The New Sudoku Players' Forum

[StrmCkr]

Strong link
0). Bivalves cells {internal relation }

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.  .  . | . AB . | . . .


1).2 bi locals in a row/Col/Box

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/  x  / | /  /  / | /  x  /


2). 1 cell in Row/Col in a box with 2-3 cells in a same row/col in a box

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/  x  / |  /  /  /  |  x  x  x


3). 2-3 cell in Row/Col in a box with 1 cells in a same row/col in a box

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x  x  x  |  /  /  /  |  /  x  /


4). 2-3 cells in a row/col in a box with 2-3 cells in same row/col in a diffrent box

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x  x  x  |  /  /  /  |  x  x  x


5). Empty rectangle intersection {E.R.I} the sum of all digits in a box are found on 1 col and 1 row see Note at bottom of section


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/ x /
x * x
/ x /


Note:ERI's are an exception to a valid chain starting spot it can be used only if the center cell is absent as this leaves either the row or col true, the * cell is used as a pivot between row/col

Weakly Linked called a Weak inference
exists in cells that are part of a strong link set, that see parts of another strong link sets without being part of it, or directly seeing all of it.
0,0). Bivalve that sees another bivalve with digit shared


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.  .  . | . AB . | . . .
.  .  . | . BC . | . . .



0,1). Bivalve that sees 1 digit of bi-local digit


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.  AB  . | .  .  . | .  .  .
/  x   / | /  /  / | /  x  /


0,2). Bivalve that sees the 1 cell in Row/Col in a box with 2-3 cells in a same row/col in a different box


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.  AB  . | .  .  . | .  .  .
/  x   / | /  /  / | x  x  x



0,3). Bivalve that sees the 2-3 cells in Row/Col in a box with 1 cells in a same row/col in a different box


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.  AB  . | .  .  . | .  .  .
x  x   x | /  /  / | /  x  /



0,4). Bivalve that sees the 2-3 cells in Row/Col in a box with 2-3 cells in a same row/col in a different box


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.  AB  . | .  .  . | .  .  .
x  x   x | /  /  / | x  x  x



0,5). Bivalve that sees an ERI's * cell


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.  AB  . | .  .  . | .  .  .
----------------------------
/  x   / |
x  *   x |
/  x   / |



1,0) a bi-local digit that 1 cell sees a bivalve


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/  x   / | /  /  / | /  x  /
.  AB  . | .  .  . | .  .  .



1,1) a bi-local digit that 1 of the cells sees a bi-local digit


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/  x   / | /  /  / | /  x  /
/  x   / | /  /  / | /  x  /



1,2) a bi-local digit that 1 of the cells sees the 1 cell in Row/Col in a box with 2-3 cells in a same row/col in a different box


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/  x   / | /  /  / | /  x  /
/  x   / | /  /  / | x  x  x



1,3) a bi-local digit that 1 of the cells sees the 2-3 cells in Row/Col in a box with 1 cells in a same row/col in a different box


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/  x   / | /  /  / | /  x  /
x  x   x | /  /  / | /  x  /



1,4) a bi-local digit that 1 of the cells sees all the 2-3 cells in Row/Col in a box with 2-3 cells in a same row/col in a different box


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/  x   / | /  /  / | /  x  /
x  x   x | /  /  / | x  x  x


1,5) a bi-local digit that 1 of the cells sees the * cell of an ERI


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/  x   / | /  /  / | /  x  /
----------------------------
/  x   / |
x  *   x |
/  x   / |


2,0). 1 cell in Row/Col in a box with 2-3 cells in a same row/col in a different box, where the 1 cell sees the bivalve


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/  x   / | /  /  / | x  x  x
.  AB  . | .  .  . | .  .  .



2,1). 1 cell in Row/Col in a box with 2-3 cells in a same row/col in a different box, where the 1 cell sees 1 cell of a bi local digit.


