**Virtual University Of Pakistan**Student Cafe: 02/05/13

Tuesday, February 5, 2013

.::VULMSIT::.eNoxel.com CS502 QUIZ NO.4 FEB 04, 2013

CS502 - Fundamentals of Algorithms

Quiz No.4 Dated FEB 05, 2013

In in-place sorting algorithm is one that uses arrays for storage :
An additional array

No additional array (Right Answer)

Both of above may be true according to algorithm

More than 3 arrays of one dimension.

The running time of quick sort depends heavily on the selection of:
No of inputs

Arrangement of elements in array

Size o elements

Pivot element (Right Answer)

In stable sorting algorithm

One array is used

In which duplicating elements are not handled.

More then one arrays are required.

Duplicating elements remain in same relative position after sorting. (Right Answer)

Which sorting algorithm is faster :

O(n^2)

O(nlogn)

O(n+k) (Right Answer)

O(n^3)

In Quick sort algorithm, constants hidden in T(n lg n) are
Large

Medium

Not known

Small (Right Answer)

Quick sort is based on divide and conquer paradigm; we divide the problem on base of pivot element and:
There is explicit combine process as well to conquer the solutin. (Right Answer)

No work is needed to combine the sub-arrays, the array is already sorted

Merging the subarrays

None of above.

There is relationship between number of back edges and number of cycles in DFS

Select correct option:

Both are equal.

Cycles are half of back edges.

Cycles are one fourth of back edges.

There is no relationship between back edges and number of cycle (Right Answer)

You have an adjacency list for G, what is the time complexity to compute Graph transpose G^T

Select correct option:

(V+E) (Right Answer)

V.E

Dijkstra's algorithm :

Select correct option:

Has greedy approach to find all shortest paths

Has both greedy and Dynamic approach to find all shortest paths

Has greedy approach to compute single source shortest paths to all other vertices (page 154)

Has both greedy and dynamic approach to compute single source shortest paths to all other vertices.

What is the time complexity to extract a vertex from the priority queue in Prim's algorithm?

Select correct option:

O (log E)

? (V)

? (V+E)

O (log V) (page #152)

Which is true statement in the following.

Kruskal algorithm is multiple source technique for finding MST.

Kruskal's algorithm is used to find minimum spanning tree of a graph, time complexity of this algorithm is O(EV)

Both of above

=>Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best tree edge) when the graph has relatively few edges.

Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best tree edge) when the graph has relatively few edges.

True (Right Answer)

False

What general property of the list indicates that the graph has an isolated vertex?

Select correct option:

There is Null pointer at the end of list.

The Isolated vertex is not handled in list. (not Sure)

Only one value is entered in the list.

There is at least one null list.

Which statement is true?

Select correct option:

If a dynamic-programming problem satisfies the optimal-substructure property, then a locally optimal solution is globally optimal.

If a greedy choice property satisfies the optimal-substructure property, then a locally optimal solution is globally optimal.

Both of above Right Answer)

None of above

A dense undirected graph is:

Select correct option:

A graph in which E = O(V^2) (Right Answer)

A graph in which E = O(V)

A graph in which E = O(log V)

All items above may be used to characterize a dense undirected graph

Which is true statement.

Select correct option:

Breadth first search is shortest path algorithm that works on un-weighted graphs (Right Answer)

Depth first search is shortest path algorithm that works on un-weighted graphs.

Both of above are true.

None of above are true.

What algorithm technique is used in the implementation of Kruskal solution for the MST?

Greedy Technique (page #142)

Divide-and-Conquer Technique

Dynamic Programming Technique

The algorithm combines more than one of the above techniques

A digraph is strongly connected under what condition?

A digraph is strongly connected if for every pair of vertices u, v e V, u can reach v .

A digraph is strongly connected if for every pair of vertices u, v e V, u can reach v and vice versa. (Page #135)

A digraph is strongly connected if for at least one pair of vertex u, v e V, u can reach v and vice versa.

A digraph is strongly connected if at least one third pair of vertices u, v e V, u can reach v and vice versa.

