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What is a perfect binary tree and how does it differ from other types of binary trees?
A perfect binary tree is a type of binary tree where all levels are completely filled with nodes, except possibly for the last level, which is filled from left to right. This means that every parent node has exactly two children.
In contrast, other types of binary trees may have missing nodes or uneven levels, resulting in a less balanced structure. This can affect the efficiency of certain operations, such as searching and inserting elements, making perfect binary trees more predictable and easier to work with in some cases.
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How many types of binary tree?
A binary tree is type of tree with finite number of elements and is divided into three main parts. the first part is called root of the tree and itself binary tree which exists towards left and right of the tree. There are a no. of binary trees and these are as follows : 1) rooted binary tree 2) full binary tree 3) perfect binary tree 4) complete binary tree 5) balanced binary tree 6) rooted complete binary tree
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.
Is a full binary tree the same as a complete binary tree, or are there differences between the two structures?
A full binary tree is a type of binary tree where each node has either 0 or 2 children. A complete binary tree is a binary tree where all levels are fully filled except possibly for the last level, which is filled from left to right. So, a full binary tree can be a complete binary tree, but not all complete binary trees are full binary trees.
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.
What are the key differences between BST and AVL trees in terms of their structure and performance?
BST (Binary Search Tree) and AVL (Adelson-Velsky and Landis) trees are both types of binary trees used for storing and searching data. The key difference lies in their structure and performance. BSTs are simple binary trees where each node has at most two children, and the left child is smaller than the parent while the right child is larger. This structure allows for efficient searching, insertion, and deletion operations. However, if the tree is not balanced, it can degrade into a linked list, leading to slower performance. On the other hand, AVL trees are a type of self-balancing binary search tree where the heights of the two child subtrees of any node differ by at most one. This balancing property ensures that the tree remains relatively balanced, leading to faster search, insertion, and deletion operations compared to BSTs. However, maintaining this balance requires additional overhead, making AVL trees slightly slower in terms of performance compared to BSTs for some operations.
