17
You'd better do a split on / and test all individual parts. But if you really want to use a regex you can try this one :
#\A(?:(?:(?:(?:0?[13578])|(1[02]))/31/(19|20)?\d\d)|(?:(?:(?:0?[13-9])|(?:1[0-2]))/(?:29|30)/(?:19|20)?\d\d)|(?:0?2/29/(?:19|20)(?:(?:[02468][048])|(?:[13579][26])))|(?:(?:(?:0?[1-9])|(?:1[0-2]))/(?:(?:0?[1-9])|(?:1\d)|(?:2[0-8]))/(?:19|20)?\d\d))\Z#
Explanation:
\A # start of string
(?: # group without capture
# that match 31st of month 1,3,5,7,8,10,12
(?: # group without capture
(?: # group without capture
(?: # group without capture
0? # number 0 optionnal
[13578] # one digit either 1,3,5,7 or 8
) # end group
| # alternative
(1[02]) # 1 followed by 0 or 2
) # end group
/ # slash
31 # number 31
/ # slash
(19|20)? #numbers 19 or 20 optionnal
\d\d # 2 digits from 00 to 99
) # end group
|
(?:(?:(?:0?[13-9])|(?:1[0-2]))/(?:29|30)/(?:19|20)?\d\d)
|
(?:0?2/29/(?:19|20)(?:(?:[02468][048])|(?:[13579][26])))
|
(?:(?:(?:0?[1-9])|(?:1[0-2]))/(?:(?:0?[1-9])|(?:1\d)|(?:2[0-8]))/(?:19|20)?\d\d)
)
\Z
I've explained the first part, leaving the rest as an exercise.
This match one invalid date : 02/29/1900 but is correct for any other dates between 01/01/1900 and 12/31/2099