R05

Code No: R05321904

Set No. 2

1. (a) Explain the strassen’s matrix multiplication.

[8+8]

ld .

(b) Write deletion algorithm of Binary search tree.

in

III B.Tech II Semester Supplementary Examinations,May 2010 DESIGN AND ANALYSIS OF ALGORITHMS Electronics And Computer Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

2. Solve the TSP problem having the following cost matrix using branch and bound technique. [16]

B 5 X 2 6

C 2 1 X 8

D 3 5 3 X



  

or

A B C D

 A X  4   4 7

3. (a) Write the non recursive algorithm for finding the Fibonacci sequence and derive its time complexity.

uW

(b) Show that n3 logn is w(n3 ).

[10+6]

4. (a) Write a pseudocode for finding the strongly connected components of directed graph. Also analyze its time complexity. (b) Explain the Inorder traversal of a tree with an example.

[8+8]

5. (a) Explain about cook’s theorem.

(b) Explain the strategy to prove that a problem is NP hard.

[8+8]

nt

6. (a) Explain the applications of single source shortest path problem. (b) Prove that Kruskal’s algorithm generates a minimum-cost spanning tree for every connected undirected graph G. (c) Write an algorithm of Greedy Knapsack.

[5+6+5]

Aj

7. Write a pseudocode of the dynamic programming algorithm for solving Optimal Binary search tree and determine its time and space efficiencies. [16]

8. (a) Let w = {5, 7, 10, 12, 15, 18, 20} and m=35. Find all possible subsets of w that sum to m. Draw the portion of the state space tree that is generated.

(b) Compare and Contrast Brute force approach and Backtracking. ?????

1

[10+6]

R05

Code No: R05321904

Set No. 4

in

III B.Tech II Semester Supplementary Examinations,May 2010 DESIGN AND ANALYSIS OF ALGORITHMS Electronics And Computer Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Write a pseudocode for finding the strongly connected components of directed graph. Also analyze its time complexity.

[8+8]

ld .

(b) Explain the Inorder traversal of a tree with an example.

2. (a) Explain the applications of single source shortest path problem.

(b) Prove that Kruskal’s algorithm generates a minimum-cost spanning tree for every connected undirected graph G.

or

(c) Write an algorithm of Greedy Knapsack.

[5+6+5]

3. (a) Explain about cook’s theorem.

(b) Explain the strategy to prove that a problem is NP hard.

[8+8]

A B C D

 A X  4   4 7

uW

4. Solve the TSP problem having the following cost matrix using branch and bound technique. [16] B 5 X 2 6

C 2 1 X 8

D 3 5 3 X



  

5. (a) Let w = {5, 7, 10, 12, 15, 18, 20} and m=35. Find all possible subsets of w that sum to m. Draw the portion of the state space tree that is generated.

nt

(b) Compare and Contrast Brute force approach and Backtracking.

[10+6]

6. (a) Write the non recursive algorithm for finding the Fibonacci sequence and derive its time complexity.

(b) Show that n3 logn is w(n3 ).

Aj

[10+6]

7. Write a pseudocode of the dynamic programming algorithm for solving Optimal Binary search tree and determine its time and space efficiencies. [16]

8. (a) Explain the strassen’s matrix multiplication. (b) Write deletion algorithm of Binary search tree. ?????

2

[8+8]

R05

Code No: R05321904

Set No. 1

in

III B.Tech II Semester Supplementary Examinations,May 2010 DESIGN AND ANALYSIS OF ALGORITHMS Electronics And Computer Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Let w = {5, 7, 10, 12, 15, 18, 20} and m=35. Find all possible subsets of w that sum to m. Draw the portion of the state space tree that is generated. [10+6]

ld .

(b) Compare and Contrast Brute force approach and Backtracking.

2. (a) Explain the applications of single source shortest path problem.

(b) Prove that Kruskal’s algorithm generates a minimum-cost spanning tree for every connected undirected graph G.

or

(c) Write an algorithm of Greedy Knapsack.

[5+6+5]

3. (a) Explain the strassen’s matrix multiplication.

(b) Write deletion algorithm of Binary search tree.

[8+8]

uW

4. (a) Write a pseudocode for finding the strongly connected components of directed graph. Also analyze its time complexity. (b) Explain the Inorder traversal of a tree with an example.

[8+8]

5. Write a pseudocode of the dynamic programming algorithm for solving Optimal Binary search tree and determine its time and space efficiencies. [16] 6. Solve the TSP problem having the following cost matrix using branch and bound technique. [16] B 5 X 2 6

C 2 1 X 8

D 3 5 3 X



nt

A B C D

 A X  4   4 7

  

Aj

7. (a) Write the non recursive algorithm for finding the Fibonacci sequence and derive its time complexity. (b) Show that n3 logn is w(n3 ).

[10+6]

8. (a) Explain about cook’s theorem. (b) Explain the strategy to prove that a problem is NP hard. ?????

3

[8+8]

R05

Code No: R05321904

Set No. 3

in

III B.Tech II Semester Supplementary Examinations,May 2010 DESIGN AND ANALYSIS OF ALGORITHMS Electronics And Computer Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. Write a pseudocode of the dynamic programming algorithm for solving Optimal Binary search tree and determine its time and space efficiencies. [16]

B 5 X 2 6

C 2 1 X 8

D 3 5 3 X

   

or

 A X A  B  4 C  4 7 D

ld .

2. Solve the TSP problem having the following cost matrix using branch and bound technique. [16]

3. (a) Write the non recursive algorithm for finding the Fibonacci sequence and derive its time complexity.

uW

(b) Show that n3 logn is w(n3 ).

[10+6]

4. (a) Let w = {5, 7, 10, 12, 15, 18, 20} and m=35. Find all possible subsets of w that sum to m. Draw the portion of the state space tree that is generated.

(b) Compare and Contrast Brute force approach and Backtracking.

[10+6]

5. (a) Explain the applications of single source shortest path problem. (b) Prove that Kruskal’s algorithm generates a minimum-cost spanning tree for every connected undirected graph G.

nt

(c) Write an algorithm of Greedy Knapsack.

[5+6+5]

6. (a) Explain the strassen’s matrix multiplication. (b) Write deletion algorithm of Binary search tree.

[8+8]

Aj

7. (a) Write a pseudocode for finding the strongly connected components of directed graph. Also analyze its time complexity. (b) Explain the Inorder traversal of a tree with an example.

[8+8]

8. (a) Explain about cook’s theorem. (b) Explain the strategy to prove that a problem is NP hard. ?????

4

[8+8]

R05 Set No. 2

(b) Write deletion algorithm of Binary search tree. [8+8] · 2. Solve the TSP ... (b) Prove that Kruskal's algorithm generates a minimum-cost spanning tree for.
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