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/  x   / | /  /  / | x  x  x
/  x   / | /  /  / | /  x  /



2,2). 1 cell in Row/Col in a box with 2-3 cells in a same row/col in a different box, where the 1 cell sees the "1" cell in Row/Col in a box with 2-3 cells in a same row/col in a different box


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/  x   / | /  /  / | x  x  x
/  x   / | /  /  / | x  x  x



2,3). 1 cell in Row/Col in a box with 2-3 cells in a same row/col in a different box, where the 1 cell sees the "2-3" cell in Row/Col in a box with 1 cells in a same row/col in a different box


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/  x   / | /  /  / | x  x  x
x  x   x | /  /  / | /  x  /



2,4). 1 cell in Row/Col in a box with 2-3 cells in a same row/col in a different box, where the 1 cell sees the "2-3" cell in Row/Col in a box with 2-3 cells in a same row/col in a different box


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/  x   / | /  /  / | x  x  x
x  x   x | /  /  / | x  x  x



2,5). 1 cell in Row/Col in a box with 2-3 cells in a same row/col in a different box, where the 1 cell sees the * cell of an eri


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/  x   / | /  /  / | x  x  x
----------------------------
/  x  /  |
x  *  x  |
/  x  /  |


3,0). the 2-3 cells in Row/Col in a box with 1 cells in a same row/col in a different box where the Bivalve that sees 2-3 cell.


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x  x   x | /  /  / | /  x  /
.  AB  . | .  .  . | .  .  .



3,1) the 2-3 cells in Row/Col in a box with 1 cells in a same row/col in a different box where the bi-local digit that 1 of the cells sees 2-3 cells


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x  x   x | /  /  / | /  x  /
/  x   / | /  /  / | /  x  /



3,2). 3-2 cell in Row/Col in a box with 1 cell in a same row/col in a different box, where the 2-3 cell sees the "1" cell in Row/Col in a box with 2-3 cells in a same row/col in a different box


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x  x   x | /  /  / | /  x  /
/  x   / | /  /  / | x  x  x



3,3). 3-2 cell in Row/Col in a box with 1 cell in a same row/col in a different box, where the 2-3 cell sees the "2-3" cells in Row/Col in a box with 1 cell in a same row/col in a different box


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x  x   x | /  /  / | /  x  /
x  x   x | /  /  / | /  x  /



3,4). 3-2 cell in Row/Col in a box with 1 cell in a same row/col in a different box, where the 2-3 cell sees the "2-3" cells in Row/Col in a box with 2-3 cell in a same row/col in a different box


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x  x   x | /  /  / | /  x  /
x  x   x | /  /  / | x  x  x



3,5).

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 NO valid formation



4,0). the 2-3 cells in Row/Col in a box with 2-3 cells in a same row/col in a different box where the 2-3 cell sees the Bivalve


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x  x   x | /  /  / | x  x  x
.  AB  . | .  .  . | .  .  .



4,1) 2-3 cells in Row/Col in a box with 2-3 cells in a same row/col in a different box where a bi-local digit sees all of one boxes digits.


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x  x   x | /  /  / | x  x  x
/  x   / | /  /  / | /  x  /



4,2). 2-3 cell in Row/Col in a box with 2-3 cells in a same row/col in a different box, where the (2-3) cell sees the "1" cell in Row/Col in a box with 2-3 cells in a same row/col in a different box


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x  x   x | /  /  / | x  x  x
/  x   / | /  /  / | x  x  x



4,3). 3-2 cell in Row/Col in a box with 2-3 cell in a same row/col in a different box, where the 2-3 cell sees the "2-3" cells in Row/Col in a box with 1 cell in a same row/col in a different box


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x  x   x | /  /  / | x  x  x
x  x   x | /  /  / | /  x  /



4,4). 3-2 cell in Row/Col in a box with 2-3 cell in a same row/col in a different box, where the 2-3 cell sees the "2-3" cells in Row/Col in a box with 2-3 cell in a same row/col in a different box


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x  x   x | /  /  / | x  x  x
x  x   x | /  /  / | x  x  x



4,5).


