alpar@1: /* A solver for the Japanese number-puzzle Shikaku
alpar@1:  * http://en.wikipedia.org/wiki/Shikaku
alpar@1:  *
alpar@1:  * Sebastian Nowozin <nowozin@gmail.com>, 27th January 2009
alpar@1:  */
alpar@1: 
alpar@1: param ndim := 10;
alpar@1: set rows := 1..ndim;
alpar@1: set rows1 := 1..(ndim+1);
alpar@1: set cols := 1..ndim;
alpar@1: set cols1 := 1..(ndim+1);
alpar@1: param givens{rows, cols}, integer, >= 0, default 0;
alpar@1: 
alpar@1: /* Set of vertices as (row,col) coordinates */
alpar@1: set V := { (i,j) in { rows, cols }: givens[i,j] != 0 };
alpar@1: 
alpar@1: /* Set of all feasible boxes of the right size: only this boxes are possible.
alpar@1:  * The box contains (i,j) and ranges from (k,l) to (m,n)
alpar@1:  */
alpar@1: set B := { (i,j,k,l,m,n) in { V, rows, cols, rows1, cols1 }:
alpar@1:     i >= k and i < m and j >= l and j < n and   /* Contains (i,j) */
alpar@1:     ((m-k)*(n-l)) = givens[i,j] and /* Right size */
alpar@1:     card({ (s,t) in V: s >= k and s < m and t >= l and t < n }) = 1
alpar@1:         /* Contains only (i,j), no other number */
alpar@1: };
alpar@1: 
alpar@1: var x{B}, binary;
alpar@1: 
alpar@1: /* Cover each square exactly once */
alpar@1: s.t. cover_once{ (s,t) in { rows, cols } }:
alpar@1:     sum{(i,j,k,l,m,n) in B: s >= k and s < m and t >= l and t < n}
alpar@1:         x[i,j,k,l,m,n] = 1;
alpar@1: 
alpar@1: minimize cost: 0;
alpar@1: 
alpar@1: solve;
alpar@1: 
alpar@1: /* Output solution graphically */
alpar@1: printf "\nSolution:\n";
alpar@1: for { row in rows1 } {
alpar@1:     for { col in cols1 } {
alpar@1:         printf{0..0: card({(i,j,k,l,m,n) in B:
alpar@1:                 col >= l and col <= n and (row = k or row = m) and
alpar@1:                 x[i,j,k,l,m,n] = 1}) > 0 and
alpar@1:             card({(i,j,k,l,m,n) in B:
alpar@1:                 row >= k and row <= m and (col = l or col = n) and
alpar@1:                 x[i,j,k,l,m,n] = 1}) > 0} "+";
alpar@1:         printf{0..0: card({(i,j,k,l,m,n) in B:
alpar@1:                 col >= l and col <= n and (row = k or row = m) and
alpar@1:                 x[i,j,k,l,m,n] = 1}) = 0 and
alpar@1:             card({(i,j,k,l,m,n) in B:
alpar@1:                 row >= k and row <= m and (col = l or col = n) and
alpar@1:                 x[i,j,k,l,m,n] = 1}) > 0} "|";
alpar@1:         printf{0..0: card({(i,j,k,l,m,n) in B:
alpar@1:                 row >= k and row <= m and (col = l or col = n) and
alpar@1:                 x[i,j,k,l,m,n] = 1}) = 0 and
alpar@1:             card({(i,j,k,l,m,n) in B:
alpar@1:                 col >= l and col <= n and (row = k or row = m) and
alpar@1:                 x[i,j,k,l,m,n] = 1}) > 0} "-";
alpar@1:         printf{0..0: card({(i,j,k,l,m,n) in B:
alpar@1:                 row >= k and row <= m and (col = l or col = n) and
alpar@1:                 x[i,j,k,l,m,n] = 1}) = 0 and
alpar@1:             card({(i,j,k,l,m,n) in B:
alpar@1:                 col >= l and col <= n and (row = k or row = m) and
alpar@1:                 x[i,j,k,l,m,n] = 1}) = 0} " ";
alpar@1: 
alpar@1:         printf{0..0: card({(i,j,k,l,m,n) in B:
alpar@1:             col >= l and col < n and (row = k or row = m) and
alpar@1:             x[i,j,k,l,m,n] = 1}) > 0} "---";
alpar@1:         printf{0..0: card({(i,j,k,l,m,n) in B:
alpar@1:             col >= l and col < n and (row = k or row = m) and
alpar@1:             x[i,j,k,l,m,n] = 1}) = 0} "   ";
alpar@1:     }
alpar@1:     printf "\n";
alpar@1: 
alpar@1:     for { (col,p) in { cols, 1 }: card({ s in rows: s = row }) = 1 } {
alpar@1:         printf{0..0: card({(i,j,k,l,m,n) in B:
alpar@1:             row >= k and row < m and (col = l or col = n) and
alpar@1:             x[i,j,k,l,m,n] = 1}) > 0} "|";
alpar@1:         printf{0..0: card({(i,j,k,l,m,n) in B:
alpar@1:             row >= k and row < m and (col = l or col = n) and
alpar@1:             x[i,j,k,l,m,n] = 1}) = 0} " ";
alpar@1:         printf{0..0: card({ (i,j) in V: i = row and j = col}) > 0} " %2d", givens[row,col];
alpar@1:         printf{0..0: card({ (i,j) in V: i = row and j = col}) = 0} "  .";
alpar@1:     }
alpar@1:     printf{0..0: card({ r in rows: r = row }) = 1} "|\n";
alpar@1: }
alpar@1: 
alpar@1: data;
alpar@1: 
alpar@1: /* This Shikaku is from
alpar@1:  * http://www.emn.fr/x-info/sdemasse/gccat/KShikaku.html#uid5449
alpar@1:  */
alpar@1: param givens : 1 2 3 4 5 6 7 8 9 10 :=
alpar@1:            1   9 . . . 12 . . 5 . .
alpar@1:            2   . . . . . . . . . .
alpar@1:            3   . . . . . . . . . 6
alpar@1:            4   8 . 6 . 8 . . . . .
alpar@1:            5   . . . . . . . . . .
alpar@1:            6   . . . . . . . . . .
alpar@1:            7   . . . . . 6 . 8 . 12
alpar@1:            8   4 . . . . . . . . .
alpar@1:            9   . . . . . . . . . .
alpar@1:           10   . . 3 . . 9 . . . 4
alpar@1:            ;
alpar@1: 
alpar@1: end;