Cartesian Product and java Algorithm Implementation

Cartesian Product and java Algorithm Implementation
In mathematics, Two SetsXAndYCartesian product, also known as the straight productX×YThe first object isXAnd the second object isYAll possible sequential pairs of a member. Assume that the Set A = {a, B}, and set B = {0, 1}, the Cartesian product of the Two sets is {(a, 0), (a, 1 ), (a, 2), (B, 0), (B, 1), (B, 2 )}.
Java implementation:

 

  
Import java. util. ArrayList;
 
  
Import java. util. List;

  


  
Public class Descartes

  
{

  


  
Public static void run (List <String> dimvalue, List <String> result, int layer, String curstring)

  
{

  
// When the value is greater than one set:

  
If (layer <dimvalue. size ()-1)

  
{

  
// When the value is greater than one set, the first set is empty.

  
If (dimvalue. get (layer). size () = 0)

  
Run (dimvalue, result, layer + 1, curstring );

  
Else

  
{

  
For (int I = 0; I <dimvalue. get (layer). size (); I ++)

  
{

  
StringBuilder s1 = new StringBuilder ();

  
S1.append (curstring );

  
S1.append (dimvalue. get (layer). get (I ));

  
Run (dimvalue, result, layer + 1, s1.toString ());

  
}

  
}

  
}

  
// When there is only one set:

  
Else if (layer = dimvalue. size ()-1)

  
{

  
// There is only one set with no elements in the Set

  
If (dimvalue. get (layer). size () = 0)

  
Result. add (curstring );

  
// When there is only one set and the set contains elements: Its Cartesian product is the set element itself.

  
Else

  
{

  
For (int I = 0; I <dimvalue. get (layer). size (); I ++)

  
{

  
Result. add (curstring + dimvalue. get (layer). get (I ));

  
}

  
}

  
}

  
}

  


  


  
/**
 
  
* @ Param args

  
*/

  
Public static void main (String [] args)

  
{

  
List <String> dimvalue = new ArrayList <List <String> ();

  
List <String> v1 = new ArrayList <String> ();

  
V1.add ("");

  
V1.add ("B ");

  
List <String> v2 = new ArrayList <String> ();

  
V2.add ("c ");

  
V2.add ("d ");

  
V2.add ("e ");

  
List <String> v3 = new ArrayList <String> ();

  
V3.add ("f ");

  
V3.add ("g ");

  


  
Dimvalue. add (v1 );

  
Dimvalue. add (v2 );

  
Dimvalue. add (v3 );

  


  
List <String> result = new ArrayList <String> ();

  


  
Descartes. run (dimvalue, result, 0 ,"");

  


  
Int I = 1;

  
For (String s: result)

  
{

  
System. out. println (I ++ ":" + s );

  
}

  
}

  


  
}
 

Output result:

 

  
1:acf
 
  
2:acg

  
3:adf

  
4:adg

  
5:aef

  
6:aeg

  
7:bcf

  
8:bcg

  
9:bdf

  
10:bdg

  
11:bef

  
12:beg
 

Program instructions (1) treat the elements of each dimension set as List <string>, multiple sets constitute List <string> dimvalue as input (2) put the result of the multi-dimensional Cartesian product into the List <string> result as the output (3) int layer. string curstring is only a parameter of two intermediate processes carrying the variable (4). The program uses recursive calls, an example of the initial call is as follows: