CS502 Solved Grand Quiz Spring 2021

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CS502 SOLVED MCQs

The sequence of merge sort algorithm is:

Divide Combine-Conquer
Conquer-Divide-Combine
c. Divide-Conquer-Combine Page 27
Combine-Divide-Conquer

In ______ Knapsack Problem, limitation is that an item can either be put in the bag or not. Fractional items are not allowed.

0
1
0/1 Page 91
Fractional

In Selection algorithm, we assume pivot selection takes theta _______ running time.

a. n Page – 36
n2
n3
log (n)

In Heap Sort algorithm (using max heap), when every time maximum elements removed from top ________.

We call merge Sort Algorithm
it becomes Order n2 Algorithm
Divide and Conquer strategy helps us
d. We are left with a hole Page – 41

If matrix A of dimension p x q is multiply with matrix B of dimension q x r, then each entry in resultant matrix takes _______ time.

a. O (q) Page – 84
O (1)
O (p x q)
O (q x r)

_________ is a method of solving a problem in which we check all possible solutions to the problem to find the solution we need.

Plane-Sweep Algorithm
Sorting Algorithm
c. Brute-Force Algorithm google
Greedy approach

The worst case running time of Quick sort algorithm _____.

Cannot be quadratic
b. Is quadratic
ls always Exponential
Is linear

In max heap (for Heap Sort algorithm), when every time maximum element is removed from top we replace it with _____ leaf in the tree.

second last
b. Last Page -41
First
Any

Quick sort algorithm was developed by –

AlferdAho
Sedgewick
John Vincent Atanasoff
d. Tony Hoare – Google wikipedia

If Matrix-A has dimensions “3×2” and Matrix-B has dimensions “2×3”, then multiplication of Matrix-A and Matrix-B will result a new Matrix-C having dimensions.

3×2
2×3
2×2
d. 3×3

For comparison-based sorting algorithms, it is possible to sort more efficiently than Omega n log(n) time.

Always

· Sometimes not
NOT Pg 54
Sometimes

Dynamic Programming approach is usually useful in solving optimization problems.

True
False

In Sorting the key value or attribute_____ from an ordered domain.

Must be page 39
Not always
May be
Occasionally

Result of asymptotical analysis of n(n -3) and 4n*n is that _______

n(n-1) is asymptotically Less
n(n-1) is asymptotically Greater
Both are asymptotically Not equivalent
Both are asymptotically Equivalent page 23 (4n*n= 4n²)

Floor and ceiling are ______ to calculate while analyzing algorithms

Very easy
3rd Option is missing
- Usually considered difficult
4th Option is missing

_____ of reference is an important fact of current processor technology.

Defining
Assigning
- Locality pg-8
Formality

In max-heap, largest element is stored at root node. Where is the smallest element stored?

Right Node
Leaf Node Not sure
Middle Node
Left Node

In average-case time analysis of Quick sort algorithm, the most balanced case for partition is when we divide the list of elements into _.

Equal no. of pieces as of input elements
Single piece exactly
Two nearly equal pieces
Three nearly equal pieces

Which of the following is calculated with Big O notation?

Medium bounds
Upper bounds Page – 25
Lower bounds
Both upper and lower bounds

Edit distance algorithm based on ________ strategy

Greedy
Dynamic Programming Page – 81
Divide and Conquer
Searching

In Heapsort Algorithm, total time taken by heapify procedure is ________

O (log n) Page-43
O (log2 n)
O (n log n)
O (n2 log n)

Al-Khwarizmi was a/an _______

Artist
Astronomer
- Mathematication p-7
Khalifah

When matrix A of 5x3is multiply with metric B of 3×4 then the number of multiplication required is: Not found exactly

15
12
36
60 Not Found exactly but as per formula at page 84,

Pseudo code of algorithms are to be read by _______.

People Page -12
RAM
Computer
Compiler

The sieve technique is a special case, where the number of sub-problems is Just

_________

1 P-34
2
3
4

When a recursive algorithm revisits the same problem over and over again, we say that the optimization problem has ________ sub-problems.

Overlapping – Google Search
Over costing
Optimized
Three

Sieve technique is very important special case of Divide-and-Conquer strategy.