The relationship between number of back edges and number of cycles in DFS is,

Both are equal

Back edges are half of cycles

Back edges are one quarter of cycles

There is no relationship between no. of edges and cycles (p131)

Question # 2 of 10 ( Start time: 10:35:36 PM ) Total Marks: 1

Suppose that a graph G = (V,E) is implemented using adjacency lists. What is the complexity of a breadth-first traversal of G?

Select correct option:

O(|V |^2)

O(|V | |E|)

O(|V |^2|E|)

O(|V | + |E|) pg 116

Question # 4 of 10 ( Start time: 10:37:30 PM ) Total Marks: 1

Forward edge is:

Select correct option:

(u, v) where u is a proper descendent of v in the tree.

(u, v) where v is a proper descendent of u in the tree. Pg 129

(u, v) where v is a proper ancesstor of u in the tree.

(u, v) where u is a proper ancesstor of v in the tree.

Question # 5 of 10 ( Start time: 10:37:58 PM ) Total Marks: 1

Using ASCII standard the string "abacdaacacwe" will be encoded with __________ bits

Select correct option:

128

96 pg 101 12*8=96

120

Question # 7 of 10 ( Start time: 10:38:40 PM ) Total Marks: 1

If you find yourself in maze the better traversel approach will be :

Select correct option:

BFS

BFS and DFS both are valid (pg 119)

Level order

DFS

Question # 8

In digraph G=(V,E) ;G has cycle if and only if

Select correct option:

The DFS forest has forward edge.

The DFS forest has back edge (pg 131)

The DFS forest has both back and forward edge

BFS forest has forward edge

Question # 9

What is generally true of Adjacency List and Adjacency Matrix representations of graphs?

Select correct option:

Lists require less space than matrices but take longer to find the weight of an edge (v1,v2)

Lists require less space than matrices and they are faster to find the weight of an edge (v1, v2) (pg 116)

Lists require more space than matrices and they take longer to find the weight of an edge (v1, v2)

Lists require more space than matrices but are faster to find the weight of an edge

(v1, v2)

Question # 10

Back edge is:

Select correct option:

(u, v) where v is an ancestor of u in the tree. (Pg 128)

(u,v) where u is an ancesstor of v in the tree.

(u, v) where v is an predcessor of u in the tree.

None of above

=================

My 3^rd Quiz

http://cs-mcqs.blogspot.com/2012/06/data-structures-algorithms-multiple.html

FINALTERM EXAMINATION

Question No: 2

Although it requires more complicated data structures, Prim's algorithm for a minimum spanning tree is better than Kruskal's when the graph has a large number of vertices.

► True ► False

Question No: 3

If a problem is in NP, it must also be in P.

► True ► False ► unknown

Question No: 5

If a graph has v vertices and e edges then to obtain a spanning tree we have to delete

► v edges. ► v – e + 5 edges ► v + e edges. ► None of these

Question No: 6

Maximum number of vertices in a Directed Graph may be |V²|

► True ► False

Question No: 7

The Huffman algorithm finds a (n) _____________ solution.

► Optimal ► Non-optimal ► Exponential ► Polynomial

Question No: 8

The Huffman algorithm finds an exponential solution ► True ► False

Question No: 9

The Huffman algorithm finds a polynomial solution ► True ► False

Question No: 10

The greedy part of the Huffman encoding algorithm is to first find two nodes with larger frequency. ► True ► False

Question No: 11

The codeword assigned to characters by the Huffman algorithm have the property that no codeword is the postfix of any other. ► True ► False

Question No: 12

Huffman algorithm uses a greedy approach to generate a postfix code T that minimizes the expected length B (T) of the encoded string. ► True ► False

Question No: 13

Shortest path problems can be solved efficiently by modeling the road map as a graph.

