20 Topological Sort Interview Questions and Answers

In computer science, a topological sort is an ordering of vertices in a directed acyclic graph (DAG). That is, it is a linear ordering of vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. A topological sort is sometimes also called a topological ordering.

Topological sorting has applications in scheduling and data dependencies (for example, in a makefile). It also forms the basis for many graph algorithms such as finding shortest paths (Dijkstra’s algorithm) and critical paths (the longest path problem) in an acyclic graph.

In this article, we will discuss the topological sort algorithm and some of the common interview questions that you may be asked about it.

Topological Sort Interview Questions and Answers

Here are 20 commonly asked Topological Sort interview questions and answers to prepare you for your interview:

1. What is a Topological Sort?

A Topological Sort is a way of ordering a set of elements such that if element A comes before element B, then all of the elements that A depends on will also come before B. This is often used as a way of ensuring that dependencies are satisfied before proceeding with a particular task.

2. Can you explain the basics of a topological sort algorithm?

A topological sort algorithm is used to order a set of vertices in a directed acyclic graph. The algorithm starts by visiting each vertex in the graph and marking it as visited. It then visits each of the unvisited vertices and marks them as visited. Finally, it outputs the list of visited vertices in topological order.

3. What’s the difference between a DFS and BFS based topological sorting algorithm?

A DFS based algorithm will visit all of the nodes in the graph before moving on to the next node, while a BFS based algorithm will visit the nodes in the order that they are found.

4. Can you give me some examples where topological sorts are used in real projects?

Topological sorts are often used in dependency management. For example, if you are managing a project with a lot of dependencies, you may use a topological sort to ensure that all of the dependencies are met before you can begin work on the project. This can help to avoid a lot of headaches down the road!

5. What conditions should exist for it to be possible to perform a topological sort on a graph?

In order for a topological sort to be possible, the graph should be directed and acyclic. A directed graph is one in which the edges all have a specific direction, and an acyclic graph is one without any cycles (meaning there is no path from any vertex back to itself).

6. Is it possible to run a topological sort on a directed acyclic graph? If yes, can you explain how it works?

Yes, it is possible to run a topological sort on a directed acyclic graph. The way it works is that you first find a vertex that has no incoming edges and you label it with the number 1. Then, you find all of the vertices that have an edge coming from that vertex and you label them with the number 2. You continue this process until all of the vertices have been labeled. The order in which the vertices are labeled is the topological sort.

7. What’s the best way to check if a cycle exists in a graph when performing a topological sort?

The best way to check if a cycle exists in a graph when performing a topological sort is to keep track of the vertices that have been visited. If a vertex is visited twice, then there is a cycle.

8. How do you implement a topological sort using Python or Java?

There are a few different ways to implement a topological sort, but the most common way is to use a depth-first search algorithm. You can find a detailed explanation and example of how to do this in Python here: https://www.geeksforgeeks.org/topological-sorting-indegree-based-solution/

9. What is the time complexity of the implementation of a topological sort in python?

The time complexity of a topological sort is O(V + E), where V is the number of vertices and E is the number of edges.

10. What happens if we try to run a topological sort on an undirected graph?

If we try to run a topological sort on an undirected graph, it will not work because topological sort only works on directed graphs. This is because an undirected graph does not have a direction associated with its edges, so there is no way to determine which order the vertices should be visited in.

11. What are the differences between a linear-time topological sort and a depth first search based topological sort?

A linear-time topological sort is one that can be done in O(n) time, where n is the number of vertices in the graph. A depth first search based topological sort is one that uses a depth first search to find the topological order of the vertices. The main difference is that a linear-time topological sort can be done in O(n) time, while a depth first search based topological sort can take up to O(n^2) time.

12. How does Kahn’s Algorithm work?

Kahn’s Algorithm is a topological sorting algorithm that works by first finding a set of “start nodes” – nodes with no incoming edges – and then removing them from the graph, one at a time. For each node that is removed, we add its outgoing edges to a queue. Once all the start nodes have been removed, we take the next node in the queue (which will now have no incoming edges) and repeat the process.

13. Is there any other alternative to Kahn’s algorithm for implementing topological sort?

There are a few other algorithms that can be used for topological sort, but Kahn’s algorithm is generally considered to be the most efficient. One alternative is the Depth-First Search (DFS) algorithm, which can be used to find the topological order of a graph. However, DFS can be less efficient than Kahn’s algorithm, particularly if the graph is large and/or dense.

14. What is the advantage of using a stack instead of a queue when running a topological sort?

The advantage of using a stack is that it allows you to process the vertices in the order that they are finished, which is the reverse of the order in which they are finished. This is helpful because it means that you can process the vertices in the order that they are needed, which can make the algorithm more efficient.

15. What’s the significance of detecting cycles when running a topological sort?

If there are cycles in the graph, then it is impossible to find a topological ordering. This is because a topological ordering must put all the vertices in a linear order, but if there are cycles then there is no linear order that can satisfy all the edges.

16. Why do you think topological sorts are important?

Topological sorts are important because they can be used to find the order in which a set of tasks need to be completed. For example, if you have a set of tasks that need to be completed in order to finish a project, a topological sort can be used to find the order in which those tasks need to be completed. This can be helpful in ensuring that all of the necessary tasks are completed in the correct order and that no task is missed.

17. What is your understanding of a Directed Acyclic Graph (DAG)?

A DAG is a graph with no cycles. That is, there is no way to start at any node and follow a path that eventually loops back to the starting node. DAGs are often used to model situations where there is a partial order between elements. For example, a topological sort of a DAG G can be used to order the vertices of G so that if there is an edge from u to v, then u appears before v in the ordering.

18. How would you avoid deadlocks in systems that use parallel execution of tasks?

One way to avoid deadlocks is to use a technique called lock ordering. With lock ordering, you establish a strict order in which locks can be acquired. Tasks must acquire all locks in the correct order, and they must release locks in the reverse order. This ensures that no two tasks can ever deadlock each other, because they will always be acquiring and releasing locks in the same order.

19. What is the main difference between a dependency graph and a precedence graph?

A dependency graph is a graph that represents the dependencies between different tasks. A precedence graph is a graph that represents the order in which those tasks must be completed. In a dependency graph, the edges represent the dependencies between the tasks, while in a precedence graph, the edges represent the order in which the tasks must be completed.

20. What is the time complexity of an iterative version of a topological sort vs a recursive version?

The time complexity of an iterative version of a topological sort is O(V + E), while the time complexity of a recursive version is O(V + E).