#Trees

Discuss the dynamic programming approach on tree structures, focusing on how to identify the correct DP state and transition for tree nodes using the Take / Not-Take strategy.

Optimally implement three functions: lock(), unlock(), and upgrade() on a tree structure.

Solve three coding problems primarily focused on trees and graphs.

You are expected to solve three interlinked tree problems within one hour, considering both time and space complexity. Demonstrate your understanding of tree traversal, balancing, and manipulation.

Implement functions to handle lock and unlock operations on an M-ary tree, ensuring proper hierarchy control as part of the Tree of Space problem, under the guidance of a mentor.