Difference between red-black trees and AVL trees

Question

Can someone please explain what the main differences between these two data structures are? I\'ve been trying to find a source online that highlights the differences/simila

Answer 1

Quoting from this: Difference between AVL and Red-Black Trees

RB-Trees are, as well as AVL trees, self-balancing. Both of them provide O(log n) lookup and insertion performance. The difference is that RB-Trees guarantee O(1) rotations per insert operation. That is what actually costs performance in real implementations. Simplified, RB-Trees gain this advantage from conceptually being 2-3 trees without carrying around the overhead of dynamic node structures. Physically RB-Trees are implemented as binary trees, the red/black-flags simulate 2-3 behaviour.

by definition, every AVL is therefore subsets of Red-Black. One should be able to color any AVL tree, without restructuring or rotation, to transform it into a Red-Black tree.

Answer 2

The max height of the trees is the paramount important to keep balance. It almost equals 1.44 * log(n) for AVL, but for RB tree, it is 2 * log(n). So we can get the conclusion that it is better to use the AVL when the problem is search incentive. What matters is another question for AVL and RB tree. RB tree is better than AVL when facing the random insertion at the lower cost of the rotation but the AVL that is good to insert the ascending or descending datas. So if the problem is insertion incentive, we can use RB tree.

Answer 3

AVL trees maintain a more rigid balance than red-black trees. The path from the root to the deepest leaf in an AVL tree is at most ~1.44 lg(n+2), while in red black trees it's at most ~2 lg (n+1).

As a result, lookup in an AVL tree is typically faster, but this comes at the cost of slower insertion and deletion due to more rotation operations. So use an AVL tree if you expect the number of lookups to dominate the number of updates to the tree.

Answer 4

AVL trees are often compared with red-black trees because both support the same set of operations and take O(log n) time for the basic operations. For lookup-intensive applications, AVL trees are faster than red-black trees because they are more rigidly balanced. Similar to red-black trees, AVL trees are height-balanced. Both are in general not weight-balanced nor μ-balanced for any μ ≤ ½; that is, sibling nodes can have hugely differing numbers of descendants.

From the Wikipedia Article on AVL Trees

Answer 5

From what I have seen it seems that AVL Trees do as many rotations(recursively up the tree sometimes) as needed to get the desired height of the AVL Tree (Log n). This makes it more rigidly balanced.

For Red Black Trees there are 5 Sets of rules you need to make sure stay through insertion and removal which you can find here http://en.wikipedia.org/wiki/Red-black_tree.

The main thing that might help you for red black trees is the fact that depending on those five rules you can recursively color the tree up to the root if the uncle is red. If the uncle is black you going to need to do maximum two rotations to fix whatever issues you have but after those one or two rotations YOU'RE DONE. Pack it in and say goodnight because that's the end of the manipulation you need to do.

The Big rule is number 5... 'Every simple path from a given node to any of its descendant leaves contains the same number of black nodes'.

This will cause most of the rotations youll need to make the tree work and that causes the tree not to go too far out of balance.

Answer 6

The fact that RedBlack trees have less rotations can make them faster on inserts/deletes, however .... . Since they are usually a bit deeper They can also be slower on inserts and deletes. Every time you go from one level in the tree to the next, there is a big change that the information requested is not in the cache and must be retrieved from RAM. Thus the time gained on less rotations can already be lost since it has to navigate deeper and thus have to update its cache more often. Being able to operate from cache or not makes a big difference. If the relevant information is in cache, then you can do multiple rotations operations, in the time needed to navigate an additional level and the next level information is not in cache. Thus in cases that RedBlack is in theory faster, looking only at the operations needed, it could be slower in practice, due to cache misses.