False
- True

In order to say anything meaningful about our algorithms, it will be important for us to settle on a ______.

Java Program
C++ Program
- Mathematically model of computation
Pseudo program

Merge sort is based on _______.

Brute-force
Plan-sweep
- Divide and Conquer
Axis-sweep

What time does Merge Sort algorithm take in order to sort an array of ‘n’ numbers?

(n)
(log n)
(n^2)
d. (n log n) Google Search 31. In Heap Sort

algorithm, the first step is to ___________.

Call Build-Heap procedure Page – 46
Sort the array in descending order
Call Heapify procedure
Find the number of input elements

The definition of theta-notation relies on proving ________ asymptotic bound.

One
Lower
Upper
Both lower & upper Page – 25

In merge sort algorithm, to merge two lists of size n/2 to a list of size n, takes

_______ time.

Theta (n) Page – 32
Theta log(n)
Theta log2(n)
Theta n log(n)

We can make _______ recursive calls in Fibonacci Sequence.

Infinite
Finite google
Only one
Zero

Following is NOT the application of Edit Distance problem.

Speech recognition
Spelling Correction
Ascending Sort Page – 76
Computational Molecular Biology

In plane sweep approach, a vertical line is swept across the 2d-plane and structure is used for holding the maximal points lying to the left of the sweep line.

Array
Queue
Stack Page – 18
Tree

When a heapify procedure is applied to the root node to restore the heap, then at each level, the comparison performed takes time:

It will take (log n).
It can not be predicted
It will take O (1). Page – 43
Time will vary according to the nature of input data.

_____ time is the maximum running time over all legal inputs.

Worst-case Page – 13
Average-case
Best-case
Good-case

Efficient algorithm requires less computational…

Memory
Running Time
Memory and Running Time Page – 9
Energy

For average-case time analysis of Quick sort algorithm, Pivot selection is on average basis from ______

half of the input values
all possible random values Page – 50
Pivot is input separately
values greater than 5

Selection algorithm takes theta ______

(n2)
(n) Page – 37
log(n)
n log(n)

Recurrence can be described in terms of a tree.

Yes Page – 31
No

Time complexity of Dynamic Programming based algorithm for computing the minimum cost of Chain Matrix Multiplication is ______

Log n
n
n^2 (n square)
d. n^3 (n cube) Page -90

The Iteration method is used for ______

Solving Recurrence relations Page 31
Merging elements in Merge sort
Comparing sorting algorithms only
Dividing elements in Merge sort

In 3-Dimensional space, a point P has ______ coordinate(s).

(X, Y)
(X, 0)
(0, Y)
(X,Y, Z)

Chain matrix multiplication problem can be solved through ______ strategy.

Dynamic programming Page – 85
Greedy
Divide and conquer
Sorting

Merge sort have running time….running time of Heap sort. Not found exactly

Greater than
Less than Google
Equal to
Different than

Median is not useful measure of central tendency of given input set especially when the distribution of values is highly skewed.

True
False Page – 34

We do not need to mathematically prove that for comparison-based sorting algorithms always takes Omega nlog (n) time.

True Google
False

The Omega-notation allows us to state only the asymptotic ______ bounds.

Middle
Lower Page 25
Upper
Both lower & upper

Both lower & upperSorting can be in ________

Increasing order only
Decreasing order only
Both Increasing and Decreasing order
- Random order

Radix sort performs sorting the numbers _______ digit (s) at a time.

One Page – 71
Two
Three
All

Quicksort is a/an ______ and ________ sorting algorithm.

Not in place, not stable one
In place , not stable one Page – 54
In place , stable one
Not in place , stable one

Consider three matrices X,Y,Z of dimensions 1×2, 2×3,3×4 respectively. The number of multiplications of (XY) Z is:

18 As per lecture slides
32
24
30

In Fibonacci Sequence, unnecessary repetitions do not exist at all.

True
False Page – 74

It is not a Fibonacci sequence . 1,1,1,2,3,5,8,13,21,34,55,…..

True Page – 73
False

Heap sort is a/ an ______ and ________ sorting algorithem.

