Engineering Questions with Answers - Multiple Choice Questions
Hamiltonian Path Problem Multiple Choice MCQ
1 - Question
Which of the following algorithm can be used to solve the Hamiltonian path problem efficiently?
a) branch and bound
b) iterative improvement
c) divide and conquer
d) greedy algorithm
View Answer
Answer: a
Explanation: The Hamiltonian path problem can be solved efficiently using branch and bound approach. It can also be solved using a backtracking approach.
2 - Question
The problem of finding a path in a graph that visits every vertex exactly once is called?
a) Hamiltonian path problem
b) Hamiltonian cycle problem
c) Subset sum problem
d) Turnpike reconstruction problem
View Answer
Answer: a
Explanation: Hamiltonian path problem is a problem of finding a path in a graph that visits every node exactly once whereas Hamiltonian cycle problem is finding a cycle in a graph.
3 - Question
Hamiltonian path problem is _________
a) NP problem
b) N class problem
c) P class problem
d) NP complete problem
View Answer
Answer: d
Explanation: Hamiltonian path problem is found to be NP complete. Hamiltonian cycle problem is also an NP- complete problem.
4 - Question
There is no existing relationship between a Hamiltonian path problem and Hamiltonian circuit problem.
a) true
b) false
View Answer
Answer: b
Explanation: There is a relationship between Hamiltonian path problem and Hamiltonian circuit problem. The Hamiltonian path in graph G is equal to Hamiltonian cycle in graph H under certain conditions.
5 - Question
Which of the following problems is similar to that of a Hamiltonian path problem?
a) knapsack problem
b) closest pair problem
c) travelling salesman problem
d) assignment problem
View Answer
Answer: c
Explanation: Hamiltonian path problem is similar to that of a travelling salesman problem since both the problem traverses all the nodes in a graph exactly once.
6 - Question
Who formulated the first ever algorithm for solving the Hamiltonian path problem?
a) Martello
b) Monte Carlo
c) Leonard
d) Bellman
View Answer
Answer: a
Explanation: The first ever problem to solve the Hamiltonian path was the enumerative algorithm formulated by Martello.
7 - Question
In what time can the Hamiltonian path problem can be solved using dynamic programming?
a) O(N)
b) O(N log N)
c) O(N2)
d) O(N2 2N)
View Answer
Answer: d
Explanation: Using dynamic programming, the time taken to solve the Hamiltonian path problem is mathematically found to be O(N2 2N).
8 - Question
In graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.
a) true
b) false
View Answer
Answer: a
Explanation: According to a handshaking lemma, in graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.
9 - Question
Who invented the inclusion-exclusion principle to solve the Hamiltonian path problem?
a) Karp
b) Leonard Adleman
c) Andreas Bjorklund
d) Martello
View Answer
Answer: c
Explanation: Andreas Bjorklund came up with the inclusion-exclusion principle to reduce the counting of number of Hamiltonian cycles.
10 - Question
For a graph of degree three, in what time can a Hamiltonian path be found?
a) O(0.251n)
b) O(0.401n)
c) O(0.167n)
d) O(0.151n)
View Answer
Answer: a
Explanation: For a graph of maximum degree three, a Hamiltonian path can be found in time O(0.251n).
11 - Question
What is the time complexity for finding a Hamiltonian path for a graph having N vertices (using permutation)?
a) O(N!)
b) O(N! * N)
c) O(log N)
d) O(N)
View Answer
Answer: b
Explanation: For a graph having N vertices traverse the permutations in N! iterations and it traverses the permutations to see if adjacent vertices are connected or not takes N iterations (i.e.) O(N! * N).
12 - Question
How many Hamiltonian paths does the following graph have?
a) 1
b) 2
c) 3
d) 4
View Answer
Answer: a
Explanation: The above graph has only one Hamiltonian path that is from a-b-c-d-e.
13 - Question
How many Hamiltonian paths does the following graph have?
a) 1
b) 2
c) 0
d) 3
View Answer
Answer: c
Explanation: The above graph has no Hamiltonian paths. That is, we cannot traverse the graph with meeting vertices exactly once.