Question $1(5$ points$)$:

Accept two integers from the user $(x$ and $y).$ Generate and print all possible

permutations of integer values in $0,x$ and $0,y.$

For example, if you input $2$ for $x,$ then you have numbers $0,1,2.$

If you input $3$ for $y,$ then you have numbers $0,1,2,3$

You are to generate all possible permutations of the $(0,1,2)$ and $(0,1,2,3)$

$(0,0)(0,1)(0,2)(0,3)(1,0),$ etc.

Question $2(10$ points$)$:

The goal of this assignment is to understand and implement a basic Run$-$Length

Encoding $($RLE$)$ algorithm in Python, which may be used to do compression. This

algorithm is a simple form of data encoding where sequences of the same data

value are stored as a single data value and a count. Run$-$Length Encoding $($RLE$)$ is

a technique that represents consecutive repeated characters $($runs$)$ as a single

character followed by the length of the run. For example, the string "aaabbcccc" can

be encoded to $"$a$3$b$2$c$4".$ This coding doesn't work well if the string contains digits

too as in the case of alphanumeric strings. i$.$e$.$ the $26$ letter alphabet and digits.

An example of a string is aaabbcccc$33335555511.$

In such a case, you need to handle this by changing the code a bit and separating

the run lengths by special characters. For example, adding $/$ between the run

lengths. The code of the above string may be: $\frac{a}{3}\frac{b}{2}\frac{c}{43}\frac{?}{?}\frac{45}{51}\frac{?}{2}.$

Write a function rle$\_$encode that takes an alphanumeric string as input and

returns its RLE encoded version. rle$\_$encode$("$aaabbcccc$33335555511").$

This will return a code like: $"$a$/3$ b$/2$ c$/43/45/51/2"$

Write a function rle$\_$decode that takes an RLE encoded string $"$a$/3$ b$/2$ c$/4$

$3/45/51/2"$ and returns the original string "aaabbcccc$33335555511".$

Ensure your functions handle special cases, such as empty strings or strings

without any repeated characters.

Test your functions with multiple test cases to validate their correctness.