Not in place, not stable one
In place , not stable one Page – 54
In place , stable one
Not in place , stable one

Identify the True Statement

The knapsack problem does not belong to the domain of optimization problems.
The knapsack problem belongs to the domain of optimization

problems. Page – 91

The Knapsack problem cannot be solved by using dynamic programming
The knapsack problem is optimally solved by using brute force algorithm.

In Dynamic Programming, our approach is to _________

Develop the solution in a top-down fashion
Express the problem non-recursively
Build the solution in a bottom-up fashion Page – 75
Input several sub-problems simultaneously

Counting sort is suitable to sort the elements in range 1 to K;

K is large
K is small Page – 57
K may be large or small
None

We can multiply two matrices A and B only when they are compatible which means

Number of columns in A must be equal to number of rows in B.

it seems Correct as per page 84

Number of columns in A must be equal to number of columns in B
Number of rows and columns do not matter
Number of rows in A must be equal to number of rows in B

Matrix multiplication is a (n) ________ operation.

Commutative
Associative Page 85
Neither commutative nor associative
Commutative but not associative

In Dynamic Programming approach, solution is modified / changed

Always once
At each stage google and wikipedia
Only for specific problems
At 4^th stage only

In Knapsack problem, the goal is to put items in the Knapsack such that the value of the items is __________ subject to weight limit of knapsack.

Minimized
Decreased
Maximized Page – 91
None of the given options

An in-place sorting algorithm is one that ________ uses additional array for storage.

Always
Permanently
Does not Page – 54
Sometime

Memoization is a part of Dynamic Programming Strategy.

True Page – 74
False

If matrix A of dimension 2×4 is multiply with matrix B of dimension 4×3, then

the dimension of resultant matrix is Not found exactly

2×4
4×3
3×4
2×3 It seems correct as per second last Para of page 84

In Dynamic Programming approach, we do not store the solution to each sub-problem in case if it reappears.

True
False Page – 75

Dynamic Programming is a problem-solving approach in which___

Problem is solved in Zero time
Solution is developed only at final stage
Both are correct
Both are incorrect google

In Fibonacci sequence, each term is calculated by____ previous__ terms.

Subtracting, Two
Adding, Three
Adding, Two Page – 73
Multiplying, Two

Selection sort is not an in-place sorting algorithm.

True Page – 54
False

If there are θ (n²) entries in edit distance matrix then the total running time is:

θ (n)
θ (1)
θ (n²) Page – 84
- θ (n logn)

The only way to convert a string of i characters into the empty string is with i deletions, represented as

E(0.j) =j
E(i.j) = 1
E(0.i) = j
E (i.0)=I Page – 78

Dynamic programming formulation of the matrix chain multiplication problem will store the solutions of each sub problem in an

Array

Variable
Table Page – 86
class

We can use the optimal substructure property to devise a formulation of the edit distance problem.

Selective
Optimum
Iterative
Recursive Page – 78

Sorting is performed on the basis of ___________.

Computational resources
Asymptotic notation
Summation
Some key value of attribute page- 39

In Heap Sort algorithm, we call Build-heap procedure ____________.

Only once page 46
Twice
Thrice
As many times as we need

Radix sort is not a non-comparative integer sorting algorithm.

True Google Search
False

In the statement “output P[1].x, P[1].y”, the number of times elements of P are accessed is _______.

1
b. 2 page 14
3
4

The main purpose of mathematical analysis is measuring the ______ required by the algorithm.

Inputs & outputs
Space
Execution TIME page 13
Execution time and memory

_______ provides us more accurate result when input values are not closer with each other

Mode
- Average
- Median P-34
Mean

The process of ______ ends when you are left with such tiny pieces remaining that it is trivial to solve them.

Brute-force
Plan-sweep
Divide and Conquer
Axis-sweep

__________ overcomes the limitations of _______ by working as per positional notations of numbers.

Counting sort, Radix sort
- Radix sort, Counting sort

Memorization is a part of Dynamic Programming strategy.

False
- True

Rank of an element can be defined as ___________.

