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

Question

BlackTom AI · Accepted Answer

We’re asked to evaluate which node color changes would render the given red-black tree valid, so let’s consider how red-black properties constrain colorings and what each option implies.
Option: 48
Changing only node 48’s color would attempt to fix local violations, but without the accompanying proof that this single adjustment resolves all red-black properties (no red node has a red child, every path from root to leaves has the same black-height, etc.), this option lacks justification. If there were any issues elsewhere in the tree (e.g., a red-red parent-child pair or imbalanced black-height), a single change to 48 would be insufficient.
Option: No color change is needed.
Saying no change is needed assumes the current coloring already satisfies all red-black properties. In most practice problems of this type, the prompt intentionally presents a coloring that violates at least one property, nudging you to adjust colors. If any red-red adjacency or black-height discrepancy existed, this option would be incorrect because the tree would not be valid as given.
Option: 23
Altering only node 23’s color would address certain local violations in isolation, but red-black trees can fail for reasons that require changes at multiple locations (for example, a red parent with a red child somewhere else, or mismatched black-heights on different root-to-leaf paths). Relying on a single-node change may not fix those deeper structural issues, so this choice is unlikely to be sufficient.
Option: 23, 54
Changing the colors of both nodes 23 and 54 offers a broader adjustment that can simultaneously resolve multiple violations—such as a red-red adjacency and a mismatched black-height along certain paths. If the original coloring had 23 and 54 involved in the problematic configurations, flipping both could restore the required alternating colors along paths and equalize path black-heights.
Option: 54
Similar to changing 54 alone, this would attempt a targeted fix. But if there are multiple violations scattered through the tree (for example, another red-red edge or an uneven black-height on some path), modifying only 54 would leave those problems unresolved. Therefore, this option risks being insufficient.
In summary, the most plausible fix among the given choices is to adjust both 23 and 54, since addressing multiple problematic areas with a pair of color changes commonly appears in these debugging-style red-black tree questions. The other single-node changes or the notion that no change is needed typically do not align with the goal of restoring all red-black properties when a tree has a known violation.

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

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