Graphs: Chapter 21
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Questions and Answers

What is the main difference between directed and undirected graphs?

  • Directed graphs contain cycles, while undirected graphs do not contain cycles.
  • In undirected graphs, nodes have labels, while in directed graphs, nodes do not have labels.
  • Directed graphs have only one connected component, while undirected graphs can have multiple connected components.
  • In directed graphs, edges have a direction, while in undirected graphs, edges do not have a direction. (correct)

    • What does it mean for nodes to be mutually reachable in a graph?

  • Nodes are mutually reachable if there is an edge between every pair of nodes.
  • Nodes are mutually reachable if there is a path from each node to every other node.
  • Nodes are mutually reachable if there is a cycle that passes through each node exactly once.
  • Nodes are mutually reachable if there is a path from one node to another, regardless of the direction. (correct)

    • What is the purpose of determining subgraphs of mutually reachable nodes in a graph?

  • To find the shortest path between any two nodes in the graph.
  • To determine if there is a path between two specific nodes in the graph.
  • To calculate the total number of nodes in the graph.
  • To identify groups of nodes that are not connected in the graph. (correct)

    • Which type of graph has separate subgraphs of mutually reachable nodes?

    <p>Undirected graphs</p> Signup and view all the answers

    What is the significance of knowing if two nodes are connected in a graph?

    <p>It helps identify components that are isolated from the rest of the graph.</p> Signup and view all the answers

    Why might determining connected components be important in analyzing a graph?

    <p>To optimize memory usage by grouping related nodes together.</p> Signup and view all the answers

    What does it mean for a node to be part of a connected component in a graph?

    <p>The node belongs to a group of nodes that are all mutually reachable.</p> Signup and view all the answers

    How can subgraphs help analyze undirected graphs?

    <p>By identifying isolated areas or clusters within the graph.</p> Signup and view all the answers

    What role do undirected graph components play in computational problem-solving?

    <p>They allow for determining if there's a connection between given nodes without needing to know the actual paths.</p> Signup and view all the answers

    Why might knowing about undirected graph components benefit software design choices?

    <p>To decide how to group related nodes for efficient data processing.</p> Signup and view all the answers

    What is the main reason the author simplified the BFS algorithm for the knight moves problem?

    <p>To avoid calculating the shortest path length</p> Signup and view all the answers

    What is the 'moral' of the problem presented in the text?

    <p>Model the problem as a graph and apply standard graph algorithms</p> Signup and view all the answers

    What is the time complexity of the approach described in the text?

    <p>Θ(n + e)</p> Signup and view all the answers

    What type of graph algorithm is used in the solution described in the text?

    <p>Breadth-First Search (BFS)</p> Signup and view all the answers

    What is the purpose of the 'test table' mentioned in the text?

    <p>To validate the correctness of the rook moves implementation</p> Signup and view all the answers

    What is the purpose of representing a problem as a graph?

    <p>To apply standard graph algorithms to the problem</p> Signup and view all the answers

    What is the significance of the length of the path in the knight moves problem?

    <p>The length of the path is not asked for, only its length</p> Signup and view all the answers

    What is the purpose of constructing the 'test table' mentioned in the text?

    <p>To validate the correctness of the rook moves implementation</p> Signup and view all the answers

    What is the main difference between directed and undirected graphs?

    <p>Directed graphs have a specific direction associated with each edge, while undirected graphs do not</p> Signup and view all the answers

    What is the significance of knowing if two nodes are connected in a graph?

    <p>It allows you to identify the connected components in the graph</p> Signup and view all the answers

    What is the purpose of the is_cyclic function described in the text?

    <p>To determine if a directed graph has a cycle</p> Signup and view all the answers

    What does the term 'strongly connected component' refer to in the context of graphs?

    <p>A set of nodes in a directed graph where every node is reachable from every other node</p> Signup and view all the answers

    What is the significance of the test cases provided in the text?

    <p>They are used to check the correctness of the <code>is_cyclic</code> function</p> Signup and view all the answers

    What is the worst-case time complexity of Bob's algorithm for detecting cycles in a digraph, as described in the text?

    <p>O(n + m)</p> Signup and view all the answers

    What is the significance of the digraph and spreadsheet variables in the test cases?

    <p>They represent different types of graphs used for testing</p> Signup and view all the answers

    What is the purpose of the test function mentioned in the text?

    <p>To compare the output of the <code>is_cyclic</code> function with the expected results</p> Signup and view all the answers

    What is the significance of the add_node and add_edge methods used in the code?

    <p>They are used to construct the input graphs for the <code>is_cyclic</code> function</p> Signup and view all the answers

    What is the purpose of the %run command used in the code?

    <p>To import the necessary functions and classes for graph operations</p> Signup and view all the answers

    What is the significance of the 'ABCDEF' string in the code?

    <p>It represents the node labels for the input graph</p> Signup and view all the answers

    What is the purpose of the 'AB', 'BC', 'CA', 'DE' tuple in the code?

    <p>It specifies the edges to be added to the input graph</p> Signup and view all the answers

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