B.Tech. (I) - ICP-132 (2009)
				Assignment 3

Level 0
-------
1. Given natural numbers x and y construct a vector with numbers
   1^2, 2^2,...,(x-1)^2,(x+1)^2,(x+2)^2,...y^2. Find the average
   value.

2. Read 'n' numbers and print the median, mode and range.

3. Find maximum of 'n' strings.
	Input:
		3
		hello
		world
		yes
	Output:
		world

Level 1
-------
1. Numbers 1^2, 2^2,...,(x-1)^2,(x+1)^2,(x+2)^2,...y^2 are given. Find x
   and y using a function.
	Input:
		1
		4
		9
		25
		36
	Output:
		x=4
		y=6


2. Logistic function is given as X_n+1 = G.(X_n).(1-X_n), where X_n is
   the population in n'th year and X_n+1 is the population in (n+1)th and
   G is the growth constant. It is used in ecology to model population of
   predetor prey systems, where their numbers and growth constant show
   interesting dynamics. For G in range (1,3) population will reach a stable
   value while more complicated results appear from higher G. For a given X_0
   and G as initial values, find the average population of predetor between
   (n-50) and n years.

3. Given nxn matrices A and B, find A*B'

Level 2
-------

1. Insert x^2 into its correct place as mentioned in Level 1 prob 1.

2. Using Lagrange interpolation formula, find sin(49) using
   sin(10), sin(10), sin(20), sin(33), sin(45), sin(48), and sin(57). Using
   math library find the difference from the actual value.

3. Given a vector write a function to sort it in descending order.

Level 3
-------

(See "Introduction to Algorithms", by TH Corman, CE Leiserson, RL Rivest)

1. Implement a Queue on a vector v of integers. The functions to be built are:
   void enqueue(v, i), where i is the number to be enqueued
   int dequeue(v),
   int size(v),
   int front(v),

2. An nxn matrix (D) is given that shows the distance between any two cities.
   Using Floyd-Warshall algorithm, find the shortest between any two cities.

3. Task scheduling problem: Given n tasks and their completion times the 
   best way to process jobs is using a 'greedy technique' in such a way 
   that the tasks with fastest completion times are taken up earlier. 
   Given a set of n tasks and their completion times, print the order in 
   which tasks should be taken up.