In my experience interviewers are looking for a detailed thought process with a comparison of solutions that demonstrates your communication, not just an optimal solution. Do you provide that as well?
EDIT: But - really - I'm not looking for feedback or critiques in this format. I've done this endlessly with people online. Instead - it would be useful to me to recommend services or experiences with mock interview services. I'm having a hard time believing anyone can give me real insight here that I haven't corrected myself. (But that insight could exist through mock interviews)
Have you ever filmed your performance in a practice session?
I've given tons of mock interviews, so if you want a fresh set of eyes let me know.