Optimal Efficiency for Binary Search Tree
The Initial State of BST
Use this order to show the initial state of the BST.
Effect of Rotations for Balanced Tree
Show the step for the effect of every rotation applied in order to BST and finish with a balanced tree that provides optimal efficiency for inserting and searching.
The Initial State of BST
Initial state of the Binary Search Tree (BST) using the given order:
Ellis - JanuaryCaitlin - February
Aliya - May
Musa - August
Frost - June
Faiza - March
Sam - April
Angela - July
Effect of Rotations for Balanced Tree
After performing rotations to achieve a balanced tree:
Faiza - MarchAngela - July
Ellis - January
Caitlin - February
Musa - August
Aliya - May
Frost - June
Sam - April
To achieve optimal efficiency for inserting and searching in a binary search tree (BST), it is important to balance the tree. The initial state of the BST provided includes a specific order of nodes. In order to create a balanced tree, rotations need to be performed.
Rotations for Balanced Tree
Based on the given order, the following rotations are needed:
1. Left rotation on the node Aliya - May.2. Left rotation on the node Ellis - January.
3. Right rotation on the node Caitlin - February.
4. Left rotation on the node Frost - June.
After these rotations, the resulting balanced tree is shown above. This balanced tree provides optimal efficiency for both inserting and searching operations in the binary search tree.
By ensuring the tree is balanced, the time complexity of operations such as insertion and searching is optimized, leading to faster and more efficient performance. Balanced trees also prevent skewness, which can result in poor performance in BST operations.