# Minimum Cut Multiple Choice Questions and Answers (MCQs)

This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Minimum Cut”.

1. Which algorithm is used to solve a minimum cut algorithm?
a) Gale-Shapley algorithm
b) Ford-Fulkerson algorithm
c) Stoer-Wagner algorithm
d) Prim’s algorithm

Explanation: Minimum cut algorithm is solved using Stoer-Wagner algorithm. Maximum flow problem is solved using Ford-Fulkerson algorithm. Stable marriage problem is solved using Gale-Shapley algorithm.

2. ___________ is a partition of the vertices of a graph in two disjoint subsets that are joined by atleast one edge.
a) Minimum cut
b) Maximum flow
c) Maximum cut
d) Graph cut

Explanation: Minimum cut is a partition of the vertices in a graph 4. in two disjoint subsets joined by one edge. It is a cut that is minimal in some sense.

3. Minimum cut algorithm comes along with the maximum flow problem.
a) true
b) false

Explanation: Minimum cut algorithm is considered to be an extension of the maximum flow problem. Minimum cut is finding a cut that is minimal.

4. What does the given figure depict?

a) min cut problem
b) max cut problem
c) maximum flow problem
d) flow graph

Explanation: The given figure is a depiction of min cut problem since the graph is partitioned to find the minimum cut.

5. ______________ separates a particular pair of vertices in a graph.
a) line
b) arc
c) cut
d) flow

Explanation: A cut separates a particular pair of vertices in a weighted undirected graph and has minimum possible weight.
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6. What is the minimum number of cuts that a graph with ‘n’ vertices can have?
a) n+1
b) n(n-1)
c) n(n+1)/2
d) n(n-1)/2

Explanation: The mathematical formula for a graph with ‘n’ vertices can at the most have n(n-1)/2 distinct vertices.

7. What is the running time of Karger’s algorithm to find the minimum cut in a graph?
a) O(E)
b) O(|V|2)
c) O(V)
d) O(|E|)

Explanation: The running time of Karger’s algorithm to find the minimum cut is mathematically found to be O(|V|2).

8. _____________ is a family of combinatorial optimization problems in which a graph is partitioned into two or more parts with constraints.
a) numerical problems
b) graph partition
c) network problems
d) combinatorial problems

Explanation: Graph partition is a problem in which the graph is partitioned into two or more parts with additional conditions.

9. The weight of the cut is not equal to the maximum flow in a network.
a) true
b) false

Explanation: According to max-flow min-cut theorem, the weight of the cut is equal to the maximum flow that is sent from source to sink.

10. __________ is a data structure used to collect a system of cuts for solving min-cut problem.
a) Gomory-Hu tree
b) Gomory-Hu graph
c) Dancing tree
d) AA tree

Explanation: Gomory-Hu tree is a weighted tree that contains the minimum cuts for all pairs in a graph. It is constructed in |V|-1 max-flow computations.

11. In how many ways can a Gomory-Hu tree be implemented?
a) 1
b) 2
c) 3
d) 4

Explanation: Gomory-Hu tree can be implemented in two ways- sequential and parallel.

12. The running time of implementing naïve solution to min-cut problem is?
a) O(N)
b) O(N log N)
c) O(log N)
d) O(N2)

Explanation: The running time of min-cut algorithm using naïve implementation is mathematically found to be O(N2).

13. What is the running time of implementing a min-cut algorithm using bidirected edges in a graph?
a) O(N)
b) O(N log N)
c) O(N4)
d) O(N2)

Explanation: The running time of a min-cut algorithm using Ford-Fulkerson method of making edges birected in a graph is mathematically found to be O(N4).

14. Which one of the following is not an application of max-flow min-cut algorithm?
a) network reliability
b) closest pair
c) network connectivity
d) bipartite matching

Explanation: Network reliability, connectivity and bipartite matching are all applications of min-cut algorithm whereas closest pair is a different kind of problem.

15. What is the minimum cut of the following network?

a) ({1,3},{4,3},{4,5})
b) ({1,2},{2,3},{4,5})
c) ({1,0},{4,3},{4,2})
d) ({1,2},{3,2},{4,5})

Explanation: The minimum cut of the given graph network is found to be ({1,3},{4,3},{4,5}) and its capacity is 23.

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