Why is insertion into my tree faster on sorted input than random input?

Question

Now I\'ve always heard binary search trees are faster to build from randomly selected data than ordered data, simply because ordered data requires explicit rebalancing to keep t

Answer 1

@Guge is right. However there is a little tiny bit more to it. I am not saying that it is the biggest factor in this case - however it is there and it is hard to do anything about it.

For a sorted input, lookups likely touch the nodes that are hot in the cache. (This is true in general for balanced trees like AVL trees, red-black trees, B-trees, etc.)

Since inserts start with a lookup, this has an effect on insert/delete performance as well.

Again, I am not claiming that it is the most significant factor in every and all cases. It is there, however, and will likely result in sorted inputs being always faster than random ones in these data structures.