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The eight queens puzzle is a special case of the more general n queens problem of placing n non-attacking queens on an n ... Algorithms and Data Structures (PDF).
Some of the better-known exact cover problems include tiling, the n queens problem, and Sudoku. The name dancing links , which was suggested by Donald Knuth , stems from the way the algorithm works, as iterations of the algorithm cause the links to "dance" with partner links so as to resemble an "exquisitely choreographed dance."
For this class of problems, the instance data P would be the integers m and n, and the predicate F. In a typical backtracking solution to this problem, one could define a partial candidate as a list of integers c = (c[1], c[2], …, c[k]), for any k between 0 and n, that are to be assigned to the first k variables x[1], x[2], …, x[k]. The ...
Graphs occur frequently in everyday applications. Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases (e.g. Facebook or LinkedIn).
A brute-force algorithm that finds the divisors of a natural number n would enumerate all integers from 1 to n, and check whether each of them divides n without remainder. A brute-force approach for the eight queens puzzle would examine all possible arrangements of 8 pieces on the 64-square chessboard and for each arrangement, check whether ...
The algorithm searches each potential move for the number of conflicts (number of attacking queens), shown in each square. The algorithm moves the queen to the square with the minimum number of conflicts, breaking ties randomly. Note that the number of conflicts is generated by each new direction that a queen can attack from. If two queens ...
When we discussed the eight queens puzzle at school, I could understand it only because of the explanation and code of N. Wirth (I still have a copy of the book "Algorithms and Data Structures"). I had a lot of trouble understanding the principle of recursion and kept adding print statements to the code and recompiling it again and again until ...
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