Topological sorting in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to identify the type of graph suitable for topological sorting.

Data Structures Theory

A topological sort can only be performed on a [1] graph.

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Adirected acyclic

Bcyclic

Cundirected

Dweighted

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing cyclic graphs because they have directions.

Thinking undirected graphs can be topologically sorted.

Topological sorting is only possible on directed acyclic graphs (DAGs) because cycles prevent a linear ordering.

2fill in blank

medium

Complete the code to describe the output of a topological sort.

Data Structures Theory

The output of a topological sort is a [1] of the vertices such that for every directed edge u -> v, u comes before v.

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Atree structure

Brandom order

Creverse order

Dlinear ordering

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing topological sort with sorting by value.

Thinking the output is a tree or graph structure.

Topological sorting produces a linear ordering of vertices respecting the direction of edges.

3fill in blank

hard

Fix the error in the statement about cycle detection in topological sorting.

Data Structures Theory

If a graph contains a cycle, topological sorting [1] be performed.

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Acan always

Bmight

Ccannot

Dshould

Attempts:

3 left

💡 Hint

Common Mistakes

Assuming cycles can be ignored.

Thinking topological sort can handle any graph.

Topological sorting cannot be performed on graphs with cycles because no linear ordering exists that respects all edges.

4fill in blank

hard

Fill both blanks to complete the description of a common algorithm for topological sorting.

Data Structures Theory

One common method uses Depth-First Search (DFS) and adds each vertex to a stack after visiting all its [1]. Then, the stack is [2] to get the topological order.

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Aneighbors

Bchildren

Creversed

Dsorted

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'neighbors' instead of 'children' which is less precise here.

Sorting the stack instead of reversing it.

The DFS method visits all children (outgoing edges) before adding a vertex to the stack. Reversing the stack gives the topological order.

5fill in blank

hard

Fill all three blanks to complete the pseudocode for Kahn's algorithm for topological sorting.

Data Structures Theory

Initialize a queue with all vertices having [1] zero. While the queue is not empty, remove a vertex [2] and add it to the result. Then, decrease the [3] of its neighbors by one.

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Ain-degree

Bfront

Dout-degree

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing in-degree with out-degree.

Removing vertices from the back instead of the front.

Kahn's algorithm starts with vertices with in-degree zero, processes them from the front of the queue, and decreases the in-degree of their neighbors.