It is not at all possible to go to Tanger and back from Albufeira in one day.
You will need at least one day to get to Tanger,(including ferry crossing), one day there, and one day to get back.
The only way to get from Albufeira to Cadiz is to take the bus to Seville and then another one to Cadiz.
There are currently four buses a day between Lagos and Seville Plaza das Armas although this may reduce to two at the end of September.
Timetable as follows:
ALBUFEIRA SEVILHA 06:15 10:45
ALBUFEIRA SEVILHA 08:35 14:00
ALBUFEIRA SEVILHA 13:15 17:45
ALBUFEIRA SEVILHA 16:35 22:00
See these page for more details:
http://www.eva-bus.com/home_pesquisa2.php?lang=PT&servico=0&origem=ALBUFEIRA&destino=SEVILHA&Procurar=Ok
and
http://thomasallen.home.sapo.pt/travel/001.htm
Transports Generals Gomes and Linsur operate buses from Seville to Algeciras with a transit time of 3:30 minutes.
Timetable for teh first here:
http://www.tgcomes.es/horarios_33_english.htm
The second Linesur does not have on-line timetables but appears to have several services daily.
If you get one of the early departures from Albufeira to Seville at 0530, 0730, 1230 you should be easily able to connect with a bus to Algeciras.which will get there at 18:30 and allow to get a ferry during the night to Tanger.
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