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I like skip lists (technically a data structure, but with associated algorithms). I love the simplicity vs. other balanced tree algorithms. Also I'm a fan because it's a relatively recent development that shows that progress is still possible in fundamental areas.

https://en.wikipedia.org/wiki/Skip_list

Some runners up: Gosling's dynamic programming algorithm for optimizing text editor screen updates and gap buffers.



I had an assignment where I needed to implement generic Skip lists in Java, I had a great time doing it, I really enjoy them as a data structure




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