One minus the number of elements that are smaller
Two plus the number of elements that are greater
One plus the number of elements that are smaller P-34
Two minus the number of elements that are smaller

If the time complexity of an algorithm is given by O (1), then its time complexity would be

Polynomial
Exponential
Constant – Wikipedia
Average

Quick sort is a recursive algorithm.

True
False

The asymptotic growth of n(n+1)/2 is:

O(n²) As the n^2 term has the largest contribution, the Big-O complexity is O(n^2)
- O(n)
O(n+2)
O(n log n)

Approach of solving geometric problems by sweeping a line across the plane is called _____ sweep.

Line
Plane Page 18
Cube
Box

As per algorithm of Dynamic Programing, we need to store

First sub-problem only
Best solution only
Intermediate sub-problems Pg:75
Final solution only

In Sieve technique, we solve the problem

In recursive manner Pg:34
Non recursively
Using Merge Sort algorithm
Using Brute force technique

One of the limitation in 0/1 knapsack is that an item can either be ________ in the bag or not.

Use
Put Pg:91
Move
Store

Which one is not passed as parameter in Quick sort algorithm?

End of the array
Middle of the array
Array (containing input elements) Google
Start of the array

In the analysis of Selection algorithm, we get the convergent _________

Harmonic
Linear
Arithmetic
Geometric Pg:37

A Random Access Machine (RAM)is an idealized machine withrandom access memory.

Infinite large Pg:10
512 MB
256 MB
2 GBs

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

n(n+1)
log(n) Pg:37
n/3
n/4

In Random Access Machine (RAM), instructions are executed in

Parallel
Batch
One by One Pg:10
Multiple times

In selection problem, the rank of an element will be its ________ position

First
final Pg:34
Second last
Last

The worst-case running time of Merge sort is _____ in order to sort an array of n elements.

O(log n)
O(n)
O(n log n) page 40 and google
O(n)

f(n) and g(n) are asymptotically equivalent. This means that they have essentially the same ______.

Results
Variables
Growth Rates
Size

An algorithm is a mathematical entity. Which is independent of _______.

Programming language
Machine and Programming language
Programing Language Compiler and Machine
Compiler and Programming language

In Quick sort algorithm, Pivots form ___

Stack
Queue
Graph
- Binary Search Tree

Counting sort is suitable for sorting the elements within range 1 to P. where

P is large
P is very large
P is undetermined
- P is Small

In asymptotical analysis of n'(5 2)-3, as n becomes large, the dominant (fastest growing) term is some constant times

n_1
n
n+1
n*n p-23

___ Items are not allowed in the 0/1 knapsack.

Lighter
Whole

Weighty
Fractional

Fibonacci Sequence was named on ______, a famous mathematician in 12th Century.

Fred Brooks
Grady Booch
Leonardo Pisano
Edgar F. Codd

In Heap Sort algorithm, we build _____ for ascending sort.

Min heap
- Max Heap pg-41

Bubble sort is not an in-place sorting algorithm.

True

b. False

P-54

In partition algorithm, the subarray ______ has elements which are greater than pivot element x.

A[p…r]
A[p…q-1]
A[q]
- S[q+1…r]

In Heap Sort algorithm, if heap property is violated

We call Heapify procedure
We ignore
Heap property can never be violated
We call Build Heap procedure

______ is not a characteristic of Random Access Machine.

Assigning a value to a variable
Locality of reference
Single-Processor P-10
Executing an arithmetic instruction

The only way to convert an empty string into a sting of j characters is by doing j insertions, represented as ______

E(i,j) = 1
E(I,0) = I
E(0,j) = j page 78
E(1,j)= j

In Selection problem, the Sieve technique works in __________.

Non-recursive manner
Constant time
Phases page 34
One complete go

Algorithm is a sequence of computational steps that —- the input into output.

Merge
Assign
Transform page 7
Integrate

If pj dominates pi and pi dominates ph then pj also dominates ph, it means dominance relation is

Transitive page 18
Non Transitive
Equation
Symbolic

To find maximal points in brute-force algorithm each point of the space is compared against ______ of that space.

