In principle programmers are supposed to write correct code. But I wonder if in practice it's possible to solve really hard problems without incorrect code as an intermediate step.
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Do not call them intermediate steps. The problems move as much as your code. You will never reach the "correct" solution. This is an adaptive system. So by definition, no it is not possible.
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Probably not. Perfect code that solves hard problems is probably NP complete. P=/=NP.
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But maybe you could create a kind of SAT solver for drafting code that uses a mix of brute force and statistical algorithms to attack the problem efficiently
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What would be considered bugs in this context if the program solves the problem?
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Analogous to writing: draft, draft, draft, draft . . . stop and publish. Each version “fixing the bugs” & introducing new ones. Typically externals determine the stop.
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I assume you don’t mean “Can we release software without bugs?” and you mean “Can we release software solving a hard problem with all intermediate discoveries (usually taking agile iterations) done beforehand and only release after we have addressed all these issues?”. Waterfall?
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Depends on the definition of the bug it self. A requirement might be inherintly buggy due to misunderstanding of the problem. Is the code buggy implicitly then? Imho speed to verify the understanding is more valuable than bug-free code aka lean practices.
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writing code is easy, solving complex problems with clean maintainable code is hard.
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