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1

A famous linguist named George Kingsley Zipf gave a law which relates to the frequency of occurrence of English words and is known as Zipf's law. This law says that he frequency of any word is inversely proportional to its rank in the frequency table. Thus the most frequent word will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc. (Use any resource to learn about Zipf's law).
Now write a program in C to do the following:
i) Read some text from a file(it should be a big file, you can download some of the free ebooks from internet). Break the read file into words.
ii) Now count the number of occurrences of each word you have read.
iii) Rank the words in order of their frequency.

Also do the following, there is no programming involved in this part:
Plot word frequency versus word rank(you can use excel here) and compare the results with Zipf's law.

2

Cryptography is a technique used to encode and decode documents. All modern web browsers have built in cryptographic schemes to allow safe transmission of data over the internet of sensitive details such as your passwords.
One of the oldest cryptographic system is known by the name Caesar shift cipher.  Here A is replaced by B, B is replaced by C,...Z is replaced by A and so on. This is a good starting point for learning cryptography.
Another very popular cryptographic technique is known as RSA. It used basic number theory and mathematics which you have already studied in first year and currently studying. Find any resources on the internet or approach any faculty member to learn the RSA technique, it is simple to understand.

Now write a C program to do the following:
i) Ask user a choice of simple cryptography or difficult cryptography. Read a file document where the technique is to be used (The document will contain simple English text).
ii) If choice is simple, simply implement the Caesar shift cipher on the contents of the document
iii) If choice is difficult implement the RSA using a very small key length

A popular topic in astronomy is '3-body Gravitational Problem.' It determines the motion of three bodies (say the Sun, Moon and Earth) in accordance with Newton's law of motion and Universal Gravitation.
Your task is to simulate a planetary system with atleast these three bodies (The Sun, Moon and Earth- you can always take more bodies if you want) in your computer screen (in simple 2-D). A very simple method can be as follows (you can always improve on it):

1) Select a small time gap
2) For all the three bodies specify their mass, velocity and the starting (initial) position.
3) Move the three bodies by an small amount depending on its velocity and the time gap chosen in Step 1.
4) Change the velocity of the three bodies by a small amount according to its acceleration and the time gap chosen in step 1.
5) Go back to Step 3.
(The above algorithm is indicative only, you can have your own steps as long as the main task is fulfilled)
You now print the positions of all the 3 bodies(Sun, Moon, Earth) in every time step. We can have a graphical display of how the system might evolve.Possible study help: Euler method of numerical integration can be helpful in this topic