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
• Greedy approach

The worst case running time of Quick sort algorithm _____.

• 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.

• 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
• 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
• 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.

• 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 4th 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

• 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

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

• Subtracting, Two
• 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.

• 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.

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
• 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.

1. True

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
• 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

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
• 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. .

• Y
• 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.

1. 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.

• 2
• 3
• 4
• 5

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

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

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

• 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?

1. 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
• size
• compile time

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

• Arrays
• 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.

• 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
• 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.

• 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
• 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

________.

1. 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 ___________.

• 15
• 12
• 36
• 60

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.

1. 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.

• 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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