The problem with normal tree structures is that they are unsorted and very unwieldy to work with. If you run a search for a file on your computer it’ll generally take a pretty long time, this is because your files are unsorted and it has to search through EVERYTHING to get a result. We can heavily improve this by upgrading how we organize the values in our trees.

A binary tree is just a normal tree with the limitation of each node only being able to, at most, have two children. A binary search tree just has the additional rule that if there’s two values then they need to be ordered, in our case from the lower number on the left to the higher on the right.

Searching on a binary search tree is a large improvement on our original O(n) search speed since now to find something we just need to compare what we want to each parent node before moving left or right until we’re at what we want, giving us O(logn) for all operations.

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