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Application of Backtracking (#25463)

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@ -6,6 +6,14 @@ title: Backtracking Algorithms
Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons each partial candidate *("backtracks")* as soon as it determines that the candidate cannot possibly be completed to a valid solution. Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons each partial candidate *("backtracks")* as soon as it determines that the candidate cannot possibly be completed to a valid solution.
Application of Backtracking
Examples where backtracking can be used to solve puzzles or problems include:
1) Puzzles such as eight queens puzzle, crosswords, verbal arithmetic, Sudoku [nb 1], and Peg Solitaire.
2) Combinatorial optimization problems such as parsing and the knapsack problem.
3) Logic programming languages such as Icon, Planner and Prolog, which use backtracking internally to generate answers.
### Example Problem (The Knight’s tour problem) ### Example Problem (The Knight’s tour problem)
*The knight is placed on the first block of an empty board and, moving according to the rules of chess, must visit each square exactly once.* *The knight is placed on the first block of an empty board and, moving according to the rules of chess, must visit each square exactly once.*