Data Structures & Algorithms Multiple Choice Questions on “N Queens Problem”.
1. In how many directions do queens attack each other? Answer: c 2. Placing n-queens so that no two queens attack each other is called? Answer: a 3. Where is the n-queens problem implemented? 4. Not more than 2 queens can occur in an n-queens problem. Answer: b 5. In n-queen problem, how many values of n does not provide an optimal solution? Answer: b 6. Which of the following methods can be used to solve n-queen’s problem? Answer: d 7. Of the following given options, which one of the following is a correct option that provides an optimal solution for 4-queens problem? Answer: a 8. How many possible solutions exist for an 8-queen problem? 9. How many possible solutions occur for a 10-queen problem? Answer: d 10. If n=1, an imaginary solution for the problem exists.
a) 1
b) 2
c) 3
d) 4
Clarification: Queens attack each other in three directions- vertical, horizontal and diagonal.
a) n-queen’s problem
b) 8-queen’s problem
c) Hamiltonian circuit problem
d) subset sum problem
Clarification: Placing n queens so that no two queens attack each other is n-queens problem. If n=8, it is called as 8-queens problem.
a) carom
b) chess
c) ludo
d) cards
Answer: b
Clarification: N-queens problem occurs in chess. It is the problem of placing n- queens in a n*n chess board.
a) true
b) false
Clarification: Unlike a real chess game, n-queens occur in a n-queen problem since it is the problem of dealing with n-queens.
a) 1
b) 2
c) 3
d) 4
Clarification: N-queen problem does not provide an optimal solution of only three values of n (i.e.) n=2,3.
a) greedy algorithm
b) divide and conquer
c) iterative improvement
d) backtracking
Clarification: Of the following given approaches, n-queens problem can be solved using backtracking. It can also be solved using branch and bound.
a) (3,1,4,2)
b) (2,3,1,4)
c) (4,3,2,1)
d) (4,2,3,1)
Clarification: Of the following given options for optimal solutions of 4-queens problem, (3, 1, 4, 2) is the right option.
a) 100
b) 98
c) 92
d) 88
Answer: c
Clarification: For an 8-queen problem, there are 92 possible combinations of optimal solutions.
a) 850
b) 742
c) 842
d) 724
Clarification: For a 10-queen problem, 724 possible combinations of optimal solutions are available.
a) true
b) false
Answer: b
Clarification: For n=1, the n-queen problem has a trivial and real solution and it is represented by
11. What is the domination number for 8-queen’s problem? Answer: d 12. Of the following given options, which one of the following does not provides an optimal solution for 8-queens problem? Answer: b
a) 8
b) 7
c) 6
d) 5
Clarification: The minimum number of queens needed to occupy every square in n-queens problem is called domination number. While n=8, the domination number is 5.
a) (5,3,8,4,7,1,6,2)
b) (1,6,3,8,3,2,4,7)
c) (4,1,5,8,6,3,7,2)
d) (6,2,7,1,4,8,5,3)
Clarification: The following given options for optimal solutions of 8-queens problem, (1,6,3,8,3,2,4,7) does not provide an optimal solution.