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

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BlackTom AI · Accepted Answer

The problem asks which node colors can be changed without violating the red-black tree properties, given a specific tree diagram (not provided here) and the answer listing 'Y, C, and D'.
First, recall the core red-black properties that must hold for the tree to remain valid: the root must be black; red nodes cannot have red children (no two consecutive red links); every path from the root to a leaf (NIL) must contain the same number of black nodes (black-height); and all leaves are considered black; every node is either red or black.
Because the diagram is missing, we can only reason at a conceptual level about which nodes might be safe to recolor. In many red-black tree exercises, certain internal nodes can switch colors without breaking properties if their children and parent colors adjust in a way that preserves the red-red and black-height constraints. Typically, a recoloring that preserves the invariants involves nodes that do not create a new red-red edge and does not alter the black-height of any path.
Option A would be unsafe if recoloring creates a red-red edge with its parent or propagates a mismatch in black-height along some paths. Without the diagram, we cannot confirm this definitively.
Option B often represents a boundary case, where changing the color of a node with a red child or a black-height-altering position could violate the invariants; thus, it requires careful checking against both its subtrees and the path to the root.
Option C, according to the provided answer, is acceptable to recolor. This suggests that changing this node’s color does not introduce adjacent red nodes and does not disturb the equal black-height property across all root-to-leaf paths.
Option D being listed as changeable implies that its recoloring also preserves all red-black properties, perhaps due to its position and the colors of its children and parent maintaining the invariants after the change.
In summary, the reasoning behind why Y, C, and D can be recolored while the other option(s) cannot hinges on maintaining: (1) no red-red parent-child pair, (2) the root remaining black (if affected), and (3) equal black-height along every path from the root to the leaves. The absence of the diagram prevents precise, node-by-node justification, but the stated answer indicates that recoloring Y, C, and D satisfies all invariants in this particular tree.
If you have the diagram available, a precise justification would track each affected path from the root to every NIL leaf, verify that the number of black nodes on those paths remains constant, and ensure no parent-child pair becomes red-red after the recoloring.

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

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

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.

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