One other point
All other points page 11
Few other points
Most of the other points

In the following code the statement “cout<<j;”executes ——— times. for (j=1; j<=5; j = j+2)

cout<<j;

5 times
2 times
3 times
0 times

In merge sort algorithm, we split the array around the ______ index q.

Mid page 17
Exiting
- Entring
Summing

In Selection problem, the Sieve technique _________.

Add some more input items each time
Do not work recursively
Do not uses Divide and Conquer approach
Eliminates undesired data items each time

Consider three matrices X, Y, Z of dimensions 1 x 2, 2 x 3, 3 x 4 respectively. The number of multiplications of X(YZ) is .

16
32
26
32 page 84

In Heap Sort algorithm, the total running time for Heapify procedure is

_______

Theta (log n)
Order (log n)
Omega (log n)
O(1) i.e. Constant time

The sieve technique works where we have to find_______ items(s) from a large input.

Single page 34
Two
Three
Similar

In Dynamic Programming based solution of Knapsack Problem, if we decide to take an object i , then we gain______

W(Total Weight of Knapsack)
V (Total Value of all items)
vi (Value of object i) page 93
Nome of the given option

While Sorting, the order domain means for any two input elements x and y

_______ satisfies only.

x < y page 39
x > y
x = y
All of the above

For solving Selection problem, we introduced Sieve technique due to

_______

Using Decrease and Conquer strategy page 34
Avoiding to sort all input data
Eliminating Rank of an element
Using Brute-force approach

________ is one of the few problems, where provable lower bounds exist on how fast we can sort.

Searching
Sorting page 38
Both Searching & sorting
Growing

In plane sweep approach, a vertical line is swept across the 2d-plane from_____.

Right to Left
Left to Right page 18
Top to Bottom
Bottom to top

In generating Fibonacci sequence, we can avoid unnecessary repetitions by

_____ process.

Tokenization
Memorization page 43
Randomization
Memorization

For _________ values of n, any algorithm is fast enough.

Medium

Large
Small page 14
Infinity

Dynamic programming comprises of _______.

Recursion only
Repetition only
Recursion with Repetition
No Repetition but Recursion page 75

The function f(n)=n(logn+1)/2 is asymptotically equalient t nlog n :Here Lower Bound means function f(n) grows asymptotically at __ as fast as nlog n.

Least page 23
Normal
Most
At

Counting sort has time complexity.

O(n+k)
O(n) page 58
O(k)
O(nlogn)

Due to left complete nature of binary tree, the heap can be stored in

Array page 40
Structures
Link List
Stack

Single item from a larger set of ________.

Constant
Pointers
Phases
n items page 34

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 page 76

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

T(n^2)
T(n)
T(log n)
T(n log n) page 40

In in-place sorting algorithm is one that uses arrays for storage.

No additional array page 54
An additional array
Both of above may be true according to algorithm
More than 3 arrays of one dimension

Brute-force algorithm for 2D-Maxima is operated by comparing ______

pairs of points.

Two
Some
Most
All page 18

While Sorting, the ordered domain means for any two input elements x and y ____ satisfies only.

x > y
x < y
x = y
All of the above page 38

Quick sort is.

Not stable but in place page 54
Stable but not in place
- Stable & in Place
Some time stable & some times in place

Which may be a stable sort?

Merger
Insertion
Both above page 54
None of the above

For the Sieve Technique we take time.

T(nk) page 34
IT(n / 3)
n^2
n/3

Continuation sort is suitable to sort the elements in range 1 to k.

K is Large
K is not known
K may be small or large
K is small page 54

Asymptotic growth rate of the function is taken over ______ case running time. .

Worst page 14
Average
- Best
Normal

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

5
Many
1 page 34
Few

In Quick sort, we don’t have the control over the sizes of recursive calls.

True page 49
False
Less information to decide
Ether true or false

Before sweeping a vertical line in plane sweep approach, in start sorting of the points is done in increasing order of their _____ coordinates. .

Z
X
X , Y

Random access machine or RAM is a/an.

Machine build by Al-Khwarizmi
Mechanical machine
Mathematical model page 10
Electronics machine

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

True
False page 99

A heap is a left-complete binary tree that confirms to the ________.

increasing order only
decreasing order only
heap order page 40
log n order

If we associate (x, y) integers pair to cars where x is the speed of the car and y is the negation of the price. High y value for a car means a ________ car.