► True ► False

Question No: 14

Dijkestra's single source shortest path algorithm works if all edges weights are non-negative and there are negative cost cycles. ► True ► False

Question No: 15

Bellman-Ford allows negative weights edges and negative cost cycles ► True ► False

Question No: 16

The term "coloring" came form the original application which was in architectural design. ► True ► False

Question No: 17

In the clique cover problem, for two vertices to be in the same group, they must be adjacent to each other. ► True ► False

Question No: 18

Dijkstra's algorithm is operates by maintaining a subset of vertices ► True ► False

Question No: 19

The difference between Prim's algorithm and Dijkstra's algorithm is that Dijkstra's algorithm uses a different key. ► True ► False

Question No: 21

We do sorting to,

► keep elements in random positions ► keep the algorithm run in linear order

► keep the algorithm run in (log n) order

► keep elements in increasing or decreasing order

Question No: 22

After partitioning array in Quick sort, pivot is placed in a position such that

► Values smaller than pivot are on left and larger than pivot are on right

► Values larger than pivot are on left and smaller than pivot are on right

► Pivot is the first element of array Pivot is the last element of array

Question No: 23

Merge sort is stable sort, but not an in-place algorithm ► True (p#54) ► False

Question No: 24

In counting sort, once we know the ranks, we simply _________ numbers to their final positions in an output array.

► Delete ► copy (p#57) ► Mark ► arrange

Question No: 25

Dynamic programming algorithms need to store the results of intermediate sub-problems. ► True p#75) ► False

Question No: 26

A p × q matrix A can be multiplied with a q × r matrix B. The result will be a p × r matrix C. There are (p . r) total entries in C and each takes _________ to compute.

► O (q) (p= 84) ► O (1) ► O (n²) ► O (n³)

FINALTERM EXAMINATION

Question No: 2

Which of the following is calculated with bigo notation?

Lower bounds Upper bounds

Both upper and lower bound Medium bounds

Question No: 3

Merge sort makes two recursive calls. Which statement is true after these recursive calls

finish, but before the merge step?

The array elements form a heap

Elements in each half of the array are sorted amongst themselves

Elements in the first half of the array are less than or equal to elements in the second half of the array

None of the above

Question No: 4

Who invented Quick sort procedure?

Hoare Sedgewick Mellroy Coreman

Question No: 6

Consider the following Huffman Tree

The binary code for the string TEA is

10 00 010

011 00 010

10 00 110

11 10 110

Question No: 7

If a graph has v vertices and e edges then to obtain a spanning tree we have to delete v edges.

v e + 5 edges v + e edges. None of these

Question No: 8

Can an adjacency matrix for a directed graph ever not be square in shape?

Yes No

Question No: 9

One of the clever aspects of heaps is that they can be stored in arrays without using any

______Pointers (p #40) constants variables functions

Question No: 10

Merge sort requires extra array storage, True p #54) False

Mergesort is a stable algorithm but not an in-place algorithm. It requires extra array storage.

Question No: 11

Non-optimal or greedy algorithm for money change takes____________

O(k) (p#99) O(kN) O(2k) O(N)

Question No: 12

The Huffman codes provide a method of encoding data inefficiently when coded using

ASCII standard. True Falase (p# 99

The Huffman codes provide a method of encoding data efficiently.

Question No: 13

Using ASCII standard the string abacdaacac will be encoded with __________ bits.

80 (p# 99 160 320 100

Consider the string " abacdaacac". if the string is coded with ASCII codes, the message length would be10 × 8 = 80 bits.

Question No: 14

Using ASCII standard the string abacdaacac will be encoded with 160 bits.

True False (p# 99)

Question No: 15

Using ASCII standard the string abacdaacac will be encoded with 320 bits.

True False (p# 99)

Question No: 16

Using ASCII standard the string abacdaacac will be encoded with 100 bits.

True False (p# 99)

Question No: 17

Using ASCII standard the string abacdaacac will be encoded with 32 bytes

True False (p# 99)

Question No: 18

The greedy part of the Huffman encoding algorithm is to first find two nodes with

smallest frequency.

True (p# 100) False

Question No: 19

The greedy part of the Huffman encoding algorithm is to first find two nodes with

character frequency

True False (p# 100)

Question No: 20

Huffman algorithm uses a greedy approach to generate an antefix code T that minimizes

the expected length B (T) of the encoded string.

True (p# 102) False

Question No: 21

Depth first search is shortest path algorithm that works on un-weighted graphs.

True False (p# 153)

The breadth-first-search algorithm we discussed earlier is a shortest-path algorithm that works on un-weighted graphs

Question No: 22

Dijkestra s single source shortest path algorithm works if all edges weights are nonnegative and there are no negative cost cycles.

True (p# 159) False

Question No: 23

Dijkestra s single source shortest path algorithm works if all edges weights are negative

and there are no negative cost cycles.

