What is the elements of public intoxication?

The Word "alleged" means it has not been proven in a court of law - it's a fancy way for a lawyer to say "he wasn't really drunk because you have not proved it" even though the person has been caught drunk.

"Public intoxication" means being drunk or stoned or high and wandering around in public bothering people or being so "out of it" that they are likely to hurt themselves or someone else - then, you get arrested for public intoxication.