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Grokking the Coding Interview Patterns in C#

Solution: Binary Tree Cameras

Explore how to use dynamic programming to determine the minimum number of cameras needed to monitor every node in a binary tree. Understand the three monitoring states for nodes and leverage recursion to optimize camera placement while ensuring full coverage. This lesson helps you apply algorithmic thinking to solve a complex tree monitoring problem effectively.

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Statement

You are given the root of a binary tree. Cameras can be installed on any node, and each camera can monitor itself, its parent, and its immediate children.

Your task is to determine the minimum number of cameras required to monitor every node in the tree.

Constraints:

  • The number of nodes in the tree is in the range [1,1000][1, 1000].

  • Node.data ==0== 0

Solution

Each node in the tree can be in one of three possible states, based on how it's monitored:

  • State 0 (Not covered): All the nodes below this node are monitored, but this node is not. ...