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Given the following memo dictionary after running an optimized recursive balance check on a binary tree: ```python heights = {None: 0, node4: 1, node5: 1, node2: 2, node3: 1, node1: 3} ``` Which of the following trees corresponds to this memo state?

hard🔄 Reverse Engineer Q9 of Q15
Tree: Depth-First Search - Balanced Binary Tree
Given the following memo dictionary after running an optimized recursive balance check on a binary tree: ```python heights = {None: 0, node4: 1, node5: 1, node2: 2, node3: 1, node1: 3} ``` Which of the following trees corresponds to this memo state?
AA tree where node2 has one leaf child, node3 is leaf, and node1 is root with children node2 and node3
BA tree where node1 is leaf, node2 and node3 are None
CA tree where node2 and node3 are leaves, node1 has only left child node2
DA tree where node2 has two leaf children, node3 is leaf, and node1 is root with children node2 and node3
Step-by-Step Solution
Solution:

  1. Step 1: Analyze heights in memo

    node4 and node5 have height 1 -> leaves; node2 height 2 -> has one child; node3 height 1 -> leaf; node1 height 3 -> root.

  2. Step 2: Match tree structure

    node2 has one child (either node4 or node5), node3 is leaf, node1 has node2 and node3 as children.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Heights match tree with node2 having one leaf child [OK]
Quick Trick: Height 2 means one child subtree of height 1 [OK]
Common Mistakes:
MISTAKES
  • Assuming node2 has two children for height 2
Trap Explanation:
PITFALL
  • Candidates confuse height with number of children instead of max subtree height.
Interviewer Note:
CONTEXT
  • Tests reasoning backward from memoized subtree heights
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