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no valid formation



5,0). an ERI's * cell sees the Bivalve


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/  x   / |
x  *   x |
/  x   / |
----------------------------
.  AB  . | .  .  . | .  .  .



5,1) the * cell of an ERI sees the 1 of the bi-local digit


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/  x   / |
x  *   x |
/  x   / |
----------------------------
/  x   / | /  /  / | /  x  /



5,2). the * cell of an eri see the "1" digit in a row/col of a box with 2-3 cells in same row/col of a different box.


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/  x  /  |
x  *  x  |
/  x  /  |
----------------------------
/  x   / | /  /  / | x  x  x



5,3).

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 NO valid formation



5,4).


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no valid formation




5,5). the * cell an ERI sees the * sell of a 2nd ERI


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/  x  /  |
x  *  x  |
/  x  /  |
----------------------------
/  x  /  |
x  *  x  |
/  x  /  |


.......work in progress........

[StrmCkr]

what to do with all that data:

data save: Show

Code: Select all

{link type data base}
Linkset : stronglk; // array [ 0..9][0..5][0..9] of numberset[0..80]//setwise
{digit selected[1..9]}
{0: bivavel,
1:  2 cells in a sector
2: cell in sector , grouped link to another = all digits in that sector
3: cells in sector, as a grouped link to a single cell = all digits in that sector
4: cells in sector, as a grouped link to a grouped node = all digits in that sector
5: ERI}
{ internal data as:
 0 starting digit,
 1 active cell,
 2  linked cells,
 3 next link digit,
 4  sector its in,
 5 peers sector the link cells are is in.
 6  previous - digit swap is applicable 0 = off
 7 digit swap is applicable 0 = off
 8 potential elimination cells for basic ...end cell
 9 potential elimination for ring codes  ...start cell
 }

strong link builder: Show

Code: Select all

Procedure links;{rebuild}
var
N,xn,q,j,a,b,c,d,e,m,n2:integer;
 output: text;
 used:numberset;
begin
setlength(Linkset,10,6,0);

for n:= 1 to 9 do
begin
q:=-1;
A:=-1;
b:=-1;
c:=-1;
D:=-1;
e:=-1;
used:=[];
 for xn:= 0 to 26 do
   begin

    {bivavle cell}
    if DigitRCB[xn,n] <> []
     then
      begin
             for J in (DigitRCB[xn,n]-used) do
        if nm[j] = 2
          then
              begin
              include(used,j);
           inc(q);         
           setlength(linkset[n][0],q+1);
         
           include(linkset[n][0][q,0],n);
           include(linkset[n][0][q,1],j);

              linkset[n][0][q,2]:=[j];
             
           for m in (pm[j]-[n]) do
            begin
              include(linkset[n][0][q,3],m);         
            linkset[n][0][q,9]:= peer[j] * digitcell[m];
            end;             

              linkset[n][0][q,4]:=cellsec[j];
              linkset[n][0][q,5]:=CellSec[j];         
         
              linkset[n][0][q,6]:=[n];
           linkset[n][0][q,7]:=[m];
              linkset[n][0][q,8]:= peer[j] * digitcell[n] ;   
               
           end;
        end;{bivavle}
     
      {bi local}       
      if (sec[xn,n] = 2 )
          then         
          for J in DigitRCB[xn,n] do
            begin
           
            inc(a);
           
             setlength(linkset[n][1],a+1);
            include(linkset[n][1][a,0],n);
             include(linkset[n][1][a,1],j);
            linkset[n][1][a,2]:= Digitrcb[xn,n] - [j];
            include(linkset[n][1][a,3],n);
            //include(linkset[n,1,a,4],xn);
             linkset[n][1][a,4]:=cellsec[j] - [xn];
           
            for m in digitRCB[xn,n] -[j] do
             linkset[n][1][a,5]:=cellsec[m]-[xn];           
                 
