13

I'm reading Advanced Data Structures by Peter Brass.

In the beginning of the chapter on search trees, he stated that there is two models of search trees - one where nodes contain the actual object (the value if the tree is used as a dictionary), and an other where all objects are stored in leaves and internal nodes are only for comparisons.

What are the advantages of the second model over the first one?

Bernhard Barker
  • 54,589
  • 14
  • 104
  • 138
fokenrute
  • 739
  • 6
  • 17

4 Answers4

9

One of the big advantages of a binary tree where data is only in the leaf nodes is that you can partition based on elements that are not in your dataset.

For example, if I have a possible dataset of 0-1 million, but the vast majority of items are either at the high end or low end but not in the middle, I may still want my first compare against 500,000 - even though that number is not in my data set. If every node had data, I could not do this. While not normally needed in theory, I've run into many times that partitioning based on a value outside my data simplified implementation.

Philip Rieck
  • 32,368
  • 11
  • 87
  • 99
3

B+ trees are an example of a case where all key/values are stored in leaf nodes. The primary advantage here is that since all items are in the leaf nodes, the leaf nodes can be linked together to form a linked list which allows rapid in-order traversal. If you access a particular element, you can always find the next element in the sequence without visiting any parents because the leaf nodes are linked together. Filesystems and database storage systems can take advantage of this structures for range searches and stuff.

Mehdi Maujood
  • 401
  • 5
  • 14
  • Then what exactly are the advantages over a regular linked list ? Since more memory is needed for the same amount of values and operations are afaik the same complexity ? – Aerus Nov 29 '11 at 16:36
  • 1
    @Aerus - A linked list can be made of all data nodes even when they are not constrained to the leaves. However, the advantage of the "hybrid" approach is that searching is fast (because of the tree structure), but inorder traversal is also fast (because of the linked list aspect). It requires a bit more memory - one more pointer per data node - and also adds a small amount of complexity to inserts. This type of structure is great when you want to find a continuous range of items starting at some arbitrary value. – Philip Rieck Nov 30 '11 at 05:10
  • Ofcourse, i was thinking searching was about the same but i had an array in mind (silly me) instead of a linked list. Thanks for your answer. – Aerus Dec 04 '11 at 12:07
1

Lets say you are building tree over some objects on some complex criteria. On example calculated from multiple properties. Sometimes you can't change this object to store calculated value and calculating this criteria is expansive. So you calculate this criteria only once, and store objects in leafs based on criteria result. Then when your tree is complete you can find required object much faster because you don't have to calculate criteria for each tree node in your path.

watbywbarif
  • 6,487
  • 8
  • 50
  • 64
0

well storing information objects in the nodes, we talking in this case about a trie, is usefull for fast retrival of information(faster than storing stuff in an array/hashtable, where the worst case auf acces is O(n), in the trie this is O(m) [m is the lenght of n])

look here: https://en.wikipedia.org/wiki/Trie

In a search tree this oerations can be much more complicated(look AVL Tree O(log n) ) and so can be slower and is more compley to implement.

What data structure to choose?? Well this depends on what u want to do

Krenair
  • 570
  • 5
  • 21
w13531
  • 21
  • 1