Serialize a given binary tree to a file and deserialize it back to a tree. Make sure that the original and the deserialized trees are identical.

• Serialize: Write the tree to a file.

• Deserialize: Read from a file and reconstruct the tree in memory.

Serialize the tree into a list of integers, and then, deserialize it back from the list to a tree. For simplicity’s sake, there’s no need to write the list to the files.

Constraints:

• The number of nodes in the tree is in the range $[0, 500]$.
• $-1000 \leq$ Node.value $\leq 1000$

So far, you’ve probably brainstormed some approaches and have an idea of how to solve this problem. Let’s explore some of these approaches and figure out which one to follow based on considerations such as time complexity and any implementation constraints.

An initial idea may be to store one of the traversals of the tree into a file when serializing a tree and read that traversal back to create a tree when deserializing. However, any one of the traversals is not unique. That is, two different trees can have the same in-order traversal. The same goes for pre-order or post-order traversal as well. As a simple example, consider a right-slanting degenerate tree and a left-slanting degenerate tree. Both of these trees have the same in-order, pre-order as well as post-order traversals, but they are different trees. However, two traversals are sufficient to uniquely represent and reconstruct a binary tree.

For ...