Implement toDot Method and File Storing Mechanism for VerkleTrie

[neotheprogramist]

Description

This issue aims to enhance the functionality of VerkleTrie in two significant ways:

1. Implementing toDot Method for String Representation:

   • Develop a method toDot for VerkleTrie to create a human-readable string representation in Dot format. This feature will aid in debugging and visualizing the VerkleTrie structure.
   • The toDot method should include:
     • BranchNodes with commitment attribute.
     • StemNodes with stem, leftCommitment, and rightCommitment attributes.
     • LeafNodes with suffix and value attributes.
     • A location attribute for each node to uniquely name them.

2. Implementing File Storing Mechanism for toDot Output:

   • Extend the toDot functionality to include the capability of saving its output into a file. This addition will facilitate users in saving the VerkleTrie graphical representation for further analysis or sharing.
   • The file storing feature should:
     • Allow efficient and user-friendly saving of the Dot format output.
     • Handle errors related to write permissions or file system issues.
     • Optionally let users specify the file path and name for storing the output.

Expected Behavior

• toDot returns the tree representation in Dot format with specified attributes for different node types.
• Users can save the Dot format output of VerkleTrie into a file, enhancing the method's usability for debugging and analysis.