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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

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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

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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.

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Steps to prove that a problem is NP-Hard 04

Proof of CDP is reducable to satisfiability problem 04