True (p# 159) False

Question No: 24

Floyd-Warshall algorithm is a dynamic programming algorithm; the genius of the

algorithm is in the clever recursive formulation of the shortest path problem.

True (p# 162) Flase

Question No: 25

Floyd-Warshall algorithm, as in the case with DP algorithms, we avoid recursive

evaluation by generating a table for

ij d

True

Flase

the case with DP algorithms, we will avoid recursive evaluation by generating a table for d(k)ij

Question No: 26

The term coloring came from the original application which was in map drawing.

True (p# 173) False

Question No: 27

In the clique cover problem, for two vertices to be in the same group, they must be_________each other.

Apart from Far from Near to Adjacent to ( P# 176)

Question No: 28

In the clique cover problem, for two vertices to be in the same group, they must be apart

from each other.

True False ( P# 176)

Question No: 29

The difference between Prims algorithm and Dijkstra s algorithm is that Dijkstra s

algorithm uses a different key.

True ( P # 156) not sure False

Question No: 30

The difference between Prim s algorithm and Dijkstra s algorithm is that Dijkstra s algorithm uses a same key.

True False ( P # 156) not sure

Quiz no# 4 06-07-2012 solved by umair sid 100%

What algorithm technique is used in the implementation of kruskal solution for the MST?

Greedy Technique page #142

in drsigne G=(V,E) ;G has cycle if and only if

The DFS forest has back edge page # 131

Question # 9 of 10

Cross edge is :

(u, v) where u and v are not ancestor of one another

(u, v) where u is ancesstor of v and v is not descendent of u.

(u, v) where u and v are not ancestor or descendent of one another pg 129

(u, v) where u and v are either ancestor or descendent of one another.

Forword edge is :

(u,v) where v ia a proper decendent of u in the tree. Page # 129

You have an adjective list for G, what is the time complexity to computer graph transpose G^T.?

(V + E ) PAGE # 138

Given an adjacency list for G, it is possible to compute G ^T in Θ(V + E) time.

It takes O(log V) to extract a vertex from the priority queue.

There is relationship between number of back edges and number of cycles in DFS

There is no relationship between back edges and number of cycles

Which is true statement:

Breadth first search is shortest path algorithm that works on un-weighted graphs

Depth first search is shortest path algorithm that works on un-weighted graphs.

Both of above are true.

Overall time for Kruskal is

Θ(E log E) = Θ(E log V) if the graph is sparse. P-149

True

Question No: 1

An optimization problem is one in which you want to find,

► Not a solution

► An algorithm

► Good solution

► The best solution

Question No: 2

Although it requires more complicated data structures, Prim's algorithm for a minimum

spanning tree is better than Kruskal's when the graph has a large number of vertices.

► True

► False

Question No: 3

If a problem is in NP, it must also be in P.

► True

► False

► unknown

Question No: 5

If a graph has v vertices and e edges then to obtain a spanning tree we have to delete

► v edges.

► v – e + 5 edges

► v + e edges.

► None of these

Question No: 6

Maximum number of vertices in a Directed Graph may be |V2|

► True

► False

Question No: 7

The Huffman algorithm finds a (n) _____________ solution.

► Optimal

► Non-optimal

► Exponential

► Polynomial

Question No: 8

The Huffman algorithm finds an exponential solution ► True ► False

Question No: 9

The Huffman algorithm finds a polynomial solution ► True ► False

Question No: 10

The greedy part of the Huffman encoding algorithm is to first find two nodes with larger

frequency. ► True ► False

Question No: 11

The codeword assigned to characters by the Huffman algorithm have the property that no

codeword is the postfix of any other. ► True ► False

Question No: 12

Huffman algorithm uses a greedy approach to generate a postfix code T that minimizes

the expected length B (T) of the encoded string. ► True ► False

Question No: 13

Shortest path problems can be solved efficiently by modeling the road map as a graph.

► True ► False

Question No: 14

Dijkestra's single source shortest path algorithm works if all edges weights are non-

negative and there are negative cost cycles. ► True ► False

Question No: 15

Bellman-Ford allows negative weights edges and negative cost cycles.

