From 0 to 1 Data Structures & Algorithms in Java - Topological Sort In A Graph

The video tutorial introduces graph algorithms, focusing on topological sort. It explains the concept of topological sort as an ordering of vertices in a directed acyclic graph, where each node precedes nodes it has outgoing edges to. The tutorial provides a detailed walkthrough of the topological sort algorithm, emphasizing the importance of in-degree and the conditions for a valid topological sort. The complexity of the algorithm is discussed, and practical examples are used to illustrate the process.

What is the primary purpose of graph algorithms?

• To eliminate nodes from graphs

• To represent data in a linear format

• To find the shortest path and sort edges

• To create cycles in graphs

In a topological sort, what must be true about the ordering of nodes?

• Nodes must be ordered alphabetically

• Each node must come before all nodes it points to

• Each node must come after all nodes it points to

• Nodes can be in any order

What is a key characteristic of a graph that can be topologically sorted?

• It must have equal in-degrees for all nodes

• It must be a directed acyclic graph

• It must be cyclic

• It must be undirected

What is the significance of a node's in-degree in topological sorting?

• It is irrelevant to topological sorting

• It helps identify the starting node for sorting

• It indicates the number of outgoing edges

• It determines the node's color

What happens to a node's in-degree when it is removed from the graph during topological sorting?

• It increases by one

• It remains the same

• It decreases by one for its neighbors

• It becomes zero

Why is it impossible to perform a topological sort on a cyclic graph?

• Because cycles increase the in-degree of all nodes

• Because cycles make the graph undirected

• Because cycles prevent any node from having an in-degree of zero

• Because cycles reduce the number of edges

What is the first step in performing a topological sort on a graph?

• Identify a node with the highest in-degree

• Identify a node with no incoming edges

• Identify a node with the most outgoing edges

• Identify a node with the lowest in-degree

What does the term 'in-degree' refer to in the context of graphs?

• The number of edges a node points to

• The number of edges pointing to a node

• The total number of nodes in the graph

• The number of cycles in the graph

What is the time complexity of the topological sort algorithm?

• O(E^2)

• O(V*E)

• O(V^2)

• O(V+E)

What analogy is used to explain topological sort in real-world terms?

• A set of random numbers

• A list of books

• A sequence of daily tasks

• A shopping list