For this assignment you are going to write code that solves problems using recursion. Note the emphasis: you must use recursion!

If you're having problems starting a question, consider the simplest possible case $($ie$,$ a $\text{'}1\text{'}$ or a single$-$character string, etc$)$ and using

induction, figure out how to get to the next case.

All questions in this assignment will be answered in the same Python file:

assign$2.$py$.$ Read the description of each question below, and refer to

the

assign$2.$py file comments for further clarification.

Pay close attention to the specifications and the submission requirements.

In the

assign$2.$py file, you will modify the recursive function called permutations $(),$ which is given on slide $17$ of Topic $2$ class notes $($refer to

that slide for further explanation$).$ The current code outputs the permutations as in the first version on slide $18.$ You must modify the code so

that the output is in a more 'systematic' ordering, as in the second version on slide $18.$

Generating Strings $40\%$

In the

assign$2.$py file, implement the recursive function called generateReverseorder $(),$ which generates all length$-n$ strings of $0\text{'}$s and $1\text{'}$s$,$

for a given non$-$negative integer $n,$ in order from largest to smallest $($aka$,$ descending order$).$

Your function must have $n$ as the only parameter and must return a list containing all length$-n$ strings of $0\text{'}$s and $1\text{'}$s $($in the correct order$).$

Run the code to get an idea of what the expected output should look like.

Note: The test output examples are in descending order, since if you consider them as binary numbers, they start at $2^n-1$ and decrement each

time.

Analyzing a String $40\%$

In the

assign$2.$py file, implement the recursive function called countChars $(),$ which analyzes the given string and returns a $3-$element list of

integers representing the number of consonants, vowels, and other characters $($respectively$)$ in that string.

Your function must have a string $s$ as the first parameter; you may add other parameters as necessary.

Sample output should be as follows:

$s=$ "abc de$"$ Consonants, Vowels, Other: $3,2,1$

$s="$To be or not to be$"$ Consonants, Vowels, Other: $7,6,5$