Practice DAGs: Longest Paths - 25.1 | 25. DAGs: Longest Paths | Design & Analysis of Algorithms - Vol 1
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25.1 - DAGs: Longest Paths

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is a directed acyclic graph?

💡 Hint: Think about graphs that allow paths but not loops.

Question 2

Easy

What do we understand by the term 'indegree'?

💡 Hint: Consider how many graphs point towards a particular node.

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 does a Directed Acyclic Graph (DAG) not contain?

  • Cycles
  • Multiple edges
  • Disconnected vertices

💡 Hint: Think about the fact that paths need to respect a starting point.

Question 2

The process of arranging the vertices in a DAG respecting dependencies is called?

  • Topological Sorting
  • Graph Traversal
  • Breadth-First Search

💡 Hint: Remember it’s about respecting a sequence of tasks.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a set of courses represented as a DAG, compute the longest path and determine the minimum number of semesters needed. The courses are: 1, 2 (no prereqs), 3 (depends on 1), 4 (depends on 1), 5 (depends on 1), 6 (depends on 3), 7 (depends on 6), 8 (depends on 2, 4, 5, and 7).

💡 Hint: Draw the graph and label dependencies step by step.

Question 2

Create a DAG to represent project tasks where tasks A, B must be done before task C; task A also leads to task D; and task D leads to task E. Find the longest path.

💡 Hint: Map out all tasks and visualize their connections to understand dependencies.

Challenge and get performance evaluation