Question

Exercise 6.7. Create a subclass of BinaryTree whose nodes have fields for storing preorder, post-order, and in-order numbers. Write methods preOrderNumber() inorderNumber), and postOrderNumbers) that assign these numbers correctly. These methods should each run in O(n) time. 5.

Answer 1

The question involves creating a subclass of BinaryTree with additional fields for preorder, inorder, and postorder numbers and writing methods to assign these numbers with O(n) time. Subclass should implement traversal methods that visit each node exactly once to maintain the required efficiency.

Step-by-step explanation:

The student's question is regarding the creation of a subclass of a BinaryTree, specifically one where the nodes have additional fields for storing traversal numbers: preorder, inorder, and postorder. To solve the exercise, you would begin by defining a subclass of BinaryTree, let's call it NumberedBinaryTree, and include additional fields in each node for the preorder, inorder, and postorder numbers. The methods preOrderNumber(), inorderNumber(), and postOrderNumber() would then need to be written to traverse the tree and assign these numbers accordingly.

In preorder traversal, you start at the root, assign the preorder number, then recursively traverse the left subtree followed by the right subtree. In inorder traversal, you traverse the left subtree, assign the inorder number to the root, and then traverse the right subtree. Lastly, for postorder traversal, you traverse both subtrees before assigning the postorder number to the root.

Each of these methods must carefully increment the pertinent counters as they traverse the tree to ensure that each node is assigned a unique number. To achieve O(n) time complexity, each of these methods should visit each node exactly once during the traversal process.