Design and code a python solution for the problems. You must come up with your own algorithm and the honor code applies (no references). It is strongly recommended that you think about your...

Design and code a python solution for the problems. You must come up with your own algorithm and the honor code applies (no references).

It is strongly recommended that you think about your problem-solving steps and verify that you follow the guidelines of the assignment.

You will be graded on the correctness of your recursive algorithm.Algorithms that are not recursive will earn a score of 0/50. Your solution should not use loops.

HINT:Helper functions are allowed.

Problem 1[50 points] Design arecursive algorithmthat will display the sum of the digits of an integer.Submit a python functionsum_digits(number)that returns the sum.

Examples:

sum_digits(126) # returns 9
sum_digits(-49) # returns 13
sum_digits(3) # returns3

Problem 2[50 points] Design arecursive algorithmthat will display whether it is possible to choose two integers from a list of integers such that the difference between the two equals a given value.Hint: You may wish to invoke another algorithm, (i.e., function), that accepts more parameters that perform the recursion. Submit a python functionis_diff_two(values, diff)that take a list and the desired difference as a non-negative integer and returns true or false.

Examples:

is_diff_two([2, 4, 8], 4)   # returns True
is_diff_two([1, 2, 4, 8, 1], 7) # returns True
is_diff_two([2, 4, 4, 8], 7)   # returns False
is_diff_two([], 7)    # returns False
is_diff_two([-1,-3,5,8,10],11) #returns True

Restrictions

• 
  Theonlyfunctions you may use are:print, str, int, float, bool, len, list, range, abs, round,andpow.
  


• Note that you may not use list slicing (AKA colons in your indices).


• We will not deduct for the use of str(), but you do not actually need it.


• Donotimport libraries.

Submission

• Upload yourHW6.pyfile to Web-CAT via your browser(not eclipse)


• There is a hard limit of 5 submissions to Web-CAT.


• We suggest you run your own tests before submitting them, but thenremovethese before submitting because they will use Web-CAT server time.

Grading

• 
  The code should be submitted to Web-CAT for testing. GTAs will award up to 15 additional points after reviewing your code.
  


• 
  They will also deduct points for code that doesn't comply with the above instructions.
  

Problem 1: 50 pts total, max penalty is -50

• P1: -50 for using forbidden functions.


• P1: -25 for not using any recursion.(up to -50 no matter what this is in combination with)*


• P1: -25 for using ‘for’ or ‘while’ loops.


• P1: -10 for a complex solution that is quite hard to follow. ( use good commenting, good variables names, and concise code that clearly progresses towards the solution)


• P1:-10 for list functions such as append(), prepend(), pop(), etc.


• P1: -5 for using list slicing (e.g., for list a, a[start:end], or a[start:], or a[:end], or a[:]).

Problem 2: 50 pts total, max penalty is -50

• P2: -50 for using forbidden functions.


• P2: -25 for not using any recursion.(up to -50 no matter what this missing recursion is in combination with)*


• P2: -25 for using ‘for’ or ‘while’ loops.


• P2: -25 for using slicing.


• P2: -10 for list functions such as append(), prepend(), pop(), etc.


• P2: -10 for a complex solution that is quite hard to follow. (Use good commenting, good variables names, and concise code that clearly progresses towards the solution.)