Hello Everyone, Output: Tree Example Building tree with root value 5 Inserted 1 to left of 5 Inserted 8 to right of 5 Inserted 6 to left of 8 Inserted 3 to right of 1 Inserted 9 to right of 8 Traversing tree Traversed 1 Traversed 3 Traversed 5 Traversed 6 Traversed 8 Traversed 9 Note: The Java algorithm efficiently builds a balanced binary search tree (BST) with O(log n) time complexity for inserting nodes and O(n) time complexity for traversing the tree (where 'n' is the number of nodes). Node insertion requires constant space (O(1)), but overall space complexity becomes linear (O(n) due to recursive traversal). In this binary tree, each node has two children, creating a straightforward structure. The algorithm employs pre-order traversal, handling the current node before its children. Asymptotic
analysis using the recurrence relation T(n) = T(n-1) + C2 shows a linear relationship (T(n) = O(n)) for worst-case time complexity. In simpler terms, Big O notation assesses efficiency based on input size. Logarithmic insertion suits a growing tree, while linear traversal correlates with the number of nodes. Although single insertions use constant space, cumulative space complexity grows linearly due to recursive traversal. In conclusion, the algorithm strikes a balance between efficient logarithmic insertion and linear traversal complexities. The binary tree structure improves search and retrieval, making it suitable for applications with frequent operations. This analysis helps comprehend the algorithm's scalability and performance, crucial for designing responsive software systems.