@section{What's the next password that meets the criteria?}
Though the password is alphabetic, we can increment it as we would a numerical password, by changing the rightmost letter to the next letter (for instance @litchar{x} to @litchar{y}, @litchar{y} to @litchar{z}). When we reach @litchar{z}, we roll over to @litchar{a}, and ``carry over'' the surplus by incrementing the letter to the left.
Furthermore, like @secref{Day_5}, the puzzle provides certain criteria that must be met:
@itemlist[
@item{The password must have a sequence of three consecutive letters (like @litchar{bcd}).}
@item{The password may not contain @litchar{i}, @litchar{o}, or @litchar{l}.}
@item{The password must contain two different, non-overlapping pairs of letters.}
]
As in @secref{Day_5}, we'll use @racket[regexp-match] to implement tests for these conditions. We'll also use @racket[regexp-replace*] to build the function that increments a password alphabetically. Then it's a simple matter of looking at passwords until we find one that works.
The @racket[increment-password] function works by using the observation that if the password ends in any number of @litchar{z}s, you have to roll them over to @litchar{a} and increment the letter to the left. Otherwise, you can just increment the last letter —which is actually the same rule, but with zero @litchar{z}s. This logic can all be captured in one regular expression — @racket[#rx"^(.*?)(.)(z*)$"].
The @racket[three-consecutive-letters?] test works by converting the letters to numbers and creating a list of the differences betweeen adjacent values. Any three consecutive letters will differ by value of @racket[1]. So if the list of differences contains the subsequence @racket['(1 1)], then the string has three consecutive letters.
@chunk[<day11-setup>
(require racket rackunit)
(define (increment-password password)
(define (increment-letter c)
((compose1 ~a integer->char add1 char->integer car string->list) c))
