CC7_03
Create a function that takes in a Binary Search Tree (BST) and a positive integer k, returning the kth largest integer value within the BST.
Assume that the BST only contains integer values and that k will always be less than or equal to the total number of nodes in the tree.
For this question, duplicate integers are treated as distinct entries. For instance, in a BST with values {5, 7, 7}, the second largest value would be 7—not 5.
Each BST node has an integer value, a left child node, and a right child node. A node is a valid BST node only if it adheres to the BST properties: its value is strictly greater than all values of nodes in its left subtree, and less than or equal to all values of nodes in its right subtree. The children nodes are either valid BST nodes themselves or None / null.

Sample input:

Sample output:
17

Given the following implementation to traverse_reverse_in_order(node, k, tree_data), which test case would fail? It is guaranteed that all the other methods are correctly implemented. The input trees depicted in the DcStrings of test cases are guaranteed to be accurate.

Question

CC7_03
Create a function that takes in a Binary Search Tree (BST) and a positive integer k, returning the kth largest integer value within the BST.
Assume that the BST only contains integer values and that k will always be less than or equal to the total number of nodes in the tree.
For this question, duplicate integers are treated as distinct entries. For instance, in a BST with values {5, 7, 7}, the second largest value would be 7—not 5.
Each BST node has an integer value, a left child node, and a right child node. A node is a valid BST node only if it adheres to the BST properties: its value is strictly greater than all values of nodes in its left subtree, and less than or equal to all values of nodes in its right subtree. The children nodes are either valid BST nodes themselves or None / null.

Sample input:

Sample output:
17

Given the following implementation to traverse_reverse_in_order(node, k, tree_data), which test case would fail? It is guaranteed that all the other methods are correctly implemented. The input trees depicted in the DcStrings of test cases are guaranteed to be accurate.

BlackTom AI · Accepted Answer

We start by restating the problem setup in our own words to ensure clarity about what is being tested.
- The task is to create a function that returns the kth largest integer value in a BST, counting duplicates as distinct entries.
- Duplicates are allowed and treated as separate nodes, so if the BST contains {5, 7, 7}, the 2nd largest is 7.
- The BST property described is: left subtree values are strictly less than the node’s value, and the right subtree values are less than or equal to the node’s value. This means equal values can appear on the right side, and the traversal must account for that.
- The question then asks which test case would fail for the given (unshown) implementation of traverse_reverse_in_order(node, k, tree_data).

Option A: The implementation would fail both test cases.
- Consider how a reverse in-order traversal works: it visits right subtree, then the node, then left subtree, which yields values from largest to smallest. If the implementation correctly handles counting each visited node (including duplicates) until k is reached, it should return the kth largest value even when duplicates occur.
- A potential reason this option could be true is if the implementation incorrectly assumes a strictly increasing sequence or relies on a property akin to a strictly increasing BST (i.e., no duplicates) and not the given variant where right subtree allows duplicates. If the code counts nodes or compares values in a way that mishandles equal values, it could miscount duplicates and fail for some cases.
- However, without seeing the exact code, we cannot confirm systematic failure on both test cases. It is plausible that a flawed assumption about duplicates could cause at least one test case to fail, but claiming both would fail requires stronger evidence.

Option B: The implementation is correct and would pass both test cases.
- A properly implemented reverse in-order traversal that counts each visited node (including duplicates) until it reaches the kth node should correctly yield the kth largest value under the provided BST semantics, since the largest elements are visited first. This aligns with the requirement that duplicates are treated as distinct entries.
- If the implementation indeed traverses right, processes the current node (incrementing a counter), and then traverses left, while maintaining k as a remaining count, it should handle the duplicates correctly and produce the correct kth largest value regardless of how many duplicates exist or where they are placed (as long as the BST property is respected as described).
- The guarantee that all other methods are correctly implemented supports the idea that the traversal logic is compatible with the tree data used in the tests, making success plausible.

Analyzing both options, we consider common pitfalls: a mistaken assumption about duplicates, an off-by-one error in counting, or mishandling the traversal order. If the code uses a straightforward reverse in-order approach with a proper decrement of k when visiting a node, those typical errors can be avoided. Conversely, if the code contains a constraint assuming no duplicates or uses a counting scheme that doesn’t align with the actual node visitation order, failures could occur.

In absence of the concrete test cases and the exact implementation, we cannot definitively declare which option is correct. The reasoning above outlines how each option could be plausible depending on specific implementation details and the treatment of duplicates during traversal.

Note: The analysis intentionally avoids asserting a definitive answer and instead maps out the plausible logical outcomes for both statements given the described BST properties and traversal method.

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