RBT_V_3
Following is a valid Red Black Tree.

Question

BlackTom AI · Accepted Answer

To assess whether the statement 'Following is a valid Red Black Tree' is true, we must check the defining properties of a Red-Black Tree against the given tree.
Option 1: Yes.
- A Red-Black Tree requires that every node is either red or black, the root is black, red nodes cannot have red children (no two reds in a row on any path), and every path from a node to its descendant leaves contains the same number of black nodes (black-height).
- If the answer key says 'Yes', the tree shown would need to satisfy all four properties above. Specifically, the root must be black, there must be no adjacent red-red pair, and all paths from the root to the NIL leaves must have identical black-height. If these conditions hold in the diagram, then the tree is valid.
- Additionally, one can check that nil leaves (often represented as black) contribute to the black-height count, ensuring consistency across all root-to-leaf paths. If any path had more or fewer black nodes, or a red-red violation occurred anywhere, the tree would not be valid.
Option 2: No.
- If one considers the alternative, a 'No' answer would be correct only if at least one Red-Black property is violated in the depicted tree. Common violations include: a red node having a red child, the root being red, or differing black-heights across different root-to-leaf paths.
- For example, a violation could be a red node with a red child, which would break the no-two-reds-in-a-row rule, or a path with more black nodes than another path, which breaks the black-height property. Another typical issue is a non-black root, which contradicts the requirement that the root be black.
- Since the provided answer key labels the statement as correct ('Yes'), the expectation is that none of these violations appear in the diagram, and all Red-Black properties are preserved.
In summary, the correctness hinges on the tree conforming to the four Red-Black properties across every path and node. If the diagram indeed shows a black root, no red-red edges, and equal black-height on all root-to-leaf paths, then 'Yes' is the appropriate choice. If any of those properties were violated, 'No' would be the correct option instead.

RBT_V_3 Following is a valid Red Black Tree.

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