► True ► False

Question No: 16

The term "coloring" came form the original application which was in architectural

design. ► True ► False

Question No: 17

In the clique cover problem, for two vertices to be in the same group, they must be

adjacent to each other. ► True ► False

Question No: 18

Dijkstra's algorithm is operates by maintaining a subset of vertices ► True ► False

Question No: 19

The difference between Prim's algorithm and Dijkstra's algorithm is that Dijkstra's

algorithm uses a different key. ► True ► False

Question No: 21

We do sorting to,

► keep elements in random positions

► keep the algorithm run in linear order

► keep the algorithm run in (log n) order

► keep elements in increasing or decreasing order

►Question No: 22

After partitioning array in Quick sort, pivot is placed in a position such that

► Values smaller than pivot are on left and larger than pivot are on right

► Values larger than pivot are on left and smaller than pivot are on right

► Pivot is the first element of array

► Pivot is the last element of array

Question No: 23

Merge sort is stable sort, but not an in-place algorithm ► True ► False

Question No: 24

In counting sort, once we know the ranks, we simply _________ numbers to their final

positions in an output array.

► Delete ► copy ► Mark ► arrange

Question No: 25

Dynamic programming algorithms need to store the results of intermediate sub-

problems. ► True ► False

Using ASCII standard the string abacdaacac will be encoded with __________ bits.

80 160 320 100

Using ASCII standard the string abacdaacac will be encoded with 160 bits.

True False

Using ASCII standard the string abacdaacac will be encoded with 320 bits.

True False

Using ASCII standard the string abacdaacac will be encoded with 100 bits.

True False

The Huffman algorithm finds a (n) _____________ solution.

► Optimal ► Non-optimal ► Exponential ► Polynomial

Huffman algorithm uses a greedy approach to generate a postfix code T that minimizes

the expected length B (T) of the encoded string.

► True

► False

2: Which statement is true?

• If a dynamic-programming problem satisfies the optimal-substructure property,

then a locally optimal solution is globally optimal.

• If a greedy choice property satisfies the optimal-substructure property, then a

locally optimal solution is globally optimal.

• both of above

• none of above

5: What general property of the list indicates that the graph has an isolated vertex?

• There is Null pointer at the end of list.

• The Isolated vertex is not handled in list.

• Only one value is entered in the list.

• There is at least one null list.

6: Which is true statement.

• Breadth first search is shortest path algorithm that works on un-weighted graphs.

• Depth first search is shortest path algorithm that works on un-weighted graphs.

• Both of above are true.

• None of above are true.

11: Using ASCII standard the string "abacdaacacwe" will be encoded with __________

bits

• 64

• 128

• 96

• 120

13: the analysis of selection algorithm shows the total running time is indeed------------in

• arithmetic

• geometric

• linear

• orthogonal

14: back edge is

(1) In Prim's algorithm, the additional information maintained by the algorithm is the

length of the shortest edge from vertex v to points already in the tree.

A) TRUE

B) FALSE

C) UNKNOWN

(2) Although it requires more complicated data structures, Prim's algorithm for a

minimum spanning tree is better than Kruskal's when the graph has a large number of

vertices.

A) TRUE. B) FALSE C: UNKNOWN

(3) If a problem is NP-complete, it must also be in NP.

A) TRUE. B) FALSE C) UNKNOWN

(4) Which statement is true

(I) The running time of Bellman-Ford algorithm is T (VE)

(II) Both Dijkstra's algorithm and Bellman-Ford are based on performing repeated

relaxations

(III) The 0-1 knapsack problem is hard to solve

• Only I • Only III • Both I and III • All of these

5) Which of the following arrays represent descending (max) heaps?

I. [10,7,7,2,4,6] II. [10,7,6,2,4,7]

III. [10,6,7,2,4,6] IV. [6,6,7,2,4,10]

• Only II • Only IV • Both II and IV • Both I and III

6. Which of the following statement(s) is/are correct?

(a) O(n log n + n2) = O(n2). (b) O(n log n + n2) = O(n2 log 2n)

(e) O(c) = O(1) where c is a constant.

• Only (a) & (e) • Both (c) and (e)

7. Which of the shortest path algorithms would be most appropriate for finding paths in

the graph with negative edge weights and cycles?