Fast

Slow
Expensive
Cheap

Which one of the following sorting algorithms is the fastest?

Merge sort
Quick sort
Insertion sort
Heap sort

Quick sort algorithm divide the entire array into ________ sub arrays.

In brute force algorithm, we measure running time T(n) based on ________.

Worst-case time and best-case time
Worst-case time and average-case time page 46
Average-case time and best-case time
Best-case time and staring-case time

For 2D Maxima problem. Plane Sweep algorithm first of all _________.

Sorts all points
Delete some points
Output the elements
Pushes all points on stack

There are ________ entries in the Edit Distance Matrix

ϴ (n)
ϴ (n2) page 84
ϴ (n+2)
ϴ (n + 100)

Which symbol is used for Omega notation?

(O)
(ϴ)
(Ω)
(@)

Selection sort is a ______ sorting algorithm

In-place page 54
Not In-Place
Stable
in-partition

In Dynamic Programming based solution of knapsack problem, to compute entries of ‘V’, we will imply a(n) ______ approach.

Subjective
Inductive
Brute Force
Combination

We do not need to prove comparison-based sorting algorithms by mathematically. It always takes _________ time.

Big Oh nlog(n)
Omega nlog(n) NOT SURE
Omega n(n^2)
Theta nlog(n)

Merge sort is a/an _______ and ________ sorting algorithm

Not in-place, not stable one
In-place, not stable one
In-place, stable one
Not in-place, stable one page 54

Cubic function will ________ a quadratic function.

Prove
be equal to
overtake Page 25
find

Insertion sort is a _________ sorting algorithm

Unstable
In-place Page 54
Not In-Place
in-partition

To check whether a function grows faster or slower than the other function, we use some asymptotic notations, which is ________.

Big-oh notation
Theta notation
Omega notation
All of the given

Asymptotic growth of 8n^2 + 2n – 3 is:

Θ(n^2 + n)
Θ (n^2) page 14
Θ(8n^2)
Θ(8n^2 + 2n)

In the analysis of algorithms, _________ plays an important role.

text analysis
time
growth rate
money

In inductive approach of knapsack problem, we consider 2 cases, _______

Or ________.

Median, Mode
Recursive, Iterative
Leave object, Take object page 93
Sequentially. Parallel

Random Access Machine (RAM) can execute _________ instructions

only logical
parallel
only arithmetic
logical and arithmetic

Using _______ algorithm, efficiency is not given much importance

Greedy
Merge sort
Processing
Brute Force

Bubble sort takes theta _________ in the worst case

(n2) page 39
(n)
log(n)
nlog(n)

If matrix A of dimension p × q is multiply with matrix B of dimension q × r, then dimension of resultant matrix is:

q × r

r × p
P x r
P x q

Dynamic Programing algorithms often use some kind of ________ to store the results of intermediate sub-problems

variable

stack
Table
loop

________________ is in-place sorting algorithm.

Bubble sort (Page 54)
Merge sort
Linear search
Binary Search

Which one of the following problems can be solved using dynamic problem?

Bubble sort problem
Matrix chain multiplication problem page 85
Greedy search problem
Fractional knapsack problem

In chain matrix multiplication, solutions of the sub-problems are stored in a

_________.

Array
Table page 86
Tree
Link list

What is the average running time of a quick sort algorithm?

O(n^2)
O(n)
O(n log n) (Page 49)
O(log n)

Sorting Algorithms having O _______ running time are considered to be slow ones.

(n)
(n^2) (Page 39)
(nlog(n))
(log(n))

While solving Selection problem, in Sieve technique we partition input data

________

In increasing order
In decreasing order
According to Pivot
Randomly

________ is the process of avoiding unnecessary repetitions by writing down the results of recursive calls and looking them up again if we need them later.

Loop
- Memoization page 74
Recursion
Function

In average-case time the probability of seeing input is denoted by _______.

p{I}
p[I]
p<i>
p(i) page 13

While applying the Sieve technique to selection sort, how to choose a pivot element.

