Awesome! So, obviously, you know what you are doing. In the case of the binary search tutorial, the first thing you pointed out was that it has to be sorted to work.
But there's obviously a cost involved with that, so adding, inserting, sorting, removing, etc... into the data structure being used, whether its represented in memory as an array, linked list, doubly-linked list, hash table where each entry points to an array (or linked list) when you get to creating dictionaries... trees, binary trees, balanced binary trees and graphs... oh the list could go on. You definitely have a lot of material to pick from!
So, getting into why you would use this data structure over that data structure for a particular implementation, maybe this data structure is fast at adding but slow at sorting, but the solution doesn't require a sorted list/array of items... etc... I think that too would be really cool and interesting to talk about.
https://www.toptal.com/developers/sorting-algorithms
It is on sorting, not searching, sorry! Still very cool to watch. Check it out!