Top MCQs on Shortest Paths in Graphs with Answers

Question 21

The Floyd-Warshall algorithm for all-pair shortest paths computation is based on:

• Greedy paradigm.
• Divide-and-Conquer paradigm.
• Dynamic Programming paradigm.
• neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.

Question 22

Consider a weighted undirected graph with positive edge weights and let uv be an edge in the graph. It is known that the shortest path from the source vertex s to u has weight 53 and the shortest path from s to v has weight 65. Which one of the following statements is always true?

• weight (u, v) < 12
• weight (u, v) ≤ 12
• weight (u, v) > 12
• weight (u, v) ≥ 12

Question 23

Which of the following algorithm solves the all-pair shortest path problem?

• Prim’s algorithm
• Dijikstra’s algorithm
• Bellman-Ford’s algorithm
• Floyd-Warshall’s algorithm

Question 24

Which one of the following algorithm design techniques is used in finding all pairs of shortest distances in a graph?

• Dynamic programming
• Backtracking
• Greedy
• Divide and Conquer

Question 25

Which of the following is application of Breath First Search on the graph?

• Finding diameter of the graph
• Finding bipartite graph
• Both (a) and (b)
• None of the above

Question 26

Which of the following data structure is useful in traversing a given graph by breadth first search?

• Stack
• List
• Queue
• None of the above.

Question 27

Let G=(V,E) be a directed, weighted graph with weight function w:E→R. For some function f:V→R, for each edge (u,v)∈E, define w′(u,v) as w(u,v)+f(u)−f(v). Which one of the options completes the following sentence so that it is TRUE ? “The shortest paths in G under w are shortest paths under w′ too, _________”.

• for every f:V→R
• if and only if ∀u∈V, f(u) is positive
• if and only if ∀u∈V, f(u) is negative
• if and only if f(u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of G

Question 28

Given a directed graph where weight of every edge is same, we can efficiently find shortest path from a given source to destination using?

• Breadth First Traversal

• Dijkstra\'s Shortest Path Algorithm

• Neither Breadth First Traversal nor Dijkstra\'s algorithm can be used

• Depth First Search