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25.1. DAGs: Longest Paths

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Try these first

  1. 1.

    What is a directed acyclic graph?

    Hint

    Think about graphs that allow paths but not loops.

  2. 2.

    What do we understand by the term 'indegree'?

    Hint

    Consider how many graphs point towards a particular node.

  3. 3.

    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.

  4. 4.

    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.

  5. 5.

    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.

  6. 6.

    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.

Exercises

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

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Quiz

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

2 more questions available

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Challenge Problems

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting