Are duplicate keys allowed in the definition of binary search trees?

Question

I\'m trying to find the definition of a binary search tree and I keep finding different definitions everywhere.

Some say that for any given subtree the left child k

Answer 1

1.) left <= root < right

2.) left < root <= right

3.) left < root < right, such that no duplicate keys exist.

I might have to go and dig out my algorithm books, but off the top of my head (3) is the canonical form.

(1) or (2) only come about when you start to allow duplicates nodes and you put duplicate nodes in the tree itself (rather than the node containing a list).