Cryptocurrencies are software evolving over time, sometimes branching into new forks which will evolve on

their own $($hard forks, e$.$g$.$: bitcoin cash, bitcoin gold$),$ mostly due to disagreements among developers who

eventually choose to break up and create their own crypto protocols of the same currency. You will write a

class specified in Part A $($below$)$ to help search the information of forking over the time of a cryptocurrency

evolution, then answer a follow$-$up question related to time complexity in Part B$.$

Part A $$ Coding $(90$ pts$)$

Implement the CryptoForkTree class in cryptotree.cpp $($code skeleton is provided$)$ to retrieve information

from a given crypto fork tree.

Files to get you started:

$$ cryptotree.h$,$ cryptotree.cpp $($you must not change their names$)$

a$.$ The CryptoForkNode class represents a new fork starting point $($node$)$ in the crypto fork tree.

You must NOT change this class.

b$.$ The CryptoForkTree class declares the tree operations, you must NOT change any signature

$($or declaration$)$ of the tree functions; otherwise, your code will automatically fail some or all

auto$-$grading tests on Gradescope. You will write the implementations for those operations

following what$$s specified in the comment section above each function. You may add helpers

in CryptoForkTree class to help with your implementation.

$$ Makefile: A makefile allows you to automate the compilation of your code. Check out the

$$Frequently Asked Questions$$ link in the C$/$C$++$ programming in Linux $/$ Unix reference page on

Canvas for simple Makefile reference.

$$ Use the $$make$$ command to compile. Use $$make clean$$ to delete compiled object code and

the executable.

$$ Use $./$cryptotree to execute.

$$ You MUST NOT change the executable file name cryptotree in the Makefile, otherwise,

autograding will automatically fail.

Assumptions:

$1)$ No two forks $($nodes$)$ can have the same fork name.

$2)$ This also implies that each fork $($node$)$ has a unique fork name. Autograder testing will use unique

fork $($node$)$ names.