Binary Search Tree

Step 1: Insertion Complexity.
In a binary search tree (BST), in the worst case, the tree can be unbalanced (e.g., resembling a linked list). In this case, inserting a key will require traversing through all nodes, making the worst case time complexity for insertion ** **.

Step 2: Deletion Complexity.
Similarly, in the worst case, deletion involves traversing the entire tree and potentially restructuring it, which takes ** ** time.

Step 3: Conclusion.
Thus, the worst case time complexity for both insertion and deletion in a binary search tree is ** **.

Step 1: Analyze the procedures.
- **TREE-SUCCESSOR**: This operation is ** ** where is the height of the tree. It involves finding the node that follows a given node in the in-order traversal.
- **TREE-MAXIMUM**: This operation is ** **, as it involves traversing down the rightmost path of the tree to find the node with the maximum value.
- **INORDER-WALK**: This operation visits each node of the tree and prints them in in-order sequence, resulting in a time complexity of ** **, where is the number of nodes in the tree.
- **TREE-MINIMUM**: This operation is ** **, similar to **TREE-MAXIMUM**, as it involves traversing the leftmost path to find the node with the minimum value.

Step 2: Conclusion.
The procedure that is distinct in terms of running time is **INORDER-WALK**, as its time complexity is ** ** while the others have ** ** complexity.

Step 1: Understanding the Concept
Binary tree traversal involves visiting all nodes of a tree in a specific order. Depth-first traversals depend on when the root node is visited relative to its subtrees.

Step 2: Traversal Rules
- Inorder: Left Subtree → Node → Right Subtree
- Preorder: Node → Left Subtree → Right Subtree
- Postorder: Left Subtree → Right Subtree → Node

Step 3: Matching Sequences
Based on the table:
1. Inorder (I): Sequence is left subtree, node, right subtree → matches L
2. Preorder (II): Sequence is node, left subtree, right subtree → matches M
3. Postorder (III): Sequence is left subtree, right subtree, node → matches N
Correct mapping: I-L, II-M, III-N

Step 4: Final Answer
Option (A)