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You need to monitor every node in a binary tree with the minimum number of cameras. Each camera covers its parent, itself, and its immediate children. Which algorithmic pattern best fits this problem?

easy🔍 Pattern Recognition Q1 of Q15
Tree: Depth-First Search - Binary Tree Cameras
You need to monitor every node in a binary tree with the minimum number of cameras. Each camera covers its parent, itself, and its immediate children. Which algorithmic pattern best fits this problem?
ADynamic programming on subsets of nodes without relying on tree structure
BDivide and conquer by splitting the tree into balanced subtrees and solving independently
CBreadth-first search with level order traversal to place cameras on alternate levels
DGreedy postorder traversal with state tracking for coverage and camera placement
Step-by-Step Solution
Solution:

  1. Step 1: Identify problem constraints

    The problem requires minimal camera placement covering parent, self, and children, naturally fitting a bottom-up approach.

  2. Step 2: Recognize traversal pattern

    Greedy postorder traversal allows deciding camera placement after knowing children's coverage states.

  3. Final Answer:

    Option D -> Option D

  4. Quick Check:

    Postorder traversal with coverage states matches problem requirements [OK]
Quick Trick: Bottom-up postorder fits coverage dependencies [OK]
Common Mistakes:
MISTAKES
  • Assuming BFS or level order suffices for coverage decisions
Trap Explanation:
PITFALL
  • Candidates often pick BFS or divide and conquer, missing that coverage depends on children's states.
Interviewer Note:
CONTEXT
  • Tests candidate's ability to recognize tree traversal patterns for coverage problems
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