Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) on “Stable Marriage Problem”.
1. Stable marriage problem is an example of? Answer: b 2. Which of the following algorithms does Stable marriage problem uses? Answer: a 3. An optimal solution satisfying men’s preferences is said to be? Answer: a 4. When a free man proposes to an available woman, which of the following happens? Answer: d 5. If there are n couples who would prefer each other to their actual marriage partners, then the assignment is said to be unstable. Answer: a 6. How many 2*2 matrices are used in this problem? Answer: b 7. What happens when a free man approaches a married woman? Answer: c 8. In case of stability, how many symmetric possibilities of trouble can occur? Answer: b 9. Consider the following ranking matrix. Assume that M1 and W2 are married. Now, M2 approaches W2. Which of the following happens? Answer: a 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? Answer: c 11. Who formulated a straight forward backtracking scheme for stable marriage problem? 12. Can stable marriage cannot be solved using branch and bound algorithm. Answer: b 13. What is the prime task of the stable marriage problem? Answer: c 14. Which of the following problems is related to stable marriage problem? Answer: a 15. What is the efficiency of Gale-Shapley algorithm used in stable marriage problem? Answer: c
a) Branch and bound algorithm
b) Backtracking algorithm
c) Greedy algorithm
d) Divide and conquer algorithm
Clarification: Stable marriage problem is an example for recursive algorithm because it recursively uses backtracking algorithm to find an optimal solution.
a) Gale-Shapley algorithm
b) Dijkstra’s algorithm
c) Ford-Fulkerson algorithm
d) Prim’s algorithm
Clarification: Stable marriage problem uses Gale-Shapley algorithm. Maximum flow problem uses Ford-Fulkerson algorithm. Prim’s algorithm involves minimum spanning tree.
a) Man optimal
b) Woman optimal
c) Pair optimal
d) Best optimal
Clarification: 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.
a) She will think and decide
b) She will reject
c) She will replace her current mate
d) She will accept
Clarification: When a man proposes to an available woman, she will accept his proposal irrespective of his position on his preference list.
a) True
b) False
Clarification: 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.
a) 1
b) 2
c) 3
d) 4
Clarification: Two 2*2 matrices are used. One for men representing corresponding woman and ranking and the other for women.
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
Clarification: If the preference of the man is greater, she replaces her current mate with him, leaving her current mate free.
a) 1
b) 2
c) 4
d) 3
Clarification: 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.
a) W2 replaces M1 with M2
b) W2 rejects M2
c) W2 accepts both M1 and M2
d) W2 rejects both M1 and M2
Clarification: W2 is married to M1. But the preference of W2 has M2 before M1. Hence, W2 replaces M1 with M2.
a) W1
b) W2
c) W3
d) All three
Clarification: M3 will approach W3 first. Since W3 is married and since her preference list has her current mate before M3, she rejects his proposal.
a) McVitie and Wilson
b) Gale
c) Ford and Fulkerson
d) Dinitz
Answer: a
Clarification: McVitie and Wilson formulated a much faster straight forward backtracking scheme for stable marriage problem. Ford and Fulkerson formulated Maximum flow problem.
a) True
b) False
Clarification: Stable marriage problem can be solved using branch and bound approach because branch and bound follows backtracking scheme with a limitation factor.
a) To provide man optimal solution
b) To provide woman optimal solution
c) To determine stability of marriage
d) To use backtracking approach
Clarification: 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.
a) Choice of school by students
b) N-queen problem
c) Arranging data in a database
d) Knapsack problem
Clarification: 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.
a) O(N)
b) O(N log N)
c) O(N2)
d) O(log N)
Clarification: The time efficiency of Gale-Shapley algorithm is mathematically found to be O(N2) where N denotes stable marriage problem.