Should I write an O(N!) algorithm in an interview?
Only if the problem explicitly asks for all permutations or combinations. If they ask for a shortest path or optimal solution, an O(N!) brute force is just a starting point.
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More FAQs in Recognizing O(N!) Factorial Time Complexity
It is an extreme time complexity where the operations multiply factorially (N * N-1 * N-2...), representing the absolute worst algorithmic scaling possible.
Problems that require generating all possible permutations (orderings) of a dataset, such as solving the brute-force Traveling Salesperson problem.
Yes, drastically worse. 20^2 is 400. 2^20 is 1 Million. 20! is 2.4 Quintillion.
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