If a programmer meets with an accident and forgets his past, will they remember how to code?

No need to tell me! I always ignore html, sir..

The languages maybe, but writing algorithms should be natural for them.

They can usually still talk and perform tasks they already learned. They remember ability, not data. So yes; you would be able to think logically, but may not remember individual things like languages or patterns.

Of course this all depends on the injury.