In chess it is possible to place eight queens on the board so that no one queen can be taken by any other. Write a program that will determine all such possible arrangements for eight queens given the initial position of one of the queens. Do not attempt to write a program which evaluates every possible 8 configuration of 8 queens placed on the board. This would require 88 evaluations and would bring the system to its knees. There will be a reasonable run time constraint placed on your program. Input The first line of the input contains the number of datasets, and it’s followed by a blank line. Each dataset contains a pair of positive integers separated by a single space. The numbers represent the square on which one of the eight queens must be positioned. A valid square will be represented; it will not be necessary to validate the input. To standardize our notation, assume that the upper left-most corner of the board is position (1,1). Rows run horizontally and the top row is row 1. Columns are vertical and column 1 is the left-most column. Any reference to a square is by row then column; thus square (4,6) means row 4, column 6. Each dataset is separated by a blank line. Output Output for each dataset will consist of a one-line-per-solution representation. Each solution will be sequentially numbered 1 . . . N . Each solution will consist of 8 numbers. Each of the 8 numbers will be the ROW coordinate for that solution. The column coordinate will be indicated by the order in which the 8 numbers are printed. That is, the first number represents the ROW in which the queen is positioned in column 1; the second number represents the ROW in which the queen is positioned in column 2, and so on. Notes: The sample input below produces 4 solutions. The full 8×8 representation of each solution is shown below. DO NOT SUBMIT THE BOARD MATRICES AS PART OF YOUR SOLUTION! SOLUTION 1 SOLUTION 2 SOLUTION 3 SOLUTION 4 10000000 10000000 10000000 10000000 00000010 00000010 00000100 00001000 00001000 00010000 00000001 00000001 00000001 00000100 00100000 00000100 01000000 00000001 00000010 00100000 00010000 01000000 00010000 00000010 00000100 00001000 01000000 01000000 00100000 00100000 00001000 00010000
2/2 Submit only the one-line, 8 digit representation of each solution as described earlier. Solution #1 below indicates that there is a queen at Row 1, Column 1; Row 5, Column 2; Row 8, Column 3; Row 6, Column 4; Row 3,Column 5; ... Row 4, Column 8. Include the two lines of column headings as shown below in the sample output and print the solutions in lexicographical order. Sample Input 1 11 Sample Output SOLN COLUMN
1 15863724 2 16837425 3 17468253 4 17582463