Sometimes you just want to test the control expression afterwards 
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Write a simple while loop in C and compile it with no optimisations then look at the output asm. Now compile it with full optimisation and look at the new output. It will essentially be a do..while loop.
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wait until you hear about operator associativity
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Only use I can ever think of is printing a load of options to the screen, processing them, then conditioning on whether the user has selected the quit option.
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There are plenty of reasons. For example, when consuming a socket connection, or any time the data is not perfectly defined (which is an increasing phenomenon).
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I prefer set based logic myself. But sometimes you need just a scalpel.
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Octopi are more into recursion then?
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I was taught never to use them because they have a tendency to never ever stop, no matter how careful you are coding them.
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do-while = while + if, no?
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I think can further condense the initialisation inside do while
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