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I wouldn't worry about stack overflow in a recursive Sudoku solver. Whether you can be faster with a self-managed stack or queue is a good empirical question, but in practice there's no overlap between the set of large puzzles that you can solve in a feasible amount of time and the set of large puzzles that will overflow your stack.
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I was definitely more curious about the performance difference between managing your own stack vs just having a recursive function and having the hardware essentially manage one for you Reading this back to myself I don't know why I would've been worried about a stack overflow, maybe I was imagining having a cpu being really taxed for some reason, weird. I'm pretty confident a self managed one will beat a recursive function.
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