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A balanced tree is a tree which is balanced - it has roughly the same height on each of its sub-nodes. A balanced tree will have the lowest possible overall height.

For example, a balanced binary search tree will have equal heights (plus or minus one) on the left and right sub-trees of each node. This ensures that operations on the tree always are guaranteed to have O(lg n) time, rather than the O(n) time that they might have in an unbalanced tree.

Certain tree algorithms are designed for ensuring that the tree stays balanced at all times, while maintaining the O(lg n) time for all operations. Such algorithms, such as red-black trees, AVL trees, and others, are generally used in standard library implementation of binary search trees.

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Related Questions

What is complexity of binary search tree?

The complexity of binary search tree : Search , Insertion and Deletion is O(h) . and the Height can be of O(n) ( if the tree is a skew tree). For Balanced Binary Trees , the Order is O(log n).


Is an AVL tree a binary search tree (BST)?

Yes, an AVL tree is a type of binary search tree (BST) that is balanced to ensure efficient searching and insertion operations.


What is the time complexity of operations on a balanced binary search tree?

The time complexity of operations on a balanced binary search tree, such as insertion, deletion, and search, is O(log n), where n is the number of nodes in the tree. This means that these operations can be performed efficiently and quickly, even as the size of the tree grows.


Are binary search trees always balanced?

No, binary search trees are not always balanced. Balancing a binary search tree involves ensuring that the height difference between the left and right subtrees of each node is at most 1. Unbalanced binary search trees can lead to inefficient search and insertion operations.


What are the key differences between an AVL tree and a binary search tree, and how do these differences impact their performance and efficiency in terms of search operations?

An AVL tree is a self-balancing binary search tree where the heights of the two child subtrees of any node differ by at most one. This ensures that the tree remains balanced, leading to faster search operations. In contrast, a binary search tree does not have this balancing property, which can result in an unbalanced tree and slower search times. Overall, AVL trees are more efficient for search operations due to their balanced nature, while binary search trees may require additional operations to maintain balance and optimize performance.


Which data structure, AVL tree or Binary Search Tree, is more efficient in terms of balancing and searching for elements?

An AVL tree is more efficient than a Binary Search Tree in terms of balancing and searching for elements. AVL trees are self-balancing, ensuring that the tree remains balanced after each operation, which results in faster search times compared to Binary Search Trees.


Which is faster binary tree or binary search tree?

A tree doesn't do anything so it has no speed...


Does binary tree and binary search tree same?

no they are not same


What is the difference between extended binary tree and a binary search tree?

A strictly binary tree is one where every node other than the leaves has exactly 2 child nodes. Such trees are also known as 2-trees or full binary trees. An extended binary tree is a tree that has been transformed into a full binary tree. This transformation is achieved by inserting special "external" nodes such that every "internal" node has exactly two children.


How can you merge two binary search trees into a single binary search tree?

To merge two binary search trees into a single binary search tree, you can perform an in-order traversal on each tree to extract their elements, combine the elements into a single sorted list, and then construct a new binary search tree from the sorted list. This process ensures that the resulting tree maintains the binary search tree property.


IS AVL-Tree IS binary tree?

An AVL tree is another balanced binary search tree. Named after their inventors, Adelson-Velskii and Landis, they were the first dynamically balanced trees to be proposed. Like red-black trees, they are not perfectly balanced, but pairs of sub-trees differ in height by at most 1, maintaining an O(logn) search time. Addition and deletion operations also take O(logn) time.Definition of an AVL treeAn AVL tree is a binary search tree which has the following properties: The sub-trees of every node differ in height by at most one.Every sub-tree is an AVL tree.


How do you print all data in a Binary Search Tree?

By using Depth First Search or Breadth First search Tree traversal algorithm we can print data in Binary search tree.