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BCS-042 : INTRODUCTION TO ALGORITHM DESIGN
(1.)Define notation Si (Big Omega). If f(n) = 2n3 + 3n2 +
1 and g(n) = 2n2 + 3, then
show f(n) = 52 (g(n)).
(2.)Arrange to the following growth rates in increasing
order :
0(n2), 0(311), 0(n), 0(log n)
(3.)Write linear search algorithm and explain its best
case, worst case and average case
time complexity
(4.)Given the following list of 8 integers, sort them
using insertion sort. Determine the
number of comparisons required by the algorithm. Also
find the total number of
assignment operations in this process.
10 7 12 6 8 15 25 11
(5.)Write any four
characteristics of greedy algorithm.
(6.)What is recurrence relation ?
Draw a recursion tree for recurrence
T(n) = 2T (n - 1) + 1.
(7.)Write binary search algorithm
and search the value 28 in the following list, using
binary search algorithm and show
the steps :
1, 7, 18, 27, 28, 30, 39
(8.)Define the following terms :
(i) Connected graph
(ii) Cycle in an undirected graph
(9.)Put the following classes of
algorithm in the increasing order of growth :
o(e), 0(n log2 n), O(log2 n),
0(n).
(10.)Write an algorithm to
compute a(n) by left to right binary exponentiation method and
illustrate through an example
(11.)Explain the following terms
with examples :
(a) Complete graph
(b) Combinatorial problems
(c) Branch and bound technique
(d) Loose bound
(e) Average case
(12.)What is a single source
shortest path problem ? What are the proposed solutions?
(13.)Define 0(Theta) Notation. By
using Basic definition of 0, show that
3x + 5 = 0(x)
(14.)Define 0 (big theta)
notation. By using a basic definition
show that
5n2 + 9n — 8 = (n2) .
(15.)Find the optimal solution to
the knapsack (fractional) problem n = 5 and m = 10, where n is the number of
objects and m is the capacity of knapsack.
Profit and weight of each object
are given below :
(Pi, P2, P3, P4, P5) = (10, 30,
35, 20, 40)
(W1, W2, W3, W4, W5) = (3, 5, 2,
6, 1).
(16.)What is recurrence relation
? Write a recurrence equation for any algorithm
which follows as to Divide and Conquer
strategy and explain it.
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