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Current Final Term Papers Spring 2012 Date: 16July2012 to 27July2012
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Final Term Paper 2012
CS502 Fundamentals of Algorithms
Attempt by Umair Saulat
Dated 16 July 2012 time 2.30 Pm
North Nazimabad Campus, Karachi
40 MCQs…. 20 MCQs were from past paper Time 2Hours
12 Questions
Q No.1 Suppose you could prove that an NPcomplete problem can not be
solved in polynomial time. What would be the consequence?
Q No.2 Let the adjacency list representation of an undirected graph is given
below. Explain what general property of the list indicates that the graph
has an isolated vertex.
a à b à c à e
b à a à d
c à a à d à e à f
d à b à c à f
e à a à c à f
f à c à d à e
g
Q No.3 What are two cases for computing
Describe Dijkstra’s algorithm working?
Q No.4 The following adjacency matrix represents a graph that consists of four
vertices labeled 0, 1, 2 and 3. The entries in the matrix indicate edge
weights.

0 
1 
2 
3 
0 
0 
1 
0 
3 
1 
2 
0 
4 
0 
2 
0 
1 
0 
1 
3 
2 
0 
0 
0 
Q No.5 In the solution of edit distance technique, please describe two solution
given (i) MATHS (ii) ARTS
Q No.6 Variants of shortest path solution briefly?
Q No.7 Explain the following two basic cases according to FloydWarshall
Algorithm,
Q No.8 Explain the topological sort?
Q No.9 Consider if point pi is dominated by another point pj, we do not need to
use pi for eliminating other points. This follows from the fact that
dominance relation is transitive. If pj dominates pi and pi dominates ph
then pj also dominates ph; pi is not needed.
(Give the answer YES or NO)
I forget other questions
CS502_Final_Term_Paper_Spring_2012
Final Term Paper 2012
CS502 Fundamentals of Algorithms
Attempt by Umair Saulat
Dated 16 July 2012 time 2.30 Pm
North Nazimabad Campus, Karachi
40 MCQs…. 20 MCQs were from past paper Time 2Hours
12 Questions
Q No.1 Suppose you could prove that an NPcomplete problem can not be
solved in polynomial time. What would be the consequence?
Q No.2 Let the adjacency list representation of an undirected graph is given
below. Explain what general property of the list indicates that the graph
has an isolated vertex.
a à b à c à e
b à a à d
c à a à d à e à f
d à b à c à f
e à a à c à f
f à c à d à e
g
Q No.3 What are two cases for computing
Describe Dijkstra’s algorithm working?
Q No.4 The following adjacency matrix represents a graph that consists of four
vertices labeled 0, 1, 2 and 3. The entries in the matrix indicate edge
weights.

0 
1 
2 
3 
0 
0 
1 
0 
3 
1 
2 
0 
4 
0 
2 
0 
1 
0 
1 
3 
2 
0 
0 
0 
Q No.5 In the solution of edit distance technique, please describe two solution
given (i) MATHS (ii) ARTS
Q No.6 Variants of shortest path solution briefly?
Q No.7 Explain the following two basic cases according to FloydWarshall
Algorithm,
Q No.8 Explain the topological sort?
Q No.9 Consider if point pi is dominated by another point pj, we do not need to
use pi for eliminating other points. This follows from the fact that
dominance relation is transitive. If pj dominates pi and pi dominates ph
then pj also dominates ph; pi is not needed.
(Give the answer YES or NO)
I forget other questions
Cs502 Fundamentals of Algorithm spring 2012 final
Subjective
ii) What is the running time for Dijkstra’s algorithm?
aàbàcàe
bàaàd
càaàdàeàf
dàbàcàf
eàaàcàf
fàcàdàe
g
6. Consider the following two problems. In P1 we are given as input a set of n squares (specified by their corner points), and a number k. The problem is to determine whether there is any point in the plane that is covered by k or more squares.
In P2 we are given as input an n–vertex graph, and a number k; the problem is to determine whether there is a set of k mutually adjacent vertices. (E.g. for k = 3 we are just looking for a triangle in the graph.).
Obviously, the problems are both in NP. There exists a simple translation from P1 to P2: just make a graph vertex for each square, and add an edge between a pair of vertices if the corresponding two squares overlap.
If P1 is NPcomplete, would this translation imply that P2 is NPcomplete?
(Give your Answer in Yes or No) (3)
7. Consider the following code:
for (j=1; j<n;j++)
for (k=1; k<15;k++)
for(l=5; l<n; l++)
{
Do_something_constant();
}
What order is the execution of this code? (3)
8. How Dijkstra’s algorithm works? (3)
9. Explain the topological sort? (5)
10. You are given the task of laying down new railway lines which will connect all n cities.
Thus for any pair of cities, you will end up with track connecting them. Note that two routes may share the same track; track lay between Lahore and Islamabad can be used to travel in both directions. Your goal is to use the minimum amount of track. How would you achieve the goal now? (Note: consider the scenario carefully and name only the best suited algorithm)
11. Arrange the following functions such that which are time wise efficient appear first and so on. Where “n” is a binary number and where ever “log” is used it has base “2”.
O (log n √n); O (n/n); O (n/log n); O (n/√n); O (√n. √n) (5)
aik question yad nhe
Dua Zahra gud keep it up & keep sharing
1) In storage components problem what complete refers to?
2) How shortest path information is propagated in graph using BellFord algorithm?
3) How can we make it possible for an array of “n” elements that every element has equal probability of ‘1/n’ to be selected as pivot elements?
4) Define according to KrasKal” salgorithm
a) Create set(u)
b) Find set(u)
c) Union (u, v)
5) Write the general property of the matrix indicate that the graph is complete?
6) What is the recurrence relation for binary search and give some details for it and write asymptotic analysis at end?
7) Prove the Lemma:
Consider a diagraph G = ( V,E ) and any DFS forest for G. G has a cycle if and only if the DFS forest has a back edges ?
Difference b/w back ward and forward 2 marks
Polynomial time algorithm 2 marks
Describe Minimum Spanning Trees Problem with examples. 2 marks
Ak code given that us ka asymptotic notation bateni the. 3 marks
3n^2+7n12 ke lower or upper bound solve kana tha 3 marks
Code that fib memorization ka. 3 marks
Ak diagram given the us ma prims algorithm batna tha. 5 mark
Ak matrix given the us ka floyed warshal step batna tha. 5 marks
DFS ka itterative step batna tha 5 marks
Aoa Dear Students,
I hope u all are fine. Today i have given my cs502 paper u can say 80 paper even subjective was full from the past papers and majority MCQ's. I would request u all to kindly study past papers for best results.I am sharing my paper here attached via.
Remember me in ur prayers!
Best of Luck!
Thanks for sharing........May Allah Bless You
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