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more minor fixes

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Anuj Kaushik 2021-07-02 00:47:19 +05:30
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@ -35,20 +35,18 @@ The library clpfd or Constraint Logic Programming over Finite Domains contains a
of built-in predicates that are useful for solving the Sudoku puzzle easily. of built-in predicates that are useful for solving the Sudoku puzzle easily.
**(ins)/2** states the domains of variables **(ins)/2** states the domains of variables
in some systems: fd_domain/3, domain/ in some systems: fd_domain/3, domain/
**all_distinct/** **all_distinct/**
or alternatively: all_different/1, fd_all_different. or alternatively: all_different/1, fd_all_different.
describes a list of different integers describes a list of different integers
_Examples_ : _Examples_ :<br>
![](sudoku-screenshots/s1.png) ![](sudoku-screenshots/s1.png)
Constraint Propagation: Constraint Propagation:<br>
![](sudoku-screenshots/s2.png) ![](sudoku-screenshots/s2.png)
<br><br>
# CONSISTENCY TECHNIQUES # CONSISTENCY TECHNIQUES
@ -56,15 +54,15 @@ Constraint Propagation:
Using the previous example, the following graph states that X can be either 1 or 2, Y Using the previous example, the following graph states that X can be either 1 or 2, Y
can be either 1 or 2 and Z can be either 1, 2 or 3. can be either 1 or 2 and Z can be either 1, 2 or 3.<br>
![](sudoku-screenshots/g1.png) ![](sudoku-screenshots/g1.png)
This is a value graph for a set of constraints. This is a value graph for a set of constraints.
Prolog automatically reasons about this value graph to detect whether there can still Prolog automatically reasons about this value graph to detect whether there can still
be a solution and also to find out which assignment can not occur in a solution. be a solution and also to find out which assignment can not occur in a solution.<br>
![](sudoku-screenshots/g2.png) ![](sudoku-screenshots/g3.png) ![](sudoku-screenshots/g2.png) &nbsp; ![](sudoku-screenshots/g3.png)
# PROGRAM # PROGRAM
@ -166,14 +164,14 @@ problem(3,Rows), sudoku(Rows), maplist(portray_clause, Rows).
# ANOTHER EXAMPLE # ANOTHER EXAMPLE
Following is the step by step method of how prolog solves the Sudoku puzzle using Following is the step by step method of how prolog solves the Sudoku puzzle using
intelligent constraint propagation. intelligent constraint propagation.<br>
![](sudoku-screenshots/01.png) ![](sudoku-screenshots/02.png) ![](sudoku-screenshots/01.png) &nbsp; ![](sudoku-screenshots/02.png)<br>
![](sudoku-screenshots/03.png) ![](sudoku-screenshots/04.png) ![](sudoku-screenshots/03.png) &nbsp; ![](sudoku-screenshots/04.png)<br>
![](sudoku-screenshots/05.png) ![](sudoku-screenshots/06.png) ![](sudoku-screenshots/05.png) &nbsp; ![](sudoku-screenshots/06.png)<br>
Inconsistent values are indicated by small dots. Black dots represent “obvious” Inconsistent values are indicated by small dots. Black dots represent “obvious”
propagation, whereas, blue dots represent “intelligent” propagation. propagation, whereas, blue dots represent “intelligent” propagation.<br>
![](sudoku-screenshots/07.png) ![](sudoku-screenshots/08.png) ![](sudoku-screenshots/07.png) &nbsp; ![](sudoku-screenshots/08.png)<br>
# REFERENCES # REFERENCES