              linkset[n][1][a,6]:=pm[j]-[n];
             linkset[n][1][a,7]:=pm[m]-[n];
             linkset[n][1][a,8]:=peer[j]*digitcell[n] -[m];                 
             linkset[n][1][a,9]:=peer[m]*digitcell[n] -[j];
           
                end; {bilocal}
           
      { single + grouped & Grouped + single}       
      if (sec[xn,n] <5) and (Sec[xn,n] >2)
          then
            for J in DigitRCB[xn,n] do
              for m in peerRCB[xn] do
                 if  ((DigitRCB[m,n] * DigitRCB[xn,n])  + [j] = DigitRCB[xn,n] )
                     and not ( J in DigitRCB[m,n])   
                      then               
                   begin
            { single + grouped}       
                  inc(b);
            setlength(linkset[n][2],b+1);
            include(linkset[n][2,b,0],n);
             include(linkset[n][2,b,1],j);
            linkset[n][2,b,2]:= Digitrcb[xn,n] - [j];
            include(linkset[n][2,b,3],n);
            linkset[n][2,b,4]:=cellsec[j] - [xn];
            include(linkset[n][2,b,5],m);           
             linkset[n][2,b,6]:=pm[j]-[n];
             linkset[n][2,b,7]:=[0];
             linkset[n][2,b,9]:= Digitrcb[m,n]- (DigitRCB[m,n] * DigitRCB[xn,n]) ;
             linkset[n][2,b,8]:= peer[j]* digitcell[n]-(DigitRCB[m,n] * DigitRCB[xn,n]);
           
                 { grouped + single}
                  inc(c);
            setlength(linkset[n][3],c+1);
            include(linkset[n][3,c,0],n);
            linkset[n][3,c,1]:= Digitrcb[xn,n] - [j];
             include(linkset[n][3,c,2],j);           
            include(linkset[n][3,c,3],n);
            include(linkset[n][3,c,4],m);
            linkset[n][3,c,5]:= cellsec[j] - [xn] ;             
            linkset[n][3,c,6]:=[0];
            linkset[n][3,c,7]:=pm[j]-[n];
            linkset[n][3,c,9]:= peer[j] * digitcell[n]-(DigitRCB[m,n] * DigitRCB[xn,n]);
            linkset[n][3,c,8]:= DigitRCB[m,n]  -(DigitRCB[m,n] * DigitRCB[xn,n]) ;
                  end;
                 
   {Grouped + grouped}       
if (sec[xn,n] <7) and (Sec[xn,n] >4)
    then
       for J in peerrcb[xn] do
        for m in (peerrcb[xn]-[0..j]) do
        if ((DigitRCB[j,n] * DigitRCB[xn,n]) + (DigitRCB[m,n] * DigitRCB[xn,n]) = (DigitRCB[xn,n]))
           and (DigitRCB[j,n] * DigitRCB[m,n] = [] )
            then
              begin
         
               inc(d);
            setlength(linkset[n][4],d+1);
            include(linkset[n][4,d,0],n);
            linkset[n][4,d,1]:=(DigitRCB[xn,n] * Digitrcb[j,n]);
            linkset[n][4,d,2]:=(DigitRCB[xn,n] * DigitRCB[m,n]);
            include(linkset[n][4,d,3],n);
            include(linkset[n][4,d,4],J);
            include(linkset[n][4,d,5],m);           
               linkset[n][4,d,6]:=[0];   
            linkset[n][4,d,7]:=[0];
            linkset[n][4,d,9]:= DigitRCB[m,n] - (DigitRCB[xn,n] * DigitRCB[m,n]);
            linkset[n][4,d,8]:= DigitRCB[j,n] - (DigitRCB[xn,n] * DigitRCB[j,n]);
           
