Graph Theory Practical Problems and Algorithms
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Questions and Answers

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?

<p>It is the largest possible subgraph of mutually reachable nodes (D)</p> Signup and view all the answers

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

<p>Depth-first search (A)</p> Signup and view all the answers

What does a strongly connected component represent in a digraph?

<p>A subgraph where all nodes are reachable from each other (A)</p> Signup and view all the answers

Which topic is covered in section 30.19.2?

<p>Knapsack (B)</p> Signup and view all the answers

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

<p>Tractable and intractable problems (C)</p> Signup and view all the answers

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

<p>30.17.4 (D)</p> Signup and view all the answers

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

<p>Beams (C)</p> Signup and view all the answers

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

<p>Back to the TSP (D)</p> Signup and view all the answers

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

<p>30.16.1 (D)</p> Signup and view all the answers

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

<p>Merge sort (B)</p> Signup and view all the answers

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

<p>$O( ext{log } n)$ (D)</p> Signup and view all the answers

Which data structure is commonly used for implementing priority queues?

<p>Heaps (D)</p> Signup and view all the answers

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

<p>Less memory usage for sparse graphs (D)</p> Signup and view all the answers

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

<p>Dijkstra's algorithm (C)</p> Signup and view all the answers

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

<p>To represent all possible states of a problem (A)</p> Signup and view all the answers

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

<p>Ordered and unordered collections (C)</p> Signup and view all the answers

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

<p>Graph modeling (B)</p> Signup and view all the answers

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

<p>Bubble sort (A)</p> Signup and view all the answers

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

<p>Dot product (A)</p> Signup and view all the answers

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

<p>Applying graphs and greedy algorithms (A)</p> Signup and view all the answers

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

<p>Radix sort (B)</p> Signup and view all the answers

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