Duplicate Entries in Binary Search Tree

Question

I have a very simple question regarding BSTs. I have seen multiple definitions of BSTs regarding duplicate entries. Some define BSTs as not allowing duplicate entries, others that node's left child is <= to the nodes value and the right child is greater than the node's value, and some definitions are the opposite of that ( left child is < than the node, right child is >=).

So my question is what is the official definition (if one exists) for BSTs regarding duplicate entries? For example what would a BST look like after inserting the values : 3, 5, 10, 8, 5, 10?

Thank you in advance for clarifying the definition and answering my question!

"official definition"? What would you consider "official"? What level of authority is required here? — S.Lott, Jan 02 '12 at 18:35
I guess it's not so much level of authority, as much as it is what is the most commonly accepted definition of BSTs regarding duplicate entries. — Tareq, Jan 02 '12 at 19:14

TonySalimi · Accepted Answer · 2012-01-02T18:57:11.410

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One of the well-known books in the algorithm and data structure area is the CLRS book, also known as the bible of data structures and algorithms:

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According to the definition of this book, the duplicate entries are placed in the right tree of the node that contains the same key. As an example, take a look at the insertion algorithm of BSTs adopted from this book:

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edited Jan 02 '12 at 18:57

answered Jan 02 '12 at 18:32

TonySalimi

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Wow very interesting and meek answer. – Saeed Amiri Feb 16 '12 at 18:13

score 3 · Answer 2 · answered Jan 02 '12 at 18:25

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the important point is that not having duplicates in the tree assures the fast lookup times. If you have duplicates in one side of the node your search time will suffer because you have to go through all duplicates before you can continue.

http://en.wikipedia.org/wiki/Binary_search_tree

answered Jan 02 '12 at 18:25

light_303

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The external link is not very helpful in this context. – Niklas B. Jan 02 '12 at 18:27
In trees where left child is < than the node and right child is >= than the node, it's not a big deal. When first node is found one just can check right childs to obtain all duplicates. – Nikolay Polivanov Jan 02 '12 at 18:54
Of course each node could just contain a count of the number of times the element appears – C. Reed Jan 02 '12 at 19:03

Duplicate Entries in Binary Search Tree

2 Answers2