DATA STRUCTURES PROBLEM

please show all steps and a way to verify answer is correct.

2.b Given the tree shown below. Draw what the tree would look like after deleting the value 7. Use one of the methods for deleting described in class or in the slides. 2.c. Give traversals of the tree shown below: write the order of the traversals... & In-Order: Post-Order: Pre-Order: Given the following tree: Verification for Tree Traversals 1. In-Order Traversal: - Given the tree: - In-order traversal follows Left, Root, Right: Start from leftmost node: 10 Move up to 9, visit 9 Move up to 14, visit 14 Move to right subtree: visit 31 first, then 30, move to 36, visit 50 last o This should give you the sequence: 10, 9, 14, 31, 30, 36, 50 2. Post-Order Traversal: - Post-order traversal follows Left, Right, Root: Start from leftmost node: visit 10 Move to right subtree, visit 31, then 30 Move up, visit 9 Move to 50, then 36 Finally, visit 14 - This should give you the sequence: 10, 9, 31, 30, 50, 36,14 3. Pre-Order Traversal: - Pre-order traversal follows Root, Left, Right: Start at the root: 14 Move to left subtree: visit 9, then 10 Move to right subtree: visit 36, then 30, then 31, finally 50 o This should give you the sequence: 14, 9, 10, 36, 30, 31, 50 Double-Check Ensure each traversal sequence meets the required traversal rules. For in-order traversal, check that the sequence is sorted in ascending order (confirming BST property). For pre-order and post-order traversals, verify the order adheres to Root-Left-Right and Left-Right-Root rules, respectively. Verification for Deleting the Value 7 1. In-order traversal of the resulting tree: - After deleting 7 and replacing it with 9, the tree looks like this: o In-order fraversal means visiting nodes in the left subtree, then the root, then the right subtree. For this tree: Start from the leftmost node: 1 Move up to 3, then visit 3 Move to 5: Visit 4 first, then 5 Move up to 9 (which replaced 7) Move to 14: Visit 12 first, then 14 Finally, visit 36 o This should give you the sequence: 1, 3, 4, 5, 9, 12, 14, 36. 2. Binary Search Tree (BST) property: - For any node, the value in the left child is smaller, and the value in the right child is larger. - Verify each node: Fornode 9:3