Code No: 15071
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Set No - 1
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III B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 DESIGN AND ANALYSIS OF ALGORITHMS Common to Information Technology, Computer Science And Systems Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
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1. Formulate an algorithm for a spanning tree problem in terms of a sequence of set operations in which take G as an undirected graph; S as an undirected tree; V as the number of vertices; E as the number of edges; T as a set used to collect the edges of the final cost function for the graph P minimum spanning tree; C as the 1 G given by { eεE 1 C (e)} for the sub graph G = (V 1 , E 1 )of G. Use set VS for the vertex set of the trees in the spanning forest to write the minimum cost spanning tree algorithm. [16]
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2. What is interpolation? Explain Lagrange interpolation algorithm & Newtonian Interpolation algorithm. [16]
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3. Write an algorithm to search a binary search tree T for an identifier X. Assume that each node in T has three fields: LCHILD, DATA and RCHILD. What is the computing time of your algorithm? [16] 4. For the followin sequence of instructions UNION (1,2,2) UNION(2,3,3) . .
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UNION(n-1,n,n) FIND(1) FIND(2) .
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FIND(n)
(a) Write the tree after (n-1)UNION operations.
[8]
(b) Compute the cost of n FIND instructions.
[8]
5. Define multistage graphs problem. Name the algorithms, which solve the problem. Write one of the algorithms and explain its working with the help of an example. [16]
1
Code No: 15071
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Set No - 1
6. Present a program schema for a FIFO branch and bound search for a Least - Cost answer node. [16] 7. (a) Write an algorithm of Quick sort and explain in detail. (b) Suggest refinements to Merge sort to make it in-place.
[8+8]
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8. Write a procedure for postorder evaluation of a game tree using alpha beta pruning [16]. and deep alpha beta pruning and analyse for its time complexity.
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Code No: 15071
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Set No - 2
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III B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 DESIGN AND ANALYSIS OF ALGORITHMS Common to Information Technology, Computer Science And Systems Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
2. For the followin sequence of instructions UNION (1,2,2) . . UNION(n-1,n,n) FIND(2) . . FIND(n)
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FIND(1)
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UNION(2,3,3)
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1. Write an algorithm to search a binary search tree T for an identifier X. Assume that each node in T has three fields: LCHILD, DATA and RCHILD. What is the computing time of your algorithm? [16]
[8]
(b) Compute the cost of n FIND instructions.
[8]
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(a) Write the tree after (n-1)UNION operations.
3. Write a procedure for postorder evaluation of a game tree using alpha beta pruning and deep alpha beta pruning and analyse for its time complexity. [16].
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4. Define multistage graphs problem. Name the algorithms, which solve the problem. Write one of the algorithms and explain its working with the help of an example. [16]
5. What is interpolation? Explain Lagrange interpolation algorithm & Newtonian Interpolation algorithm. [16] 6. Present a program schema for a FIFO branch and bound search for a Least - Cost answer node. [16] 7. (a) Write an algorithm of Quick sort and explain in detail. (b) Suggest refinements to Merge sort to make it in-place. 3
[8+8]
Code No: 15071
NR
Set No - 2
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8. Formulate an algorithm for a spanning tree problem in terms of a sequence of set operations in which take G as an undirected graph; S as an undirected tree; V as the number of vertices; E as the number of edges; T as a set used to collect the edges of the final cost function for the graph P minimum spanning tree; C as the G given by { eεE 1 C (e)} for the sub graph G1 = (V 1 , E 1 )of G. Use set VS for the vertex set of the trees in the spanning forest to write the minimum cost spanning tree algorithm. [16]
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or
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4
Code No: 15071
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Set No - 3
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III B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 DESIGN AND ANALYSIS OF ALGORITHMS Common to Information Technology, Computer Science And Systems Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
ld .
1. What is interpolation? Explain Lagrange interpolation algorithm & Newtonian Interpolation algorithm. [16]
2. Write an algorithm to search a binary search tree T for an identifier X. Assume that each node in T has three fields: LCHILD, DATA and RCHILD. What is the computing time of your algorithm? [16]
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3. Formulate an algorithm for a spanning tree problem in terms of a sequence of set operations in which take G as an undirected graph; S as an undirected tree; V as the number of vertices; E as the number of edges; T as a set used to collect the edges of the final cost function for the graph P minimum spanning tree; C as the 1 G given by { eεE 1 C (e)} for the sub graph G = (V 1 , E 1 )of G. Use set VS for the vertex set of the trees in the spanning forest to write the minimum cost spanning tree algorithm. [16] 4. Present a program schema for a FIFO branch and bound search for a Least - Cost answer node. [16] 5. For the followin sequence of instructions UNION (1,2,2) UNION(2,3,3) .
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.
UNION(n-1,n,n) FIND(1)
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FIND(2) . .
FIND(n)
(a) Write the tree after (n-1)UNION operations.
[8]
(b) Compute the cost of n FIND instructions.
[8]
6. Write a procedure for postorder evaluation of a game tree using alpha beta pruning and deep alpha beta pruning and analyse for its time complexity. [16]. 5
Code No: 15071
NR
Set No - 3
7. (a) Write an algorithm of Quick sort and explain in detail. (b) Suggest refinements to Merge sort to make it in-place.
[8+8]
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8. Define multistage graphs problem. Name the algorithms, which solve the problem. Write one of the algorithms and explain its working with the help of an example. [16]
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or
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6
Code No: 15071
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Set No - 4
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III B.Tech I Semester Supplimentary Examinations,Nov/Dec 2009 DESIGN AND ANALYSIS OF ALGORITHMS Common to Information Technology, Computer Science And Systems Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
ld .
1. Write a procedure for postorder evaluation of a game tree using alpha beta pruning [16]. and deep alpha beta pruning and analyse for its time complexity.
2. Present a program schema for a FIFO branch and bound search for a Least - Cost answer node. [16] 3. (a) Write an algorithm of Quick sort and explain in detail.
[8+8]
or
(b) Suggest refinements to Merge sort to make it in-place.
4. Define multistage graphs problem. Name the algorithms, which solve the problem. Write one of the algorithms and explain its working with the help of an example. [16]
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5. What is interpolation? Explain Lagrange interpolation algorithm & Newtonian Interpolation algorithm. [16] 6. For the followin sequence of instructions UNION (1,2,2) UNION(2,3,3) . .
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UNION(n-1,n,n) FIND(1) FIND(2)
Aj
. .
FIND(n)
(a) Write the tree after (n-1)UNION operations.
[8]
(b) Compute the cost of n FIND instructions.
[8]
7. Formulate an algorithm for a spanning tree problem in terms of a sequence of set operations in which take G as an undirected graph; S as an undirected tree; V as the number of vertices; E as the number of edges; T as a set used to collect the 7
Code No: 15071
NR
Set No - 4
edges of the final cost function for the graph P minimum spanning tree; C as the 1 1 G given by { eεE C (e)} for the sub graph G = (V 1 , E 1 )of G. Use set VS for the vertex set of the trees in the spanning forest to write the minimum cost spanning tree algorithm. [16]
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8. Write an algorithm to search a binary search tree T for an identifier X. Assume that each node in T has three fields: LCHILD, DATA and RCHILD. What is the computing time of your algorithm? [16]
Aj
nt
uW
or
ld .
?????
8