I.Dijkstra's Algorithm

II. Bellman-Ford Algorithm

III. Floyd Warshall Algorithm

• Only II • Only III • Both II & III

9. Suppose we have two problems A and B .Problem A is polynomial-time reducible and

problem B is NP-complete. If we reduce problem A into B then problem A becomes NP-

complete • Yes • No

11. The recurrence relation of Tower of Hanoi is given below

? 1 if n =1

T n =?

-133( )

2 (T n- +1) 1if n>1

In order to move a tower of 6 rings from one peg to another, how many moves are

required?

• 15 • 7 • 63 • 32

12. Edge (u, v) is a forward edge if

• u is a proper descendant of v in the tree

• v is a proper descendant of u in the tree

• None of these

13. Is 22n= O?

2n -26? ?

14. If, in a DFS forest of digraph G = (V, E), f[u] = f[v] for an edge (u, v) ? E then the

edge is called

• Back edge • Forward edge • Cross Edge • Tree Edge • None of these

16. Best and worst case times of an algorithm may be same.

• True • False

17. Can an adjacency matrix for a directed graph ever not be square in shape?

• Yes • No

1. In which order we can sort?

• increasing order only • decreasing order only

• increasing order or decreasing order • both at the same time

2. heap is a left-complete binary tree that conforms to the ___________

• increasing order only • decreasing order only • heap order • (log n) order

3. In the analysis of Selection algorithm, we make a number of passes, in fact it could be

as many as,

• T(n) • T(n / 2) • log n • n / 2 + n / 4

4. How much time merge sort takes for an array of numbers?

• T(n^2) • T(n) • T( log n) • T(n log n)

5. One of the clever aspects of heaps is that they can be stored in arrays without using any

_______________.

• pointers • constants • variables • functions

6. the analysis of Selection algorithm, we eliminate a constant fraction of the array with

each phase; we get the convergent _______________ series in the analysis

• linear • arithmetic • geometric • exponent

7:. Sieve Technique applies to problems where we are interested in finding a single item

from a larger set of _____________

• n items • phases • pointers • constant

8. The sieve technique works in ___________ as follows

• phases • numbers • integers • routines

9. For the heap sort, access to nodes involves simple _______________ operations.

• arithmetic • binary • algebraic • logarithmic

10. The analysis of Selection algorithm shows the total running time is indeed

________in n,

• arithmetic • geometric • linear • orthogonal

11. Divide-and-conquer as breaking the problem into a small number of

• pivot • Sieve • smaller sub problems • Selection

12. Slow sorting algorithms run in,

• T(n^2) • T(n) • T( log n) • T(n log n)

13. A heap is a left-complete binary tree that conforms to the

• increasing order only • decreasing order only • heap order • (log n) order

14. For the heap sort we store the tree nodes in

• level-order traversal • in-order traversal • pre-order traversal • post-order traversal

15. The reason for introducing Sieve Technique algorithm is that it illustrates a very

important special case of,

• divide-and-conquer, • decrease and conquer • greedy nature • 2-dimension Maxima

16. We do sorting to, Select correct option:

• keep elements in random positions • keep the algorithm run in linear order

• keep the algorithm run in (log n) order • keep elements in increasing or decreasing order

17. Sorting is one of the few problems where provable ________ bonds exits on how fa

we can sort, Select correct option:

• upper • lower • average • log n

For the heap sort we store the tree nodes in Select correct option:

• level-order traversal • in-order traversal • pre-order traversal • post-order traversal

20: In Sieve Technique we do not know which item is of interest Select correct option:

• True • False

21: Slow sorting algorithms run in,

• T(n^2) • T(n) • T( log n) • T(n log n)

22: Divide-and-conquer as breaking the problem into a small number of

• pivot • Sieve • smaller sub problems • Selection

23: For the sieve technique we solve the problem,

• recursively • mathematically • precisely • accurately

24: we do sorting to,

• keep elements in random positions • keep the algorithm run in linear order

• keep the algorithm run in (log n) order • keep elements in increasing or decreasing order

