N Queen Problem

Title

N Queen Problem

Problem

Given the size of a chessboard and the number of Queens n as an input parameter, write a solution function that returns the number of possible ways to place n Queens on an n $\times$ n chessboard such that no two Queens attack each other.

Background Information

• The N-Queen problem is a classical problem in which n Queens are placed on an n $\times$ n chessboard such that no two Queens attack each other.
• A Queen can attack any other piece in all vertical, horizontal, and diagonal directions, regardless of distance.

Constraints

• n is a natural number between 3 and 12, inclusive.

Test Case Explanation

Explanation for Test Case 1

• For a 3 $\times$ 3 chessboard, it is impossible to place 3 Queens such that no two Queens attack each other. Thus, the result is 0.

Explanation for Test Case 2

• For a 5 $\times$ 5 chessboard, there are 10 ways to place 5 Queens such that no two Queens attack each other.
• One of these arrangements is shown below:

Explanation for Test Case 3

• For an 8 $\times$ 8 chessboard, there are 92 ways to place 8 Queens such that no two Queens attack each other.
• One of these arrangements is shown below: