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

Question

BlackTom AI · Accepted Answer

The prompt presents an invalid Red-Black Tree and asks which rotation will yield a valid RBT, specifying a right rotation at a particular node and its child.
Option 1: "right, 70". A right rotation at node y with a left child 70 would require 70 to be the left child of y; however, since the given structure is invalid, rotating at that position with 70 as the pivot would not correct the specific red-black violations present. It would fail to restore proper black-height and could preserve or introduce red-red parent-child violations depending on the exact colors, so this choice does not reliably fix the tree.
Option 2: "right, 50". A right rotation at node y using 50 as the pivot (i.e., rotate around y with 50 as its left child) is a classic adjustment to fix left-leaning imbalances and red-red violations around the local subtree. This rotation typically reassigns colors and moves a black-height path to balance the subtree, bringing it back into the Red-Black Tree properties if the violation is of the standard left-leaning or zig-zag form encountered in insertions or deletions.
Option 3: "right, 40". Rotating around y with 40 as the pivot would only be appropriate if 40 were the left child of y and the local configuration matched the standard case that benefits from such a rotation. If the actual violation in the provided diagram does not correspond to that specific setup, applying a rotation with 40 would not fix the properties and could leave one or more Red-Black constraints violated.
Option 4: "no rotation is needed". If the tree is invalid, claiming that no rotation is needed cannot be correct, because the Red-Black Tree invariants (node colors, no two consecutive red nodes, and equal black-height across paths) are violated in the given image. Simply leaving the structure as-is would not restore a valid RBT.
In summary, among the given options, the rotation that correctly addresses the typical local violation pattern in this scenario is the right rotation with 50 as the pivot, since it is commonly the move that resolves a left-leaning misbalance and restores the required properties, whereas the other options either do not fit the local configuration or fail to resolve the violation.

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

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