59 lines
2.3 KiB
Markdown
59 lines
2.3 KiB
Markdown
---
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title: Backtracking Algorithms
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---
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# Backtracking Algorithms
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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.
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### Example Problem (The Knight’s tour problem)
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*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.*
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### Path followed by Knight to cover all the cells
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Following is chessboard with 8 x 8 cells. Numbers in cells indicate move number of Knight.
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[](https://commons.wikimedia.org/wiki/File:Knights_tour_(Euler).png)
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### Naive Algorithm for Knight’s tour
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The Naive Algorithm is to generate all tours one by one and check if the generated tour satisfies the constraints.
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```
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while there are untried tours
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{
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generate the next tour
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if this tour covers all squares
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{
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print this path;
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}
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}
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```
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### Backtracking Algorithm for Knight’s tour
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Following is the Backtracking algorithm for Knight’s tour problem.
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```
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If all squares are visited
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print the solution
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Else
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a) Add one of the next moves to solution vector and recursively
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check if this move leads to a solution. (A Knight can make maximum
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eight moves. We choose one of the 8 moves in this step).
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b) If the move chosen in the above step doesn't lead to a solution
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then remove this move from the solution vector and try other
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alternative moves.
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c) If none of the alternatives work then return false (Returning false
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will remove the previously added item in recursion and if false is
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returned by the initial call of recursion then "no solution exists" )
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```
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### More Information
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[Wikipedia](https://en.wikipedia.org/wiki/Backtracking)
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[Geeks 4 Geeks](http://www.geeksforgeeks.org/backtracking-set-1-the-knights-tour-problem/)
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[A very interesting introduction to backtracking](https://www.hackerearth.com/practice/basic-programming/recursion/recursion-and-backtracking/tutorial/)
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[A YouTube demonstration](https://www.youtube.com/watch?v=gBC_Fd8EE8A)
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