csc325

Design and Analysis of Algorithms

Medium Exam Preparation: 3 - 4 days

Question Papers (7)

Selected Question Paper: 2083 Boards

Community

FM: 60 PM: 24

Design and Analysis of Algorithms

2076 Boards

FM: 60 PM: 24

Section A

Answer any two questions.

1

What do you mean by the complexity of an algorithm? Explain the asymptotic notations used to describe the time/space complexity of any algorithm with their geometrical interpretation and example.

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2

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.

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3

Explain in brief the Backtracking approach for algorithm design. How it differs with recursion? Explain the N-Queen problem and algorithm using backtracking and analyze its time complexity.

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Section B

Answer any eight questions.

4

Write the algorithm for selection sort and explain its time and space complexity.

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5

Solve the following recurrence relation using the master method.
a. $T(n) = 7T\left(\frac{n}{2}\right) + n^2$
b. $T(n) = 4T\left(\frac{n}{4}\right) + kn$

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6

Explain the greedy algorithm for the fractional knapsack problem with its time complexity.

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7

Trace heap sort algorithm for the following data:
{2, 9, 3, 12, 15, 8, 11}

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8

What do you mean by Dynamic programming strategy? Explain the element of DP.

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9

Explain the approximation for solving vertex cover with a suitable example.

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10

Explain Prism’s algorithm for MST problem and analyze its time complexity.

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11

Explain in brief about the classes P, NP, and NP complete with examples.

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12

Write short notes on

a. Backtracking strategy
b. Tractable and Intractable Problem

✓

#Answer

Backtracking Strategy

A general algorithm for finding solutions to computational problems, incrementally building candidates to the solutions, and abandoning a candidate ("backtracking") as soon as it determines that the candidate cannot possibly lead to a valid solution.
Often used for constraint satisfaction problems.
Explores the solution space as a tree.
Key components:
- Choice: Selecting an option.
- Constraint: Checking if the current choice is valid.
- Goal: Determining if a complete solution is found.
Example: Solving the N-Queens problem.

Tractable and Intractable Problem

Tractable Problem: A problem for which an algorithm exists that can solve all instances of the problem in polynomial time (e.g., O(n), O(n²), O(n³)). Considered efficiently solvable.
Intractable Problem: A problem for which no polynomial-time algorithm is known, and it is believed that no such algorithm exists. Often requires exponential time (e.g., O(2ⁿ), O(n!)).
P vs. NP: A major unsolved problem in computer science. P is the class of tractable problems. NP is the class of problems for which a solution can be verified in polynomial time. It is unknown whether P = NP.
Example of intractable problem: Traveling Salesperson Problem (TSP).

Community

Design and Analysis of Algorithms

2076 Boards

Section A

Answer any two questions.

1 What do you mean by the complexity of an algorithm? Explain the asymptotic notations used to describe the time/space complexity of any algorithm with their geometrical interpretation and example.

2 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.

3 Explain in brief the Backtracking approach for algorithm design. How it differs with recursion? Explain the N-Queen problem and algorithm using backtracking and analyze its time complexity.

Section B

Answer any eight questions.

4 Write the algorithm for selection sort and explain its time and space complexity.

5 Solve the following recurrence relation using the master method.a. ﻿﻿T(n)=7T(n2)+n2T(n) = 7T\left(\frac{n}{2}\right) + n^2T(n)=7T(2n​)+n2﻿﻿ b.﻿﻿T(n)=4T(n4)+knT(n) = 4T\left(\frac{n}{4}\right) + knT(n)=4T(4n​)+kn﻿﻿

6 Explain the greedy algorithm for the fractional knapsack problem with its time complexity.

7 Trace heap sort algorithm for the following data: {2, 9, 3, 12, 15, 8, 11}

8 What do you mean by Dynamic programming strategy? Explain the element of DP.

9 Explain the approximation for solving vertex cover with a suitable example.﻿

10 Explain Prism’s algorithm for MST problem and analyze its time complexity.

11 Explain in brief about the classes P, NP, and NP complete with examples.

12 Write short notes on a. Backtracking strategyb. Tractable and Intractable Problem

1

What do you mean by the complexity of an algorithm? Explain the asymptotic notations used to describe the time/space complexity of any algorithm with their geometrical interpretation and example.

2

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.

3

Explain in brief the Backtracking approach for algorithm design. How it differs with recursion? Explain the N-Queen problem and algorithm using backtracking and analyze its time complexity.

4

Write the algorithm for selection sort and explain its time and space complexity.

5

Solve the following recurrence relation using the master method.
a. $T(n) = 7T\left(\frac{n}{2}\right) + n^2$
b. $T(n) = 4T\left(\frac{n}{4}\right) + kn$

6

Explain the greedy algorithm for the fractional knapsack problem with its time complexity.

7

Trace heap sort algorithm for the following data:
{2, 9, 3, 12, 15, 8, 11}

8

What do you mean by Dynamic programming strategy? Explain the element of DP.

9

Explain the approximation for solving vertex cover with a suitable example.

10

Explain Prism’s algorithm for MST problem and analyze its time complexity.

11

Explain in brief about the classes P, NP, and NP complete with examples.

12

Write short notes on

a. Backtracking strategy
b. Tractable and Intractable Problem