22nd Feb, 2011

1. Inversions 								(25)
An inversion in an array of real numbers A is any pair (i,j) such that i<j and A[i]>A[j]. 
For e.g. in the array [25,7,51,3], the inversions would be (0,1),(0,3),(1,3) and (2,3). 
You have to write a program which takes 7 distinct non-negative integers from the user as array entries. 
The program then should print out the inversions in the given array-each separated by a tab character. 
If there are no inversions in the given array (i.e. array is sorted), your program should output "No inversions here!" 

2. Linked list 								(50)
A singly-linked list is a data structure that consists of a sequence of nodes each of which contains a reference (i.e., a link) to the next node in the sequence. 
In a list though only the head (i.e. the first element of the list) can be accessed, to access the k-th element of the list, one must follow the references. 
You have to implement a list with the following two operations:
	a) addElement - adds an element at the tail of the list 
	b) removeElement - removes an element at the head of list and shifts all the elements to the left and returns the removed element.
For e.g. in a list {4,3,9}, addElement(25) would result in {4,3,9,25} whereas removeElement() results in {3,9} with 3 as the new head.
Such a list can be modelled by intializing a global int array of size 10 and a counter to keep a count of number of elements in the list currently. 
To add a new element you will have to traverse (in a loop) all the elements of the array until you reach the tail and only then add it to the list.
While removing, you will have to shift accordingly. 
Protoypes:
	void addElement(int elemToAdd)
	int remeoveElement()
Create a list of 10 elements using addElement operation, print the resultant list. 
Then remove 5 elements out of it by using removeElement. You must print your list after every remove operation.
Extra Credit : 
Make the above program menu driven. eg . Display the following menu :
	1. addElement
	2. removeElement
	3. Exit 
Take input from user choosing the operation. Exit from program only if user chooses exit.

3. Euclid number							(25)
Primorial of n is defined as the product of first n prime numbers (first prime
number is 2). 
For example, P(0) = 1 (base case); 
             P(1) = 2; P(2) = 2 x 3 = 6
             P(5) = 2 x 3 x 5 x 7 x 11 = 2310.
This idea is a bit similar to that of factorial but here only successive primes are
multiplied.
Euclid numbers E(n) are positive integers of the form E(n) = P(n) + 1, where
P(n) is the primorial of n.
It is known that not all Euclid numbers are primes. You have to write a function which 
finds the nth Euclid number. Using this or otherwise write a function which prints
(from n=1) all the 
Euclid numbers till the first composite Euclid number is encountered. 
In your solution you may want to write the following two helper functions:
    int getPrimorial(int k) : returns the primorial of k.
    int isPrime(int k): reports if k is a prime or not.