# NPTEL Design and analysis of algorithms Assignment 3 Answer 2023

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**“NPTEL Design and analysis of algorithms Assignment 3 Answer 2023”**

Table of Contents

## NPTEL Design and analysis of algorithms Assignment

- Asymptotic complexity, O() notation
- Sorting and search
- Algorithms on graphs: exploration, connectivity, shortest paths, directed acyclic graphs, spanning trees
- Design techniques: divide and conquer, greedy, dynamic programming
- Data structures: heaps, union of disjoint sets, search trees
- Intractability

**Next Week Assignment Answers**

This course can have Associate in Nursing unproctored programming communication conjointly excluding the Proctored communication, please check announcement section for date and time. The programming communication can have a weightage of twenty fifth towards the ultimate score.

- Assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
**( All assignments in a particular week will be counted towards final scoring – quizzes and programming assignments).**- Unproctored programming exam score = 25% of the average scores obtained as part of Unproctored programming exam – out of 100
- Proctored Exam score =50% of the proctored certification exam score out of 100

**YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF ASSIGNMENT SCORE >=10/25 AND**

**UNPROCTORED PROGRAMMING EXAM SCORE >=10/25 AND PROCTORED EXAM SCORE >= 20/50.**

**If any one of the 3 criteria is not met, you will not be eligible for the certificate even if the Final score >= 40/100.**

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**?**:

- A connected undirected graph G has 2775 edges. What can we say about n, the number of vertices in G?
**Answer: 75 ≤ n ≤ 2775**

- An airline serves 1000 cities and runs 5500 direct flights each day between these cities. Which of the following is a good data structure to represent the collection of flights?
**Answer: A 1000 × 1000 array A, where A[i][j] = 1 if there is a direct flight from city i to city j and 0 otherwise.**

- Suppose we obtain the following BFS tree rooted at node J for an undirected graph with vertices {A,B,C,D,E,F,G,H,I,J,K}.
Which of the following cannot be an edge in the original graph?

**Answer: (A,D)**

- We are interested in topological orderings of the following DAG which satisfy the constraint that whenever 9 appears after 8, 2 must appear after 4. How many such orderings are there?
**Answer: 10**

- Applying for permits to put up a factory is an 11 step process. Some steps depend on others, as described below.
- Step 1 must be completed before steps 3 and 4 start.
- Step 2 must be completed before steps 3, 6, and 7 start.
- Step 3 must be completed before step 7 starts.
- Step 4 must be completed before step 5 starts.
- Step 5 must be completed before step 7 starts.
- Step 7 must be completed before steps 8 and 9 start.
- Step 9 must be completed before steps 10 and 11 start.

Each step takes a week to complete. What is the minimum number of weeks required to get all the permits in place?

**Answer: 8**