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Bsc CSIT Semester 5 – Design and Analysis of Algorithms – Unit 3. Divide and Conquer Algorithms

Comprehensive questions and detailed answers for Unit 3. Divide and Conquer Algorithms. Perfect for exam preparation and concept clarity.

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1

Explain the divide and conquer paradigm from algorithm design with a suitable example. Write the Quick sort algorithm using a randomized approach and explain its time complexity.

MediumTHEORY10 marks2076(TU Final)

2

Solve the following recurrence relation using the master method.

$T(n) = 7 T(n/2) + n2\\ T(n) = 4 T(n/4) + kn$

MediumTHEORY5 marks2076(TU Final)

3

Explain about the divide and conquer paradigm for algorithm design with suitable example. Write the Quick sort algorithm using randomized approach and explain its time complexity.

MediumTHEORY10 marks2078(TU Final)

4

Explain the recursion tree method for solving the recurrence relation. Solve following recurrence relation using this method.

T(n)=2T(n/2) +1 \text{ for } n> 1,\space T(n) =1 \text{ for } n =1

MediumTHEORY5 marks2078(TU Final)

5

Explain the divide and conquer strategy for problem solving. Describe the worst-case linear time selection algorithm and analyze its complexity.

MediumTHEORY10 marks2079(TU Final)

6

Solve the following recurrence relations using masters method a. T(n) = 2T(n/4) + kn2, n > 1 =1 , n=1 b. T(n) = 5T(n/4) + kn , n > 1 =1 , n=1

MediumTHEORY5 marks2079(TU Final)

7

Trace the quick sort algorithm for sorting the array A[ ]={15,7,6,23, 18,34,25} and write it’s best and worst complexity.

MediumTHEORY5 marks2079(TU Final)

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Sample Questions

Explain the divide and conquer paradigm from algorithm design with a suitable example. Write the Quick sort algorithm using a randomized approach and explain its time complexity.

Marks: 10Chapter: Unit 3. Divide and Conquer Algorithms

Solve the following recurrence relation using the master method. \[ T(n) = 7 T(n/2) + n2\\ T(n) = 4 T(n/4) + kn \]

Marks: 5Chapter: Unit 3. Divide and Conquer Algorithms

Explain about the divide and conquer paradigm for algorithm design with suitable example. Write the Quick sort algorithm using randomized approach and explain its time complexity.

Marks: 10Chapter: Unit 3. Divide and Conquer Algorithms

Explain the recursion tree method for solving the recurrence relation. Solve following recurrence relation using this method. \[ T(n)=2T(n/2) +1 \text{ for } n> 1,\space T(n) =1 \text{ for } n =1 \]

Marks: 5Chapter: Unit 3. Divide and Conquer Algorithms

Explain the divide and conquer strategy for problem solving. Describe the worst-case linear time selection algorithm and analyze its complexity.

Marks: 10Chapter: Unit 3. Divide and Conquer Algorithms

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