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## Prim's Algorithm Multiple choice Questions and Answers (MCQs)

Question 1 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

Which of the following is true?

Prim's algorithm initialises with a vertex | |

Prim's algorithm initialises with a edge | |

Prim's algorithm initialises with a vertex which has smallest edge | |

Prim's algorithm initialises with a forest |

Question 1 Explanation:

Steps in Prim's algorithm: (I) Select any vertex of given graph and add it to MST (II) Add the edge of minimum weight from a vertex not in MST to the vertex in MST; (III) It MST is complete the stop, otherwise go to step (II).

Question 2 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

Consider the given graph.

What is the weight of the minimum spanning tree using the Prim's algorithm, starting from vertex a?

23 | |

28 | |

27 | |

11 |

Question 3 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

Worst case is the worst case time complexity of Prim's algorithm if adjacency matrix is used?

O(log V) | |

O(V ^{2}) | |

O(E ^{2}) | |

O(V log E) |

Question 3 Explanation:

Use of adjacency matrix provides the simple implementation of the Prim's algorithm. In Prim's algorithm, we need to search for the edge with a minimum for that vertex. So, worst case time complexity will be O(V

^{2}), where V is the number of vertices.Question 4 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

Prim's algorithm is a .....

Divide and conquer algorithm | |

Greedy algorithm | |

Dynamic Programming | |

Approximation algorithm |

Question 4 Explanation:

Prim's algorithm uses a greedy algorithm approach to find the MST of the connected weighted graph. In greedy method, we attempt to find an optimal solution in stages.

Question 5 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

Prim's algorithm resembles Dijkstra's algorithm.

True | |

False |

Question 5 Explanation:

In Prim's algorithm, the MST is constructed starting from a single vertex and adding in new edges to the MST that link the partial tree to a new vertex outside of the MST. And Dijkstra's algorithm also rely on the similar approach of finding the next closest vertex. So, Prim's algorithm resembles Dijkstra's algorithm.

There are 5 questions to complete.