Complete the following task with appropriate documentation.

$$ For each function, high$-$level description of that function. This should be a two or three

sentence explanation of what this function does.

$$ Your main function in the assignment should contain a generalised description of the

approach your solution uses to solve the assignment task.

$$ For each function, specify what the input to the function is$,$ and what output the function

produces or returns $($if appropriate$).$

$$ For each function, the appropriate Big$-$O or Big$-\backslash$Theta time and space complexity of that

function, in terms of the input size. Make sure you specify what the variables involved

in your complexity refer to$.$ Remember that the complexity of a function includes the

complexity of any function calls it makes.

$$ Within functions, comments where appropriate. Generally speaking, you would comment

complicated lines of code $($which you should try to minimise$)$ or a large block of code

which performs a clear and distinct task $($often blocks like this are good candidates to be

their own functions!$).$

you may not use python dictionaries or sets. This is because

the complexity requirements for the assignment are all deterministic worst$-$case requirements,

and dictionaries$/$sets are based on hash tables, for which it is difficult to determine the deterministic worst$-$case behaviour.