Through mean
Linear
Randomly page 35
Sequentially

Number of _______ of the pseudo code are counted to measure the running time.

Inputs
Outputs
Steps page 13
Pages

Developing a dynamic programming algorithm generally involves ______

separate steps.

One
Two page 75
Three
Four

8n^2+2n+3 will exceed c28(n), no matter how large we make _____.

n
2n
c2 page 25
this quadratic equation

The running time of quick sort algorithm_________.

Is impossible to compute
Has nothing to do with pivot selection
Is Random upon each execution
Greatly influenced by the selection of pivot page 49

_________ involves breaking up the problem into sub problems whose solutions can be combined to solve the global problem.

Complexity Theory
Dynamic programming solution
Divide and Conquer Strategy page 34
Greedy Algorithms

In _____________ we have to find rank of an element from given input.

Merge sort algorithm
Selection problem page 34
Brute force technique
Plane Sweep algorithm

How many steps are involved to design the dynamic programming strategy?

2
3
1
4 page 92

In Bucket sort, if there are duplicates then each bin can be replaced by a

Linked list page 69
Hash table
- Stack
Heap

In merge sort algorithm, we split the array ______ to find index q.

from end
from start
midway page 28
both from start or end

Find the maximum value of the items which can carry using knapsack Knapsack weight capacity = 50.

Item Weight Value

11070

22020

33080

470 200

280
100
90
200

In 2-d maxima problem a point p is said to be dominated by point q if

_________.

p.x <= q.x
bp.x <= q.x and p.y <= q.y page 17
p.y <= q.y
p.x >= q.x and p.y >=q.y

Sorting can be in ______________.

Increasing order only
Decreasing order only
Both increasing and decreasing order
Random order

Recurrence can be described in terms of _______________.

Array
Linear
Tree page 31
Graph

The brute-force algorithm for 2D-Maxima runs in order O(__) time.

n
n(log n)
n*n page 18
n3

In plane sweep approach of solving geometric problems, a _________ is swept across the plane.

Line page 18
Plane
Cube
Box

Which of the following is calculated with Big Omega notation?

Medium bounds

Upper bounds

c. Lower bounds Page – 25

Both upper and lower bounds

_________ is always based on divide and conquer strategy.

Bubble sort
Selection sort
Pigeon sort
Quick sort page 46

If a matrix has three rows and two columns, then dimensions of matrix will be:

3×2
2×3
3×3
2×2

Asymptotic notations are used to describe _______ of an algorithm.

Length
running time google
size
compile time

Catalan numbers are related the number of different ______ on ‘n’ nodes.

Arrays
linked lists
binary trees page 85
functions

Applying the sieve technique to selection problem, ________ element is picked from array.

Output
Total
Input
Pivot page 35

Dynamic Programming approach is usually useful in solving _______

problems.

Optimization google
Array
Normal
Loop

In recursive formulation of knapsack Problem: V [0, j] = ________ for j>=0

-1
0 page 93
1
2

________ is a linear time sorting algorithm.

Merge sort
Radix sort page 71
Quick sort
Bubble sort

Quick sort is one of the _____ sorting algorithm.

Fastest page 19
Slowest
Major
Average

The time assumed for each basic operation to execute on RAM model of computation is _____.

Infinite
Continuous
Constant page 10
Variable

In Sieve Technique, we know the item of interest.

True
False

While analyzing algorithms, _______ and _______ usually considered difficult to calculate.

Floor, ceiling google
Row, Column
- Finite, Infinite
Graph, Tree

While analysis of the brute-force maxima algorithm, an array sorted in the reverse order is the type of _________ case input.

Best
Worst page 14
Somewhat bad
Average

_________ is not useful measure of central tendency of given input set especially when the distribution of values is highly skewed.

Mean
Mode
Average
Median page 34

In asymptotical analysis of n(n-3) and 4n*n, as n becomes large, the dominant (fastest growing) term is some constant times _______.

n+1
n-1
n
n*n page 23

In addition to passing in the array itself to Merge Sort algorithm, we will pass in other arguments which are indices.

