1. Use only commands, functions, datatypes from Python Part 1 class.
2. You are free to use whatever resource to learn about the subject of task. Please avoid plagiarism - the task is for you to learn, not for us to evaluate you.
3. Refrain from using pre-existing libraries/functions/other structures. Both problems are completely doable using the content for Python Part 1 class.
4. Both the problems are mandatory.

Lagrange interpolation is a polynomial interpolation method which uses polynomials known as Lagrange Polynomials. This method works on a set of uniqe points, and results in a polynomial with degree one less than the number of data points - which passess through all the data points.

Your task is to write a function lagrange_polynomial() which takes in a list of data points (which are two element lists themselves), and another argument, and returns the value of the interpolating polynomial at the given argument.

lagrange_polynomial(datalist, xvalue)
# datalist is a list of points, like [[1,2],[4,9],[13,27]] etc.
# xvalue is value at which we need the interpolating polynomial to be evaluated.

An example workflow would be:

yval = lagrange_polynomial([[8, 6], [1, 3], [3, 8]], 4)
print(yval)

Output:

9.257142857142858

Cipher is an element of cryptography - which is essentially a set of rules to encrypt (and decrypt) a message (encrypted message). One example of such cipher is the ROT13 cipher, which is: shift each alphabet of the message forward by 13 counts. By this rule a becomes n, b becomes o and so on:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
│ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼
N O P Q R S T U V W X Y Z A B C D E F G H I J K L M

The cipher we discuss will have the number of shifts as a variable, rather than sticking to 13 like ROT-13 does (hence the name ROT-N).

Another simple example of cipher is the Atbash cipher, where the letters of the alphabet are reversed. The goal of this problem is to create a two functions inv_rotn_encrypt() and inv_rotn_decrypt() - one for encrypting, one for decrypting. The arguments for these functions is as follows:

inv_rotn_encrypt(message, shift)
# message is the message to be encrypted
# shift is the number of letters to shift
inv_rotn_decrypt(secret, shift)
# secret is the encrypted message to be decrypted to obtain original message
# shift is the number of shifts used to encrypt the original message

Encrypting process:

1. Shift the letters of the message by the number specified by shift argument. (note that the shift argument should always be an integer, as the concept of fractional shift is absurd).
2. Reverse the order of the letters obtained from previous step.
3. Return the encrypted message obtained thus.

Decrypting process:

1. Reverse the order of characters in the given encrypted message.
2. Shift backwards the string obtained from previous step by the specified shift number.
3. Return the decrypted message obtained thus.

An example workflow would be:

message = 'bobody'
print("Message: ", message)
secret = inv_rotn_encrypt(message, 17)
print("Encrypted message: ", secret)
message_again = inv_rotn_decrypt(secret, 17)
print("Decrypted message: ", message_again)

Output:

Message: bobody
Encrypted message: pufsfs
Decrypted message: bobody

1. Fork this repository.
2. Make a copy of template.ipynb inside submissions directory with your roll number e.g. ph19b003.ipynb (in lowercase).
3. Add responses (1 function in Problem 1, and 2 functions in Problem 2) in the jupyter notebook you copied.
4. Commit the changes, push to your account.
5. Create a pull request with title format rollnumber_name. It should be in all lowercase, and replace spaces in name with -.
6. And that's it!