            inc(d);
            setlength(linkset[n][4],d+1);
            include(linkset[n][4,d,0],n);
            linkset[n][4,d,2]:=(DigitRCB[xn,n] * Digitrcb[j,n]);
            linkset[n][4,d,1]:=(DigitRCB[xn,n] * DigitRCB[m,n]);
            include(linkset[n][4,d,3],n);
            include(linkset[n][4,d,4],m);
            include(linkset[n][4,d,5],j);           
            linkset[n][4,d,6]:=[0];
            linkset[n][4,d,7]:=[0];   
               linkset[n][4,d,9]:= DigitRCB[j,n] - (DigitRCB[xn,n] * DigitRCB[j,n]);   
               linkset[n][4,d,8]:= DigitRCB[m,n] - (DigitRCB[xn,n] * DigitRCB[m,n]);         

              end;
         
if (sec[xn,n] <6) and (Sec[xn,n] >1) and (xn in [18..26])
   then
     for J in eri[xn-18,n] do
      begin
     
      inc(e);
      setlength(linkset[n][5],e+1);
      include(linkset[n][5,e,0],n);
      linkset[n][5,e,1]:=(DigitRCB[xn,n] * Digitrcb[Rx[secset[xn,j]],n]);
      linkset[n][5,e,2]:=(DigitRCB[xn,n] * DigitRCB[Cy[secset[xn,j]]+9,n]);
      include(linkset[n][5,e,3],n);
      include(linkset[n][5,e,4], rx[secset[xn,j]]);
      include(linkset[n][5,e,5],  Cy[secset[xn,j]]+9);
       linkset[n][5,e,6]:=[0];
      linkset[n][5,e,7]:=[0];
      linkset[n][5,e,8]:= DigitRCB[Rx[secset[xn,j]],n]  - (Digitrcb[xn,n] * Digitrcb[Rx[secset[xn,j]],n]);
      linkset[n][5,e,9]:= DigitRCB[Cy[secset[xn,j]]+9,n]  - (Digitrcb[xn,n] * Digitrcb[Cy[secset[xn,j]]+9,n]);
     
      inc(e);
      setlength(linkset[n][5],e+1);
      include(linkset[n][5,e,0],n);
      linkset[n][5,e,2]:=(DigitRCB[xn,n] * Digitrcb[Rx[secset[xn,j]],n]);
      linkset[n][5,e,1]:=(DigitRCB[xn,n] * DigitRCB[Cy[secset[xn,j]]+9,n]);
      include(linkset[n][5,e,3],n);
      include(linkset[n][5,e,5], rx[secset[xn,j]]);
      include(linkset[n][5,e,4],  Cy[secset[xn,j]]+9);       
       linkset[n][5,e,6]:=[0];
      linkset[n][5,e,7]:=[0];
      linkset[n][5,e,9]:= DigitRCB[Rx[secset[xn,j]],n]  - (Digitrcb[xn,n] * Digitrcb[Rx[secset[xn,j]],n]);
      linkset[n][5,e,8]:= DigitRCB[Cy[secset[xn,j]]+9,n]  - (Digitrcb[xn,n] * Digitrcb[Cy[secset[xn,j]]+9,n]);
     
     
      end;

end;
end;
{
assign(output,'C:\sudoku\combotest.txt');
erase(output);
rewrite(output);
close(output);

for n2 in [1..9] do
for xn in [0..5] do
 for J:= low(linkset[n2][xn]) to high(linkset[n2][xn]) do
 begin
   append(output);
      writeln(output);   
         write(output,'#',n2,' | ');
          write(output,'type:',xn,' | ');     
      for n:= low(linkset[n2][xn,j]) to high(linkset[n2][xn,j]) do
       begin
          for M in linkset[n2][xn,j,n] do
        write(output,m,',');
        write(output,' | ');
      end;
      close(output);     
 end}

end;{strong link builder}

originally i had a 2ndary table of weak-links which i realized is wasted space
since a weak link only occurs on a shared sector that sees all the digits my strong link setup already included that information!

all you have to do is reference the start and end cells of the initial link
saved sectors all those cells are found in for start/end
then run your program to line up the end cells sector to the next starting sector and off to the races we go.

for reference
my solver is in free pascal using setwise operations