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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×n chessboard. Solutions exist for all natural numbers n with the exception of n = 2 and n = 3.
The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of k queens in the first k rows of the board, all in different rows and ...
Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm that finds all solutions to the exact cover problem. 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
Puzzles involving chessboards, including the eight queens puzzle, knight's tours, and the mutilated chessboard problem [1] [3] [4] Balance puzzles [3] River crossing puzzles [3] [4] The Tower of Hanoi [4] Finding the missing element in a data stream [1] The geometric median problem for Manhattan distance [1]
Some hobbyists have developed computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search. [3] Backtracking is a depth-first search (in contrast to a breadth-first search), because it will completely explore one branch to a possible solution before moving to another branch.
Algorithm X is an algorithm for solving the exact cover problem. It is a straightforward recursive , nondeterministic , depth-first , backtracking algorithm used by Donald Knuth to demonstrate an efficient implementation called DLX, which uses the dancing links technique.
I think this is a more clear solution of the problem in Python, but the article's current recursive solution is probably better for readers because it represents how the problem would be solved in most languages. # Print all solutions to 8-queens problem. Public domain, Connelly Barnes 2006.
One way to speed up a brute-force algorithm is to reduce the search space, that is, the set of candidate solutions, by using heuristics specific to the problem class. For example, in the eight queens problem the challenge is to place eight queens on a standard chessboard so that no queen attacks any other.