20.8. Pseudo Code for Warshall’s Algorithm

Try these first

1. 1.

   What is the time complexity of Warshall's Algorithm?

   Hint

   Consider the number of nodes involved and the operations performed.

2. 2.

   Define what an intermediate node is.

   Hint

   Think about the structure of the paths in a directed graph.

3. 3.

   What is the output of Warshall's Algorithm?

   • The original matrix.
   • The transitive closure matrix.
   • The adjacency list of the graph.

   Hint

   Consider what the transitive closure represents.

4. 4.

   In Warshall's Algorithm, how do we handle a path when the entry is 0 in the previous matrix?

   • True
   • False

   Hint

   Focus on the update rules for transitioning between matrices.

5. 5.

   Given a directed graph with edges A-B, B-C, and C-D, write the matrices for W(0), W(1), and W(2).

   Hint

   Start with the original edges and follow the definitions for intermediate paths.

6. 6.

   Construct the W(k) matrices from a given relationship and illustrate any new paths formed due to an intermediate node.

   Hint

   Consider the role of each node added as an intermediate in the paths.