Graph Theory Practical Problems and Algorithms

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What is the complexity of finding weakly connected components in a digraph?

Θ(n^2)

Θ(n)

Θ(e)

Θ(n + e) (correct)

How can a strongly connected component in a digraph be found?

By computing the connected components of the undirected version of the digraph

By ignoring the direction of edges in the digraph

By finding the largest subgraph of mutually reachable nodes

By repeatedly traversing the original graph and its reverse (correct)

What is the purpose of computing the reverse graph of a digraph?

To represent the inverse relation of the original graph (correct)

To ignore the direction of edges

To find weakly connected components

To increase the size of the graph

How is a connected component defined in an undirected graph?

It is the largest possible subgraph of mutually reachable nodes Signup and view all the answers

Which traversal technique can be used to find weakly connected components in a digraph?

Depth-first search Signup and view all the answers

What does a strongly connected component represent in a digraph?

A subgraph where all nodes are reachable from each other Signup and view all the answers

Which topic is covered in section 30.19.2?

Knapsack Signup and view all the answers

What is covered under the 'Complexity classes' section in the text?

Tractable and intractable problems Signup and view all the answers

In which section of the text can you find information about 'State graphs'?

30.17.4 Signup and view all the answers

What does the topic 'Up and down' relate to in the text?

Beams Signup and view all the answers

What is the focus of the 'Backtracking' section in the text?

Back to the TSP Signup and view all the answers

Which section among 30.16.x talks about 'Jousting'?

30.16.1 Signup and view all the answers

Which sorting algorithm has the best average-case time complexity?

Merge sort Signup and view all the answers

In a binary search tree, what is the time complexity of finding a specific element?

$O( ext{log } n)$ Signup and view all the answers

Which data structure is commonly used for implementing priority queues?

Heaps Signup and view all the answers

What is the main advantage of adjacency list representation over adjacency matrix representation for graphs?

Less memory usage for sparse graphs Signup and view all the answers

Which graph traversal technique guarantees the shortest path between two nodes in a weighted graph?

Dijkstra's algorithm Signup and view all the answers

What is the main purpose of state graphs in computer science?

To represent all possible states of a problem Signup and view all the answers

What topic is covered in the text related to Python language constructs?

Ordered and unordered collections Signup and view all the answers

Which of the following is NOT discussed as a part of rooted trees in the text?

Graph modeling Signup and view all the answers

In Python, which technique is not used for sorting as mentioned in the text?

Bubble sort Signup and view all the answers

Which specific practice exercise is included in the text to reinforce learning?

Dot product Signup and view all the answers

What is the main focus of TMA 02 part 2 as mentioned in the text?

Applying graphs and greedy algorithms Signup and view all the answers

Which of the following is not a sorting technique explained with recursive and iterative versions in the text?

Radix sort Signup and view all the answers