Identify the error in the red-black tree.

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BlackTom AI · Accepted Answer

The prompt presents a question about identifying an error in a red-black tree, but no answer options are provided to analyze.
To proceed meaningfully, here are ways to reason about common errors in red-black trees and how they relate to the typical properties that must hold:

- Red-black trees have five defining properties: (1) Each node is either red or black. (2) The root is always black. (3) All leaves (null pointers) are considered black. (4) If a node is red, then both of its children are black (no two red nodes in a row). (5) For each node, all paths from that node to its descendant leaves contain the same number of black nodes (black-height).

With these in mind, typical errors you might look for include:
- A violation of the black-height property: if some path from the root to a null leaf contains more or fewer black nodes than another path, this would indicate an error. When you see the statement 'The path from the root to a null leaf node does not have the same number of black nodes,' that points directly at a potential violation of property (5).
- A red-red parent/child violation: if a red node has a red child, that breaks property (4).
- A violation of the root-black rule: if the root ends up being red after operations, that would violate property (2).
- Incorrect black-height due to insertion/deletion fixes: after insertions or deletions, failure to properly rotate or recolor can lead to some paths gaining or losing black nodes relative to others, again breaking property (5).

Since there are no answer options provided in the data, I cannot evaluate why a specific listed choice would be correct or incorrect. If you supply the possible options, I can walk through each one, indicating precisely why it is true or false, and how it aligns with or violates the red-black tree invariants. In general, when diagnosing errors in a red-black tree, you should check:
- Are all null leaves considered black, and do they align in black-height across all root-to-leaf paths?
- Are red nodes never directly above red nodes?
- Is the root black, and are any violations corrected through rotations and recolorings according to the standard fix-up cases?

Providing the options will let me map each option to the corresponding property and explain the reasoning step by step.

Identify the error in the red-black tree.

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Identify the error in the red-black tree.

View Explanation

Log in for full answers

Similar Questions

RBT_RTT_11 Consider invalid Red Black Tree below. A___ rotation at node_____yields a valid red-black tree.

RBT_RTT_13 Consider invalid Red Black Tree below. A___ rotation at node_____yields a valid red-black tree.

RBT_Ch_5 Which node(s) color change would make this a valid red-black tree?

RBT_V_3 Following is a valid Red Black Tree.

Identify the correct rotation to balance the red-black tree.

The red-black tree below remains valid if the color of nodes _____ are changed.

Identify the balanced tree after inserting node 7 in the given red-black tree.

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