Practice Induction Setup for Shortest Paths - 1.3 | 1. All-pairs Shortest Paths | Design & Analysis of Algorithms - Vol 2
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge

1.3 - Induction Setup for Shortest Paths

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define what is meant by All-pairs Shortest Paths.

💡 Hint: Consider the necessity of comparing distances for multiple vertex pairs.

Question 2

Easy

What is a weighted graph?

💡 Hint: Think about how distances are represented in a graph.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the primary goal of the Floyd-Warshall algorithm?

  • To find minimum spanning trees
  • To find shortest paths between all pairs of vertices
  • To find the largest cycle

💡 Hint: Consider what the algorithm is focused on.

Question 2

True or False: The Floyd-Warshall algorithm can handle graphs with negative cycles.

  • True
  • False

💡 Hint: Think about the impact of cycles on path definitions.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Design a graph with vertices A, B, C, D, and edges with various weights including negative ones. Apply the Floyd-Warshall algorithm and determine all-pairs shortest paths.

💡 Hint: Start initializing your weights based on direct edges then iterate through the vertex combinations.

Question 2

Discuss the implications of allowing negative weights in graphs. What types of real-world scenarios can affect the shortest path calculations?

💡 Hint: Think about situations like city planning where costs might fluctuate or topographical changes could affect distances.

Challenge and get performance evaluation