Given a solution and image the chess board is transparent. Another solution can be got immediately by turn this chess board (left-right turn). That is, look the solution from other side of chess board. It can be implementing in the manner of computing haft solutions and store these solution in a container in the algorithm. To output all solutions, just output all solutions in container and output others by reversely access the container elements. But things will not so easy. In fact it is almost impossible to utilize this feature when I found that the symmetry solutions generated from one solution can be eight at most and the distribution of symmetry solutions is not regular. For example, 7 queen problem, 0531642 is a solution and because chess board can be viewed from four directions. So label this solution with South indicating view it at South. Respectively label North, East and West on the chess board like map. Then we have solutions: 6304125 E; 4152630 W; 4205316 N and solutions generated by reverse above four solutions: 2461350 RS; 5214036 RE; 0362514 RW; 6135024 RN. Although these 8 solutions are distinct, not all solutions generated with this method will be distinct. For example, 4 queen problem, there are only 2 solutions for it. Apparently, utilizing feature of n queen problem to generating solutions has repetition.
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