57 lines
2.3 KiB
Markdown
57 lines
2.3 KiB
Markdown
---
|
||
title: Backtracking Algorithms
|
||
---
|
||
|
||
# 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.
|
||
|
||
### 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.*
|
||
|
||
|
||
|
||
### Path followed by Knight to cover all the cells
|
||
Following is chessboard with 8 x 8 cells. Numbers in cells indicate move number of Knight.
|
||
[![The knight's tour solution - by Euler](https://upload.wikimedia.org/wikipedia/commons/d/df/Knights_tour_%28Euler%29.png)](https://commons.wikimedia.org/wiki/File:Knights_tour_(Euler).png)
|
||
|
||
### Naive Algorithm for Knight’s tour
|
||
The Naive Algorithm is to generate all tours one by one and check if the generated tour satisfies the constraints.
|
||
```
|
||
while there are untried tours
|
||
{
|
||
generate the next tour
|
||
if this tour covers all squares
|
||
{
|
||
print this path;
|
||
}
|
||
}
|
||
```
|
||
|
||
### Backtracking Algorithm for Knight’s tour
|
||
Following is the Backtracking algorithm for Knight’s tour problem.
|
||
```
|
||
If all squares are visited
|
||
print the solution
|
||
Else
|
||
a) Add one of the next moves to solution vector and recursively
|
||
check if this move leads to a solution. (A Knight can make maximum
|
||
eight moves. We choose one of the 8 moves in this step).
|
||
b) If the move chosen in the above step doesn't lead to a solution
|
||
then remove this move from the solution vector and try other
|
||
alternative moves.
|
||
c) If none of the alternatives work then return false (Returning false
|
||
will remove the previously added item in recursion and if false is
|
||
returned by the initial call of recursion then "no solution exists" )
|
||
```
|
||
|
||
|
||
### More Information
|
||
|
||
[Wikipedia](https://en.wikipedia.org/wiki/Backtracking)
|
||
|
||
[Geeks 4 Geeks](http://www.geeksforgeeks.org/backtracking-set-1-the-knights-tour-problem/)
|
||
|
||
[A very interesting introduction to backtracking](https://www.hackerearth.com/practice/basic-programming/recursion/recursion-and-backtracking/tutorial/)
|