Which of the following most completely explains why we prefer Red Black trees…
2025
Which of the following most completely explains why we prefer Red Black trees over AVL trees?
Answer: D. Red Black trees require fewer rotations than AVL trees, and AVL trees need extra memory to store the balance factor — Concept: AVL trees and Red Black trees are both self-balancing binary search trees guaranteeing O(log n) height, but they differ in how strictly balance is…
- A.
Red Black trees are not as strictly balanced as AVL trees
- B.
Red Black trees have a smaller worst-case height than AVL trees, which is why fewer rotations are needed
- C.
AVL trees need extra memory per node to store the balance factor
- D.
Red Black trees require fewer rotations than AVL trees, and AVL trees need extra memory to store the balance factor
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Correct answer: D
Concept: AVL trees and Red Black trees are both self-balancing binary search trees guaranteeing O(log n) height, but they differ in how strictly balance is enforced and how that balance is tracked.
AVL trees enforce a strict height-balance condition — the heights of the two child subtrees of any node can differ by at most 1 — checked using an explicit balance factor stored at every node. Red Black trees use a looser invariant instead: no root-to-leaf path is more than twice as long as any other path, guaranteed by simple coloring rules (root is black, no two adjacent red nodes, every path has the same number of black nodes), tracked with just one color bit per node.
Application: on insertion, both AVL and Red Black trees are bounded to at most 2 rotations — the invariant is cheap to restore either way. On deletion, the two diverge sharply: AVL deletion can require up to O(log n) rotations in the worst case as imbalance propagates toward the root, while Red Black deletion stays bounded at at most 3 rotations regardless of tree height. So it is specifically the delete path where Red Black trees clearly win on rotation count, and every node also stores only a single color bit instead of a multi-bit balance factor — together these are why Red Black trees cost less to maintain, which is exactly why they are the standard choice for frequently-updated structures (e.g., the Linux kernel's scheduler, C++ std::map, Java's TreeMap).
Red Black trees are not as strictly balanced as AVL trees — true, and that relaxed rule is what enables the performance benefits below, but stated alone it's a structural description, not itself one of the two counted reasons.
Fewer rotations during deletion specifically (both trees are bounded to at most 2 rotations on insertion, so that side shows no real difference) — true, and one real reason, but only half the picture.
Less memory needed for the balance information — also true, and the other real reason.
Since both of these performance reasons hold at once, the complete justification combines them — matching the option that bounds deletion rotations and needs less per-node memory together.