itself off.