I work for Google and have never been good at the “Here’s an NP-hard problem you haven’t heard of, write correct code for nlogn solution on whiteboard in language of choice” question. I had to train extensively (reading CLR, practicing) to be able to pass.
However, large numbers of engineers at Google are very good at solving whiteboard questions. A lot of it comes from practice, a lot comes from knowing the common problems and solutions, and a lot comes from knowing the algorithmic primitives from which modern algorithms are born.
For many, whiteboard questions are “fun”- in the same way my parents like to do crossword puzzles for the intellectual exercise, Googlers like to discuss challenging, abstract-but-related-to-ads-or-search questions.
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