Design And Analysis Of Algorithms Set 5

Computer Science Engineering (CSE)

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This set of Design and Analysis of Algorithms Multiple Choice Questions & Answers (MCQs) focuses on Design And Analysis Of Algorithms Set 5

Q1 | Quick sort uses join operation rather than merge operation.
  • true
  • false
Answer: true
Explaination:
quick sort uses join operation since join is a faster operation than merge.
Q2 | How many sub arrays does the quick sort algorithm divide the entire array into?
  • one
  • two
  • three
  • four
Answer: two
Explaination:
the entire array is divided into two partitions, 1st sub array containing elements less than the pivot element and 2nd sub array containing elements greater than the pivot element.
Q3 | Which is the worst method of choosing a pivot element?
  • first element as pivot
  • last element as pivot
  • median-of-three partitioning
  • random element as pivot
Answer: first element as pivot
Explaination:
choosing the first element as pivot is the worst method because if the input is pre-sorted or in reverse order, then the pivot provides a poor partition.
Q4 | The shortest distance between a line and a point is achieved when?
  • a line is drawn at 90 degrees to the given line from the given point
  • a line is drawn at 180 degrees to the given line from the given point
  • a line is drawn at 60 degrees to the given line from the given point
  • a line is drawn at 270 degrees to the given line from the given point
Answer: a line is drawn at 90 degrees to the given line from the given point
Explaination:
the shortest distance between a line and a point is achieved when a line is drawn at 90 degrees to the given line from the given point.
Q5 | What is the shortest distance between the line given by -2x + 3y + 4 = 0 and the point (5,6)?
  • 4.5 units
  • 5.4 units
  • 4.3 units
  • 3.3 units
Answer: 3.3 units
Explaination:
the shortest distance between a line and a point is given by the formula (ax1+by1+c)/(√a2+b2). using this formula we get the answer 3.3 units.
Q6 | What is the distance between the lines 3x- 4y+7=0 and 3x-4y+5=0?
  • 1 unit
  • 0.5 unit
  • 0.8 unit
  • 0.4 unit
Answer: 0.4 unit
Explaination:
as the given lines are parallel so the distance between them can be calculated by using the formula (c1- c2)/(√a2+b2). so we get the distance as 0.4 unit.
Q7 | What will be the slope of the line given by ax + by + c = 0?
  • -a/b
  • -b/a
  • -c/a
  • a/c
Answer: -a/b
Explaination:
the slope of a line given by the equation ax + by + c=0 has the slope of -a/b. so two lines having the same ratio of the coefficient of x and y will be parallel to each other.
Q8 | What will be the slope of the line given by 10x + 5y + 8=0?
  • -5
  • -2
  • -1.25
  • 5
Answer: -2
Explaination:
the slope of a line given by the equation ax + by + c=0 has the slope of -a/b. so the slope of the given line will be -2.
Q9 | Which of the following areas do closest pair problem arise?
  • computational geometry
  • graph colouring problems
  • numerical problems
  • string matching
Answer: computational geometry
Explaination:
closest pair problem arises in two most important areas- computational geometry and operational research.
Q10 | What is the runtime efficiency of using brute force technique for the closest pair problem?
  • o(n)
  • o(n log n)
  • o(n2)
  • o(n3 log n)
Answer: o(n2)
Explaination:
the efficiency of closest pair algorithm by brute force technique is mathematically found to be o(n2).
Q11 | The most important condition for which closest pair is calculated for the points (pi, pj) is?
  • i>j
  • i!=j
  • i=j
  • i
Answer: i
Explaination:
to avoid computing the distance between the same pair of points twice, we consider only the pair of points (pi, pj) for which i
Q12 | What is the basic operation of closest pair algorithm using brute force technique?
  • euclidean distance
  • radius
  • area
  • manhattan distance
Answer: euclidean distance
Explaination:
the basic operation of closest
Q13 | Which of the following is similar to Euclidean distance?
  • manhattan distance
  • pythagoras metric
  • chebyshev distance
  • heuristic distance
Answer: pythagoras metric
Explaination:
in older times, euclidean distance metric is also called a pythagoras metric which is the length of the line segment connecting two points.
Q14 | Which of the following strategies does the following diagram depict?
  • divide and conquer strategy
  • brute force
  • exhaustive search
  • backtracking
Answer: brute force
Explaination:
brute force is a straight forward approach to solve critical problems. here, we use brute force technique to find the closest distance between p1 and p2.
Q15 | Manhattan distance is an alternative way to define a distance between two points.
  • true
  • false
Answer: true
Explaination:
manhattan distance is an alternative way to calculate distance. it is the distance between two points measured along axes at right angles.
Q16 | What is the optimal time required for solving the closest pair problem using divide and conquer approach?
  • o(n)
  • o(log n)
  • o(n log n)
  • o(n2)
Answer: o(n log n)
Explaination:
the optimal time for solving using a divide and conquer approach is mathematically found to be o(n log n).
Q17 | In divide and conquer, the time is taken for merging the subproblems is?
  • o(n)
  • o(n log n)
  • o(n2)
  • o(log n)
Answer: o(n log n)
Explaination:
the time taken for merging the smaller subproblems in a divide and conquer approach is mathematically found to be o(n log n).
Q18 | The optimal time obtained through divide and conquer approach using merge sort is the best case efficiency.
  • true
  • false
Answer: true
Explaination:
the optimal time obtained through divide and conquer approach is the best class efficiency and it is given by Ω(n log n).
Q19 | Which of the following strategies does the following diagram depict?
  • brute force
  • divide and conquer
  • exhaustive search
  • branch and bound
Answer: divide and conquer
Explaination:
the above diagram depicts the implementation of divide and conquer. the problem is divided into sub problems and are separated by a line.
Q20 | Which of the points are closer to each other?
  • p1 and p11
  • p3 and p8
  • p2 and p3
  • p9 and p10
Answer: p2 and p3
Explaination:
from symmetry, we determine that the closest pair is p2 and p3. but the exact calculations have to be done using euclid’s algorithm.
Q21 | Cross product is a mathematical operation performed between                                  
  • 2 scalar numbers
  • a scalar and a vector
  • 2 vectors
  • any 2 numbers
Answer: 2 vectors
Explaination:
cross product is a mathematical operation that is performed on 2 vectors in a 3d plane. it has many applications in computer programming and physics.
Q22 | Cross product is also known as?
  • scalar product
  • vector product
  • dot product
  • multiplication
Answer: vector product
Explaination:
cross product is also known as a vector product. it is a mathematical operation that is performed on 2 vectors in 3d plane.
Q23 | The concept of cross product is applied in the field of computer graphics.
  • true
  • false
Answer: true
Explaination:
the concept of cross product find its application in the field of computer graphics. it can be used to find the winding of polygon about a point.
Q24 | Which of the following equals the a x b ( a and b are two vectors)?
  • – (a x b)
  • a.b
  • b x a
  • – (b x a)
Answer: – (b x a)
Explaination:
the vector product a x b is equal to – (b x a). the minus sign shows that these vectors have opposite directions.
Q25 | Cross product of two vectors can be used to find?
  • area of rectangle
  • area of square
  • area of parallelogram
  • perimeter of rectangle
Answer: area of parallelogram
Explaination:
cross product of two vectors can be used to find the area of parallelogram. for this, we need to consider the vectors as the adjacent sides of the parallelogram.
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