Which change to the algorithm is necessary to maintain minimal camera placement?
hard🎤 Interviewer Follow-up Q15 of Q15
Tree: Depth-First Search - Binary Tree Cameras
Suppose the problem is modified so that cameras can monitor nodes up to distance 2 away (i.e., parent, self, children, and grandchildren). Which change to the algorithm is necessary to maintain minimal camera placement?
AUse the same three-state postorder traversal but add a fourth state to track grandchildren coverage
BPlace cameras greedily on all nodes with uncovered children as before, no change needed
CModify DFS to track coverage states up to distance 2 and place cameras accordingly, increasing state complexity
DSwitch to brute force recursion since greedy no longer works
Step-by-Step Solution
Step 1: Understand coverage radius increase
Cameras now cover nodes up to distance 2, so coverage states must reflect grandchildren coverage, not just immediate children.
Step 2: Adjust algorithm states
The original three states are insufficient; DFS must track coverage at a larger radius, increasing complexity and requiring more nuanced state management.
Step 3: Evaluate options
Simply adding a fourth state (A) is vague and insufficient without redesign. Greedy placement without state changes (B) fails minimality. Brute force (D) is inefficient and unnecessary.
Final Answer:
Option C -> Option C
Quick Check:
Expanded coverage radius requires more complex state tracking [OK]
Quick Trick:Larger coverage radius -> more complex states in DFS [OK]
Common Mistakes:
MISTAKES
Assuming original states suffice for extended coverage
Relying on naive greedy placement
Switching to brute force unnecessarily
Trap Explanation:
PITFALL
Naive greedy looks simpler but misses minimality; state complexity must increase.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt algorithm to problem variants.
Master "Binary Tree Cameras" in Tree: Depth-First Search
3 interactive learning modes - each teaches the same concept differently
