If duplicates are allowed in a binary search tree, it is important to have a convention that determines the relationship between the duplicates. Items that duplicate the root of a tree should either...

If duplicates are allowed in a binary search tree, it is important to have a convention that determines the relationship between the duplicates. Items that duplicate the root of a tree should either all be in the left sub tree or all be in the right sub tree, and, of course, this property must hold for every sub tree. Why is this convention critical to the effective use of the binary search tree?