Tree Sort algorithm with unbalanced tree may yield $O(n^2)$ worst-case time complexity/performance. But Tree Sort algorithm with balanced tree guarantees $O(n\log n)$ worst-case time performance. So I do not see any practical use-cases to prefer unbalanced tree variant of Tree Sort algorithm - Tree Sort with balanced tree seems to be a clear winner on all accounts.Is my conclusion correct? Is Tree Sort algorithm with balanced tree is always the best choice (when Tree Sort is applicable generally)?In what cases Tree Sort algorithm with unbalanced tree can be better in some respect?
What are drawbacks of Tree Sort algorithm (with balanced tree) vs Tree Sort (with unbalanced tree)?
sorting;binary trees;search trees
The advantages of unbalanced trees over balanced trees in practical situations are little to none. A large number of predefined algorithms/ data structures that many programming languages use implement a variety of the Tree Sort algorithm in order to keep time complexity of emplacement and retrieval of data to a minimum (keeping in mind that space complexity stays the same). Such varieties are AVL trees and Red-Black trees.For instance, in STL (Standard Template Library in C++), structures such as map/ multimap, set/ multiset implement a BST as to keep the time factor to a minimum value.An example of usage of an unordered tree (although not a binary tree) is a tree used to represent TRIE structures. You can find more about these from Wikipedia or Geeksforgeeks.Hope this was helpful!