1 Problem descriptionMain objective: Solve the n queens problems. You have to place n queenson an n n chessboard such that no two attack each other. Important: thechessboard should be indexed startin

1 Problem description

Main objective: Solve the n queens problems. You have to place n queens

on an n n chessboard such that no two attack each other. Important: the

chessboard should be indexed starting from 1, in standard (x; y) coordinates.

Thus, (4; 3) refers to the square in the 4th column and 3rd row.

We have a slight twist in this assignment. We will take as input the position

of one queen, and have to generate a solution with a queen in this position.

Format: You should provide a Makele. On running make, it should create

\NQueens.jar". You should run the jar with two command line arguments:

the rst is an input le, the second is the output le. For example, we would

call the command java -jar NQueens.jar in.txt solution.txt. The le

in.txt will have inputs to the main program (as described below), and the le

solution.txt will have the desired solution.

Each line of the input le corresponds to a dierent instance. Each line of

the input le will have three integers: the chessboard size, the column where

the input queen is placed, and the row where the input queen is placed. For

example, the le may look like:

7 3 2

4 1 1

The rst line means we have a 7 7 chessboard, with one queen placed at

(3; 2). We wish to place 6 more queens without any attacking the other. The second line means we have a 4 4 chessboard, with one queen at (1; 1). We

wish to place 3 more queens without any attacks. So on and so forth.

Output: On running the command, the following should be printed in the

output le. For each line of the input le, there is a line in the output le with

the placement of queens.

• If there is no solution to the problem, print \No solution" (with a newline

at the end)

• If there is a solution, print the position of each queen as <column> <space>

<row> <space> followed by the position for the next queen. The positions

should be in increasing order of column, so rst column rst, second col-

umn second, etc. Please follow this format exactly, so that the checking

script works for you.

For example, the output for the input describe above could be

1 1 2 5 3 2 4 6 5 3 6 7 7 4

No solution

Observe how \3 2" is part of the rst solution, since we started with a queen

there. The solution is not unique, so your code might nd some other placement.

On the other hand, a 4 4 chessboard with a queen at (1; 1) has no solution.