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25. DAGs: Longest Paths
The chapter covers the concept of Directed Acyclic Graphs (DAGs) and focuses on identifying the longest path within them. It discusses practical applications, such as scheduling courses based on prerequisites. The chapter emphasizes the use of topological sorting to determine the longest path efficiently, showcasing the relationship between longest paths and task scheduling with dependencies.
Sections
This section explores the longest path problem in Directed Acyclic Graphs (DAGs), identifying how to calculate the longest path using topological ordering.
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Directed Acyclic Graph (DAG)
A directed graph that contains no cycles, allowing for a topological order where each vertex is listed before its dependents.
Topological Sorting
An ordering of the vertices in a directed acyclic graph such that for every directed edge from vertex j to vertex k, j comes before k in the ordering.
Longest Path Problem
The problem of finding the longest path in a graph or DAG, which corresponds to maximizing the number of sequential tasks based on dependencies.
Practice 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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