Most people freeze on interviews and its normal entirely.
Also, most problems are not solved in the 45 minutes and in day to day coding , we generally have a minimum of day to think on the problem and solve it without people looking over our shoulder, google or ask someone :)
> Most people freeze on interviews and its normal entirely
And presumably fail said interviews because they froze. Usually "I think I need to think about this for a while, or maybe even sleep on it" isn't the answer that the interviewer requires.
As you note, it's normal to need more than 45 minutes to think about a problem that you haven't seen before. Many leetcode type problems puzzled eminent computer scientists and/or algorists/mathematicians for years before they were solved.
Then there's the psychological aspect of when interviewers try to "help" you by asking questions, providing clues or even the specific clever (or stupid) trick needed to solve the algorithm puzzle but really you're in no condition to understand the hints they might be providing.
Also, most problems are not solved in the 45 minutes and in day to day coding , we generally have a minimum of day to think on the problem and solve it without people looking over our shoulder, google or ask someone :)