25: The reason for introducing Sieve Technique algorithm is that it illustrates a very

important special case of,

• divide-and-conquer • decrease and conquer • greedy nature • 2-dimension Maxima

26: In Sieve Technique we do not know which item is of interest

• true • false

27: In the analysis of

Selection algorithm, we make a number of passes, in fact it could be as many as,

• T(n) • T(n / 2) • log n • n / 2 + n / 4

28: Divide-and-conquer as breaking the problem into a small number of

• pivot • Sieve • smaller sub problems • Selection

29: A heap is a left-complete binary tree that conforms to the ___________

• increasing order only • decreasing order only • heap order • (log n) order

30: Slow sorting algorithms run in,

• T(n^2) • T(n) • T( log n) • T(n log n)

31: One of the clever aspects of heaps is that they can be stored in arrays without using

any _______________.

• pointers • constants • variables • functions

32: Sorting is one of the few problems where provable ________ bonds exits on how fast

we can sort, • upper • lower • average • log n

33: For the sieve technique we solve the problem,

• mathematically • precisely • accurately • recursively

34: Sieve Technique can be applied to selection problem?

• True • False

37: Heaps can be stored in arrays without using any pointers; this is due to the

____________ nature of the binary tree,

• left-complete • right-complete • tree nodes • tree leaves

38: How many elements do we eliminate in each time for the Analysis of Selection

algorithm?

• n / 2 elements • (n / 2) + n elements • n / 4 elements • 2 n elements

39: We do sorting to,

• keep elements in random positions • keep the algorithm run in linear order

• keep the algorithm run in (log n) order • keep elements in increasing or decreasing order

40: In which order we can sort?

• increasing order only • decreasing order only

• increasing order or decreasing order • both at the same time

41: : In the analysis of Selection algorithm, we make a number of passes, in fact it could

be as many as, • T(n) • T(n / 2) • log n • n / 2 + n / 4

42: The sieve technique is a special case, where the number of sub problems is just

• 5 • Many • 1 • few

Question No: 1 no need

Random access machine or RAM is a/an

► Machine build by Al-Khwarizmi

► Mechanical machine

► Electronics machine

► Mathematical model

Question No: 2

_______________ is a graphical representation of an algorithm

► Σ notation

► Θnotation

► Flowchart

► Asymptotic notation

Question No: 3

A RAM is an idealized machine with ______________ random-access memory.

► 256MB

► 512MB

► an infinitely large

► 100GB

Question No: 4

What type of instructions Random Access Machine (RAM) can execute? Choose best

answer

► Algebraic and logic

► Geometric and arithmetic

► Arithmetic and logic

► Parallel and recursive

Question No: 5 -

What will be the total number of max comparisons if we run brute-force maxima

algorithm with n elements?

► n ²

► 2n/n

► n

► 8n

Question No: 6

What is the solution to the recurrence T(n) = T(n/2)+n .

► O(logn)

► O(n)

► O(nlogn)

► O(n2)

Question No: 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 is the order of execution for this code.

► O(n)

► O(n3)

► O(n2 log n)

► O(n2)

Question No: 8

Consider the following Algorithm:

Factorial (n){

if (n=1)

return 1

else

return (n * Factorial(n-1))

{

Recurrence for the following algorithm is:

► T(n) = T(n-1) +1

► T(n) = nT(n-1) +1

► T(n)= T(n-1) +n

► T(n)=T(n(n-1)) +1

Question No: 9 -

What is the total time to heapify?

► Ο(log n)

► Ο(n log n)

► Ο(n2 log n)

► Ο(log2 n)

Question No: 10

When we call heapify then at each level the comparison performed takes time

► It will take Θ (1)

► Time will vary according to the nature of input data

► It can not be predicted

► It will take Θ (log n)

Zindagi mein 2 Logo ka buhat khayal rahkoooo
Ist woh jiss ney tumhari jeet ke Liye buhat kuch hara hoo

(Father)

2nd woh jiss ko tum ney har dukh me pukaara hoo (Mother)

Regards,

Umair Saulat Mc100403250

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Virtual University of Pakistan*** IT n CS Blog
================================
http://www.eNoxel.com
http://www.enoxelit.tk
http://www.geniusweb.tk

and Please do Share this group with your Friends and Class Fellows so that our Circle would expand and can be more useful for other Students.

Thanks, n Best of Luck......

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