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
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:
64
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 3rd Quiz
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
k
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
n.
• 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)
(c) O(c n2) = O(n2) where c is a constant. (d) O(c n2) = O(c) where c is a constant.
(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)
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