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On the adaptability of algorithms and the use of commutators

Introduction You may have come across immense algorithms for certain puzzles which are so difficult to wrap your head around, you don't even consider learning them by heart. These (in many cases computer-generated) algorithms don't always show their structure and you aren't always sure why it does what it's supposed to do. In this article, I'll talk about the adaptability of algorithms and the use of commutators to invent your own algorithms. In my opinion; something you've reasoned your way through is better remembered than something you've tried to memorize. Algorithms Anatomy When you look up algorithms for certain cases, you may recognize some of its internal structure. For example: if you know some speedcubing PLL algorithms, you might have noticed that the F-perm is actually the T-perm with a set-up move. If you know what the T-perm does, than it's easy to see what the F-perm is for. Another example is the opposite edge swap algorit