Three
Two
Four
Five

In 2d-maximal problem, a point is said to be if it is not dominated by any other point in that space.

Member
Minimal
- Maximal
Joint

Counting sort assumes that the numbers to be sorted are in the range

________.

K to n where n is large

K to n where k is small
- 1 to k where k is small
k to n where n is small

Insertion sort is an efficient algorithm for sorting a __________ number of elements

Small
Extra large
- Large
Medium

If the indices passed to merge sort algorithm are _________ then this means that there is only one element to sort.

Small page 28
Large
Equal
Not Equal

In Knapsack Problem, each item must be entirely accepted or rejected, is called ______ problem.

Linear
Fractional
0-1
Optimal

If the time complexity of an algorithm is O(n). then it is called _______ time complexity.

Linear Wikipedia
Constant
Average
Exponential

In the case of _________ analysis does not depend upon on the distribution of input.

Merge sort
Insertion sort
- Quick Sort
Heap sort

We can use the ___________ Property to devise a recursive formulation of the edit distance problem.

Small substructure
Algorithmic
Real
Optimal substructure page 78

The following sequence is called ____________

1,2,3,5,8,13,21,34,55,…..
- Fibonacci sequence page 73
Optimal sequence
- Optimize Sequence
Overlapping sequence

Which one sorting algorithm is best suited to sort an array of 2 million elements?

Bubble sort
Insert sort
Merge sort
Quick sort
Ridx Sort page 71

We can improve the performance of quick sort if we could be able to _,__________.

Select two or more pivots page 34
Skip any sub-array completely
- Skit Input elements somehow
Eliminate recursive calls

The problem with the brute-force algorithm is that is uses ________ in pruning out de

Worst-case time
No intelligence page 18
Outside looping
Artificial intelligence

In chain matrix multiplication, the order of the matrices __________.

Can be changed
Can not be changed page 85
is equal
is reverse

In quick sort algorithm, we choose pivot___________.

Always the smallest element
Greater than 5
Randomly page 35
Less than 5
In Heap Sort algorithm. Heapify procedure is ________ in nature.
Recursive
Non-Recursive page 43
Fast
Slow

When matrix A of 5x 3 is multiplied with matrix B of 3 x 4 then the number of multiplications required will be ___________.

An algorithm is said to be correct if for every ______ instance, it halts with the correct ______.

Input, Output page 13
Design, Analysis
Value, Key
Key, Analysis

In chain matrix multiplication, table is filled _________ to find the multiplication of matrix.

row wise
column wise
diagonally
bottom-to-up page 86

If we have an equation 8n2+7f*n + 5f + 6 then is large, ________ term will be muchxxxxxxxthe n term and will dominate the running time.

f g (n)
g (n) * 2
n * 2 page 23
f (n)

For quick sort algorithm. Partitioning takes theta ________.

(n)
log(n)
n log (n)
n2log (n)

In Heap Sort algorithm, the maximum levels an element can move upward is

_______

Theta (log n) page 43
Big-ch (log n)
Omega (log n)
0 (1) i.e. Constant time

_______ programming is essentially recursion without repetition.

Array
Fast
Dynamic
n (log n)

There are no hard formal rules to the syntax of the ________ code.

Basic

Programming
Pseudo
Assembly

In Heap Sort algorithm, to remove the maximum element every time.

We call Build-Heap procedure
Heap Sort algorithm terminates without result
We call heapify procedure
Nothing happens

Which process is used for avoiding unnecessary repetitions and looking them up again if we need them later.

Greedy Approach
Memoization page 74
Divide and conquer
Recursion

The worst-case running time of Quick sort is _________ in order to sort an array of n element.

O(n log n) page 49
O(n)
O(n²)
- O(log n)

Boolean operation is a _________ operation on an idealized RAM model of computation.

Advance
String
Basic
Normal

In chain matrix multiplication, if there are n items, there are ________ ways in which outer most pair of parentheses can placed.

n^2
2n
n+1
d. n-1 page 85

The number of nodes in a complete binary tree of height h is:

* (h+1) – 1

* (h+1)
b. 2^(h+1) – 1 page 40
((h+1)^2) – 1

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