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Why single or double rotate a child or parent in a tree?

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I learned about single and double rotations of trees in data structures class. But I know I am not seeing the big picture of rotations. I got some questions that been in my head that were left unanswered.

 

How do you come up with the algorithm for rotating? On my exam, I wrote the rotation code very similar to a swap function only with tree type variables.

 

Are rotations used in game programming or when to use rotations in certain applications?

 

I know the terminologies for a tree like depth, height, level but it does not seem to be helping me understand rotations conceptually and programming-wise.

 

 

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