5.1. Design and Analysis of Algorithms

Try these first

1. 1.

   What is Kruskal’s algorithm used for?

   Hint

   Think about connecting points with the least cost.

2. 2.

   What is the first step in Kruskal’s algorithm?

   Hint

   Remember the importance of edge weight.

3. 3.

   What is the primary purpose of Kruskal's algorithm?

   • To find the shortest path in a graph
   • To find the minimum spanning tree of a graph
   • To sort the vertices of a graph

   Hint

   Think about the tree that connects all points with the least cost.

4. 4.

   True or False: Prim's algorithm and Kruskal's algorithm can be used interchangeably.

   • True
   • False

   Hint

   Consider how each algorithm builds its solution.

5. 5.

   Given a graph with vertices A, B, C, and D and edges with weights AB: 1, AC: 4, BD: 3, CD: 2, demonstrate the application of Kruskal's algorithm step by step.

   Hint

   Visualize each step, keeping an eye on what edges you can add.

6. 6.

   Consider a scenario where an edge in Kruskal's algorithm with the lowest weight forms a cycle. How would the algorithm proceed?

   Hint

   Think about the conditions necessary for an edge to be part of the tree.