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I have read it in a couple of places that avl tree search faster, but not able to understand. As I understand : max height of red-black tree = 2*log(N+1) height of AVL tree = 1.44*logo(N+1)
Is it because AVL is shorter?
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Red-black trees maintain a slightly looser height invariant than AVL trees. Because the height of the red-black tree is slightly larger, lookup will be slower in a red-black tree. However, the looser height invariant makes insertion and deletion faster.
As we can see, the find operation is performed much faster by AVL trees than by the BST trees. The reason is, the AVL tree is a self- balancing trees and so the height is as small as possible. So the element is found is immediately. The insertion of elements in sorted order is done faster by the AVL tree.
Since the AVL tree is packed tighter (i.e. it has a lower max height) it means more items are closer to the root than in the red-black case. The extra tight packing also means the AVL tree requires more work when inserting elements.
B-Trees are better suited for compression: there is more data per node to compress. In certain cases this can be a huge benefit.
Yes.
The number of steps required to find an item depends on the distance between the item and the root.
Since the AVL tree is packed tighter (i.e. it has a lower max height) it means more items are closer to the root than in the red-black case.
The extra tight packing also means the AVL tree requires more work when inserting elements. The best choice for any app depends on whether it is insert intensive or search intensive...
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AVL tree is better than red-black tree if the input key is almost ascending/descending because then we would have to do single rotation(left-left or right-right case) to add this element. Also, since the tree would be tightly balanced, the search would also be faster.
But for randomly selected input key, RBTree are better since they require less rotation for insertion in comparison to AVL.
Overall, it depends on the input sequence, which would decide how tilted our tree is, and the operation performed.For insert-intensive use Red-Black Tree and for search-intensive use AVL.
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