Azrael1o
asked on
Balancing a binary tree
I have a binary tree that i can alot with but to make things simplier i want to be able to make it balanced. Does any EXPERT know the algorithum or the code for this. I can not figure it out for the life of me
ASKER
thanks for the help but i also have to be able to balance the tree later on not just when i am adding to the tree. I know this is alot harder but its an option that i want to add
ASKER CERTIFIED SOLUTION
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
Looked around and found some lecture notes http://user.it.uu.se/~pierref/courses/AD1/Slides/AVLtrees.pdf
-bcl
-bcl
Hi Azrael1o,
I know of 2 kinds of balanced trees. One is calle 2-3-4 tree, and the swcond is called red-black tree.
The 2-3-4 is made of nodes containing 2, 3 or 4 subnodes (surprisingly), so it isn't a binary tree. Inserting (and deleting) in such a tree is matter of changing the node types (2, 3, 4) and splitting the higher level nodes into lower level ones. Draw some pictures and you'll find what to do and whot to not.
The red-black is exactly the same as 2-3-4 (almost). The 2, 3, 4 nodes there are transfered into binary structures (little subtrees) where leaves are coloured red and the rest is coloured black (or vice versa). All the folowing algorithms are used similar to 2-3-4 trees.
Search the web and read something about the trees. You may try: http://www.cs.brown.edu/courses/cs016/book/slides/234_RB_trees2x2.pdf but there are many other good resources.
Cheers!
I know of 2 kinds of balanced trees. One is calle 2-3-4 tree, and the swcond is called red-black tree.
The 2-3-4 is made of nodes containing 2, 3 or 4 subnodes (surprisingly), so it isn't a binary tree. Inserting (and deleting) in such a tree is matter of changing the node types (2, 3, 4) and splitting the higher level nodes into lower level ones. Draw some pictures and you'll find what to do and whot to not.
The red-black is exactly the same as 2-3-4 (almost). The 2, 3, 4 nodes there are transfered into binary structures (little subtrees) where leaves are coloured red and the rest is coloured black (or vice versa). All the folowing algorithms are used similar to 2-3-4 trees.
Search the web and read something about the trees. You may try: http://www.cs.brown.edu/courses/cs016/book/slides/234_RB_trees2x2.pdf but there are many other good resources.
Cheers!
It is typically easiest to balance a binary tree while building it. The AVL tree (http://sky.fit.qut.edu.au/~maire/avl/System/AVLTree.html) uses a mechanism known as rotation to restore balance to an almost balanced tree. The insertion operation is standard for a BST but is followed by a step that checks if the tree has gone out of balance. If it has, a rotation (right or left) is performed. Similar rebalancing might be necessary following a deletion. If you need more explanation, ask.
-bcl