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It's an interview programming question, so what matters is that it's a good interview programming question, not that it's something you would ever want to do. It's an important distinction. Generally you're looking to test candidates' abilities to come up with efficient algorithms to solve problems, which you're not going to get if you ask them to, say, tweak the order that fields are displayed on a web app form (even though that's a "real programming task").

Although I do see this as something you could possibly do "for real". Sometimes you'd rather change your existing data once than continue carrying forward what amounts to hacks, which is what inverting the output would amount to. Reversing a binary tree would be what you'd run in a tool to migrate all of your data over from the old format to the new format.



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