How does this change the optimal solution approach?
hard🎤 Interviewer Follow-up Q10 of Q15
Tree: Depth-First Search - Binary Tree Cameras
Suppose the Binary Tree Cameras problem is modified so that each camera can monitor nodes up to distance 2 away (parent, self, children, and grandchildren). How does this change the optimal solution approach?
AThe problem reduces to a standard vertex cover problem solvable by known DP
BA bottom-up DP with extended states tracking coverage up to distance 2 is required
CThe greedy postorder traversal with three states still applies without modification
DA simple BFS placing cameras on every third level suffices
Step-by-Step Solution
Solution:
Step 1: Understand coverage radius increase
Cameras now cover nodes up to distance 2, including grandchildren.
Step 2: Recognize problem transformation
This coverage matches vertex cover on edges or nodes with extended neighborhood.
Step 3: Apply vertex cover DP
Standard vertex cover DP on trees can solve this efficiently.
Final Answer:
Option A -> Option A
Quick Check:
Extended coverage changes problem class to vertex cover [OK]
