DAA Marking Scheme
-
Upload
evan-robertson -
Category
Documents
-
view
213 -
download
0
Transcript of DAA Marking Scheme
-
8/2/2019 DAA Marking Scheme
1/4
JSPMs
Rajarshi Shahu College of Engineering
Tathawde, Pune 33
Department of Information Technology
2011-12 (Sem-II)
End Term Test Marking Scheme
Class: T.E Date: 16 /04/12
Subject: DAA Max Marks: 50
Time: 9.00 am to 10.30 am
Que1)a) State and explain graph coloring problem. Solve the same using backtracking
algorithm. 12
Ans.
Explaination of Backtracking technique: 02
Define Graph coloring problem 01
Figure 01
Algorithm for graph coloring 06
Explaination of algorithm. 02
b) Draw the state space tree for 4-queens problem using backtracking technique. 04
Ans.
Define 4-queens problem
Explicit and implicit constraints 01
State space tree 02
Final chess board configuration
OR
Que2)a) Solve the following instance of Sum of subset problem using suitable algorithm
design technique. n=7, (w1,w2,w3,w4, w5, w6)=(5,7,10,12,15,18,20) m=35. Show
the solutions using variable and fixed size tuple formulation. 10
Ans:
Explaination of suitable technique.(Backtracking technique/ Branch and bound ) 01
Define Sum of subset problem 01
Figure state space tree 01
variable and fixed size tuple formulation trees, 06
Answer nodes, solution nodes 01
-
8/2/2019 DAA Marking Scheme
2/4
b) Explain the following along with the examples: 06
1. Breadth first search
2. Depth first search
3. D-search
Ans. For each of the above, One mark for each definition and example.
Que3)Solve the following instance of job sequencing with deadlines problem using LC and
FIFO branch and bound solution. n=4, (p1, d1, t1)=(5, 1, 1) (p2, d2, t2)= (10, 3, 2)
(p3, d3, t3)=(6, 2, 1) (p4, d4, t4)=(3, 1, 1) 16
Ans.
Define Branch and bound 01
Define LC branch and bound technique 02
Define FIFO Branch and bound technique 02
State 0/1 knapsack problem , 01
Solution using LC BB technique. 05
Solution using FIFOBB technique 05
OR
Que4) Solve the following Travelling salesperson problem using branch and bound
technique. For n=5(Vertices Starting vertex=1)
Cost matrix= 0 20 30 10 11
15 0 16 04 02
03 05 0 02 04
19 06 18 0 03
16 04 07 16 0
Ans.
Define Branch and bound 01
Define LC branch and bound technique 02
Define FIFO Branch and bound technique 02
State Travelling salesperson problem ,
Steps to solve travelling sales personal problem 01
Solution using LC BB technique.
Reduced cost matrix 01
Table for each node 01*09=09 09
Que5) Write short note on the following (any three) 18
-
8/2/2019 DAA Marking Scheme
3/4
a) Deterministic v/s Non deterministic algorithm
Ans.
Definition of both deterministic algorithm and nondeterministic algorithm 02
Non deterministic algorithm functions: Choice(), failure(), Success(). 03
Eg.Nondeterministic search algorithm ( deterministic and nondeterministic
time complexity of search algorithm) 01
b) The classes of NP-hard and NP-Complete
Ans.
Definition of NP-hard and NP-complete problem 02
Examples 02
Fig. Showing relationship among P, NP, NP-hard, NP- complete relationship
02
c) Satisfiability problem
Ans.
Problem definition 02
Algorithm for Non deterministic satisfiability 02
Explanation 02
d) Vertex Cover Problem
Ans.
Problem definition 01
Define Vertex cover optimization and decision problem 01
Example fig. 01
Proof of CDP reduces to NCDP 03
OR
Que6) a) Explain the nondeterministic algorithm to sort n elements and for searching
of an element from given array. 10Ans.
Define nondeterministic algorithm 01
Explanation of Choice(), failure(), Success() 02
Non-deterministic Algorithm for searching 02
Non-deterministic Algorithm for sorting 03
Deterministic and non-deterministic time complexities for above problems 02
b) Explain how to prove that a problem is NP-hard. Show that CDP is NP-Hard. 08
Ans.
-
8/2/2019 DAA Marking Scheme
4/4
Steps to prove that a problem is NP-Hard 04
Proof of CDP is reducable to satisfiability problem 04