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Given the following partial memoization cache for a subtree rooted at node X in the Binary Tree Cameras problem: Cache states: - dfs(X.left) = HAS_CAM - dfs(X.right) = NOT_COVERED What must be true about node X's camera placement and coverage state after dfs(X)?

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Tree: Depth-First Search - Binary Tree Cameras
Given the following partial memoization cache for a subtree rooted at node X in the Binary Tree Cameras problem: Cache states: - dfs(X.left) = HAS_CAM - dfs(X.right) = NOT_COVERED What must be true about node X's camera placement and coverage state after dfs(X)?
ANode X returns NOT_COVERED and places no camera
BNode X returns COVERED_NO_CAM without placing a camera
CNode X places a camera and returns HAS_CAM
DNode X places a camera but returns COVERED_NO_CAM
Step-by-Step Solution
Solution:

  1. Step 1: Analyze children's states

    Left child has camera (HAS_CAM), right child is NOT_COVERED.

  2. Step 2: Rule for placing camera

    If any child is NOT_COVERED, current node must place camera.

  3. Step 3: Return HAS_CAM after placing camera

    Node X places camera and returns HAS_CAM.

  4. Final Answer:

    Option C -> Option C

  5. Quick Check:

    NOT_COVERED child triggers camera placement at parent [OK]
Quick Trick: NOT_COVERED child -> parent places camera [OK]
Common Mistakes:
MISTAKES
  • Returning wrong coverage state after camera placement
Trap Explanation:
PITFALL
  • Candidates confuse coverage states or forget to place camera when child uncovered.
Interviewer Note:
CONTEXT
  • Tests deep understanding of coverage state propagation
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