This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Stable Marriage Problem”.

1. Stable marriage problem is an example of?

a) Branch and bound algorithm

b) Backtracking algorithm

c) Greedy algorithm

d) Divide and conquer algorithm

View Answer

Explanation: Stable marriage problem is an example for recursive algorithm because it recursively uses backtracking algorithm to find an optimal solution.

2. Which of the following algorithms does Stable marriage problem uses?

a) Gale-Shapley algorithm

b) Dijkstra’s algorithm

c) Ford-Fulkerson algorithm

d) Prim’s algorithm

View Answer

Explanation: Stable marriage problem uses Gale-Shapley algorithm. Maximum flow problem uses Ford-Fulkerson algorithm. Prim’s algorithm involves minimum spanning tree.

3. An optimal solution satisfying men’s preferences is said to be?

a) Man optimal

b) Woman optimal

c) Pair optimal

d) Best optimal

View Answer

Explanation: An optimal solution satisfying men’s preferences are said to be man optimal. An optimal solution satisfying woman’s preferences are said to be woman optimal.

4. When a free man proposes to an available woman, which of the following happens?

a) She will think and decide

b) She will reject

c) She will replace her current mate

d) She will accept

View Answer

Explanation: When a man proposes to an available woman, she will accept his proposal irrespective of his position on his preference list.

5. If there are n couples who would prefer each other to their actual marriage partners, then the assignment is said to be unstable.

a) True

b) False

View Answer

Explanation: If there are n couples such that a man and a woman are not married, and if they prefer each other to their actual partners, the assignment is unstable.

6. How many 2*2 matrices are used in this problem?

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: Two 2*2 matrices are used. One for men representing corresponding woman and ranking and the other for women.

7. What happens when a free man approaches a married woman?

a) She simply rejects him

b) She simply replaces her mate with him

c) She goes through her preference list and accordingly, she replaces her current mate with him

d) She accepts his proposal

View Answer

Explanation: If the preference of the man is greater, she replaces her current mate with him, leaving her current mate free.

8. In case of stability, how many symmetric possibilities of trouble can occur?

a) 1

b) 2

c) 4

d) 3

View Answer

Explanation: Possibilities- There might be a woman pw, preferred to w by m, who herself prefers m to be her husband and the same applies to man as well.

9. Consider the following ranking matrix.

Assume that M1 and W2 are married. Now, M2 approaches W2. Which of the following happens?

a) W2 replaces M1 with M2

b) W2 rejects M2

c) W2 accepts both M1 and M2

d) W2 rejects both M1 and M2

View Answer

Explanation: W2 is married to M1. But the preference of W2 has M2 before M1. Hence, W2 replaces M1 with M2.

10. Consider the following ranking matrix.

Assume that M1 and W1 are married and M2 and W3 are married. Now, whom will M3 approach first?

a) W1

b) W2

c) W3

d) All three

View Answer

Explanation: M3 will approach W3 first. Since W3 is married and since her preference list has her current mate before M3, she rejects his proposal.

11. Who formulated a straight forward backtracking scheme for stable marriage problem?

a) McVitie and Wilson

b) Gale

c) Ford and Fulkerson

d) Dinitz

View Answer

Explanation: McVitie and Wilson formulated a much faster straight forward backtracking scheme for stable marriage problem. Ford and Fulkerson formulated Maximum flow problem.

12. Can stable marriage cannot be solved using branch and bound algorithm.

a) True

b) False

View Answer

Explanation: Stable marriage problem can be solved using branch and bound approach because branch and bound follows backtracking scheme with a limitation factor.

13. What is the prime task of the stable marriage problem?

a) To provide man optimal solution

b) To provide woman optimal solution

c) To determine stability of marriage

d) To use backtracking approach

View Answer

Explanation: The prime task of stable marriage problem is to determine stability of marriage (i.e) finding a man and a woman who prefer each other to others.

14. Which of the following problems is related to stable marriage problem?

a) Choice of school by students

b) N-queen problem

c) Arranging data in a database

d) Knapsack problem

View Answer

Explanation: Choice of school by students is the most related example in the given set of options since both school and students will have a preference list.

15. What is the efficiency of Gale-Shapley algorithm used in stable marriage problem?

a) O(N)

b) O(N log N)

c) O(N^{2})

d) O(log N)

View Answer

Explanation: The time efficiency of Gale-Shapley algorithm is mathematically found to be O(N

^{2}) where N denotes stable marriage problem.

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