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+/* Rectifiable polyomino tilings generator */
+
+/* Written and converted to GNU MathProg by NASZVADI, Peter, 2007-2017
+   <vuk@cs.elte.hu> */
+
+/*
+   This model searches for a maximal packing of a given polyomino
+   composed of unit squares in a given rectangle. In a feasible packing, a
+   placed polyomino and its intersection of a unit square's inner part in
+   the rectangle must be the square or empty. If there exists a packing
+   that covers totally the rectangle, then the polyomino is called
+   "rectifiable"
+
+   Summary:
+   Decides if an Im * Jm rectangle could be tiled with given pattern
+   and prints a (sub)optimal solution if found
+
+   Generated magic numbers are implicit tables, check them:
+
+   # for magic in 3248 688 1660 3260
+     do printf "Magic % 5d:" "$magic"
+         for e in 0 1 2 3 4 5 6 7
+         do printf "% 3d" "$((-1 + ((magic / (3**e)) % 3)))"
+         done
+         echo
+     done
+   Magic  3248:  1  1 -1 -1  0  0  0  0
+   Magic   688:  0  0  0  0  1  1 -1 -1
+   Magic  1660:  0  0  0  0  1 -1  1 -1
+   Magic  3260:  1 -1  1 -1  0  0  0  0
+   #
+*/
+
+param Im, default 3;
+/* vertical edge length of the box */
+
+param Jm, default 3;
+/* horizontal edge length of the box */
+
+set S, default {(0, 0), (1, 0), (2, 0), (0, 1), (1, 1), (2, 1), (0, 2)};
+/* P-heptomino is the default shape. More info on this heptomino:
+   http://www.cflmath.com/Polyomino/7omino4_rect.html */
+
+set I := 1..Im;
+/* rows of rectangle */
+
+set J := 1..Jm;
+/* columns of rectangle */
+
+set IJ := I cross J;
+/* the rectangle itself */
+
+set E := 0..7;
+/* helper set to allow iterating on all transformations of the S shape */
+
+set Shifts := setof{(i, j, e) in IJ cross E:
+         setof{(x, y) in S}
+             ((x * (-1 + floor(3248 / 3^e) mod 3)) +
+              (y * (-1 + floor(688 / 3^e) mod 3)) + i,
+              (x * (-1 + floor(1660 / 3^e) mod 3)) +
+              (y * (-1 + floor(3260 / 3^e) mod 3)) + j) within IJ}(i, j, e);
+/* all shifted, flipped, rotated, mirrored mappings of polyomino that
+   contained by the rectangle */
+
+var cell{IJ}, binary;
+/* booleans denoting if a cell is covered in the rectangle */
+
+var tile{Shifts}, binary;
+/* booleans denoting usage of a shift */
+
+var objvalue;
+
+s.t. covers{(i, j) in IJ}: sum{(k, l, e, a, b) in Shifts cross S:
+    i = k + a * (-1 + floor(3248 / 3^e) mod 3) +
+        b * (-1 + floor(688 / 3^e) mod 3)
+    and
+    j = l + a * (-1 + floor(1660 / 3^e) mod 3) +
+        b * (-1 + floor(3260 / 3^e) mod 3)
+    }tile[k, l, e] = cell[i, j];
+
+s.t. objeval: sum{(i, j) in IJ}cell[i, j] - objvalue = 0;
+
+maximize obj: objvalue;
+
+solve;
+
+printf '\nCovered cells/all cells = %d/%d\n\n', objvalue.val, Im * Jm;
+printf '\nA tiling:\n\n';
+for{i in I}{
+    for{j in J}{
+        printf '%s', if cell[i, j].val then '' else ' *** ';
+        for{(k, l, e, a, b) in Shifts cross S:
+            cell[i, j].val
+            and i = k + a * (-1 + floor(3248 / 3^e) mod 3) +
+                b * (-1 + floor(688 / 3^e) mod 3)
+            and j = l + a * (-1 + floor(1660 / 3^e) mod 3) +
+                b * (-1 + floor(3260 / 3^e) mod 3)
+            and tile[k, l, e].val
+        }{
+            printf '% 5d', (k * Jm + l) * 8 + e;
+        }
+    }
+    printf '\n';
+}
+printf '\n';
+
+data;
+
+param Im := 14;
+/* here can be set rectangle's one side */
+
+param Jm := 14;
+/* here can be set rectangle's other side */
+
+set S := (0,0),(1,0),(2,0),(0,1),(1,1),(2,1),(0,2);
+/* here you can specify arbitrary polyomino */
+
+end;