[Solved] You need to place the minimum number of cameras in a binary tree so that every node is monitored.... Which approach guarantees an optimal solution for this problem? | Tree: Depth-First Search

Tree: Depth-First Search - Binary Tree Cameras

You need to place the minimum number of cameras in a binary tree so that every node is monitored. A camera at a node monitors its parent, itself, and its immediate children. Which approach guarantees an optimal solution for this problem?

ABrute force recursion trying all combinations of camera placements

BGreedy postorder traversal using explicit states to track coverage and camera placement

CTop-down dynamic programming with memoization based on node coverage

DLevel order traversal placing cameras on all nodes with uncovered children

Step-by-Step Solution

Step 1: Understand problem constraints
The problem requires minimal cameras covering all nodes, where a camera covers parent, self, and children.
Step 2: Evaluate approaches
Brute force is exponential and inefficient. Level order placing cameras on all uncovered children is greedy but not minimal. Top-down DP is complex and less intuitive here. Greedy postorder with explicit states ensures children are processed before parent decisions, enabling minimal camera placement.
Final Answer:
Option B -> Option B
Quick Check:
Postorder traversal with states is known optimal for this problem [OK]

Quick Trick: Optimal solution uses postorder traversal with states [OK]

Common Mistakes:

MISTAKES

Assuming level order greedy placement is minimal
Trying brute force without pruning
Confusing top-down DP with bottom-up greedy

Trap Explanation:

PITFALL

Level order greedy looks intuitive but overplaces cameras; brute force is correct but impractical.

Interviewer Note:

CONTEXT

Tests if candidate recognizes the pattern beyond brute force or naive greedy.

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Which approach guarantees an optimal solution for this problem?

Step 1: Understand problem constraints

Step 2: Evaluate approaches

Final Answer:

Quick Check:

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