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  2. AVL trees are more rigidly balanced and hence provide faster look-ups. Thus for a look-up intensive task use an AVL tree. For an insert intensive tasks, use a Red-Black tree. AVL trees store the balance factor at each node. This takes O(N) extra space. However, if we know that the keys that will be inserted in the tree will always be greater ...

  3. Min nodes in avl tree with height h are when it has a balancing factor of either 1 or-1. In that kind of avl tree One sub tree has height h-1 and other sub tree's height is h-2. Therefore we calculate no. Of nodes of tree of height h-1 and h-2 recursively and add 1 to it. 1 is added to count root node of previous tree.

  4. AVL tree insertion, deletion, and lookups take O(log n) time each. Splay trees have these same guarantees, but the guarantee is only in an amortized sense. Any long sequence of operations will take at most O(n log n) time, but individual operations might take as much as O(n) time.

  5. The way I coded it is, as you're searching the tree for the element to delete, temporarily change the child link that you traverse (left or right) to be a link in a stack of traversed nodes (effectively a temporary parent pointer).

  6. Now for the problem of maximum height of an AVL tree:-lets assume that the AVL tree is of height h, F(h) being the number of nodes in the AVL tree, for its height to be maximum lets assume that its left subtree FL and right subtree FR have a difference in height of 1(as it satisfies the AVL property). Now assuming FL is a tree with height h-1 ...

  7. That said, it is too inefficient to be practical - notice that you're recursively exploring the entire tree trying to do rebalancing operations, which will make all insertions and deletions take O(n) time, eating away all the efficiency gains of having a balanced tree. The idea behind AVL trees is that globally rebalancing the tree can be done ...

  8. I wrote a Python version of the Java TreeMap/TreeSet, of which the underlying data structure is a balanced binary tree (Red-Black tree to be precise). Source code and documentation can be accessed in this repo

  9. Just to add some more detail: B-trees can have variable number of children which allow it to hold many records but still maintain a short height tree. RB Tree has less strict rules around rebalancing which make insertions/deletions quicker than AVL tree. Conversely, AVL tree is more strictly balanced so lookups are faster than RB tree. –

  10. Here is the code i wrote and worked fine for AVL Tree to get the rank of a particular value. difference is just you used a node as parameter and i used a key a parameter. you can modify this as your own way. Sample code:

  11. How to check if my AVL tree implementation is correct?

    stackoverflow.com/questions/3955680

    A key property of an AVL tree is that each of its sub-trees is also an AVL tree. That means that covering the basic scenarios should give you a broad coverage of the AVL tree functionality. In other words, these tests done on the smallest tree structure that allows them are the most important ones: Creating a new tree. Inserting the first value.