Data update

Task/Pentomino-tiling/Jq/pentomino-tiling.jq

@@ -0,0 +1,178 @@
+# Output: a PRN in range(0; .)
+def prn:
+  if . == 1 then 0
+  else . as $n
+  | (($n-1)|tostring|length) as $w
+  | [limit($w; inputs)] | join("") | tonumber
+  | if . < $n then . else ($n | prn) end
+  end;
+
+### Generic functions
+
+def array($n): . as $in | [range(0;$n)|$in];
+
+def array_swap($i; $j):
+  if $i < $j then array_swap($j;$i)
+  elif $i == $j then .
+  else .[$i] as $t | .[:$j] + [$t] + .[$j:$i] + .[$i + 1:]
+  end ;
+
+### Pentominos
+
+def F: [
+    [1, -1, 1,  0, 1, 1, 2,  1], [0,  1, 1, -1, 1,  0, 2, 0],
+    [1,  0, 1,  1, 1, 2, 2,  1], [1,  0, 1,  1, 2, -1, 2, 0],
+    [1, -2, 1, -1, 1, 0, 2, -1], [0,  1, 1,  1, 1,  2, 2, 1],
+    [1, -1, 1,  0, 1, 1, 2, -1], [1, -1, 1,  0, 2,  0, 2, 1]
+];
+
+def I: [
+    [0, 1, 0, 2, 0, 3, 0, 4], [1, 0, 2, 0, 3, 0, 4, 0]
+];
+
+def L: [
+    [1, 0, 1, 1, 1, 2, 1, 3], [1,  0, 2,  0, 3, -1, 3, 0],
+    [0, 1, 0, 2, 0, 3, 1, 3], [0,  1, 1,  0, 2,  0, 3, 0],
+    [0, 1, 1, 1, 2, 1, 3, 1], [0,  1, 0,  2, 0,  3, 1, 0],
+    [1, 0, 2, 0, 3, 0, 3, 1], [1, -3, 1, -2, 1, -1, 1, 0]
+];
+
+def N: [
+    [0, 1, 1, -2, 1, -1, 1, 0], [1,  0, 1,  1, 2,  1, 3,  1],
+    [0, 1, 0,  2, 1, -1, 1, 0], [1,  0, 2,  0, 2,  1, 3,  1],
+    [0, 1, 1,  1, 1,  2, 1, 3], [1,  0, 2, -1, 2,  0, 3, -1],
+    [0, 1, 0,  2, 1,  2, 1, 3], [1, -1, 1,  0, 2, -1, 3, -1]
+];
+
+def P: [
+    [0, 1, 1, 0, 1, 1, 2, 1], [0,  1, 0,  2, 1,  0, 1, 1],
+    [1, 0, 1, 1, 2, 0, 2, 1], [0,  1, 1, -1, 1,  0, 1, 1],
+    [0, 1, 1, 0, 1, 1, 1, 2], [1, -1, 1,  0, 2, -1, 2, 0],
+    [0, 1, 0, 2, 1, 1, 1, 2], [0,  1, 1,  0, 1,  1, 2, 0]
+];
+
+def T: [
+    [0, 1, 0,  2, 1, 1, 2, 1], [1, -2, 1, -1, 1, 0, 2, 0],
+    [1, 0, 2, -1, 2, 0, 2, 1], [1,  0, 1,  1, 1, 2, 2, 0]
+];
+
+def U: [
+    [0, 1, 0, 2, 1, 0, 1, 2], [0, 1, 1, 1, 2, 0, 2, 1],
+    [0, 2, 1, 0, 1, 1, 1, 2], [0, 1, 1, 0, 2, 0, 2, 1]
+];
+
+def V: [
+    [1, 0, 2,  0, 2,  1, 2, 2], [0, 1, 0, 2, 1, 0, 2, 0],
+    [1, 0, 2, -2, 2, -1, 2, 0], [0, 1, 0, 2, 1, 2, 2, 2]
+];
+
+def W: [
+    [1, 0, 1, 1, 2, 1, 2, 2], [1, -1, 1,  0, 2, -2, 2, -1],
+    [0, 1, 1, 1, 1, 2, 2, 2], [0,  1, 1, -1, 1,  0, 2, -1]
+];
+
+def X: [[1, -1, 1, 0, 1, 1, 2, 0]];
+
+def Y: [
+    [1, -2, 1, -1, 1, 0, 1, 1], [1, -1, 1,  0, 2, 0, 3, 0],
+    [0,  1, 0,  2, 0, 3, 1, 1], [1,  0, 2,  0, 2, 1, 3, 0],
+    [0,  1, 0,  2, 0, 3, 1, 2], [1,  0, 1,  1, 2, 0, 3, 0],
+    [1, -1, 1,  0, 1, 1, 1, 2], [1,  0, 2, -1, 2, 0, 3, 0]
+];
+
+def Z: [
+    [0, 1, 1, 0, 2, -1, 2, 0], [1,  0, 1,  1, 1, 2, 2,  2],
+    [0, 1, 1, 1, 2,  1, 2, 2], [1, -2, 1, -1, 1, 0, 2, -2]
+];
+
+def shapes: [F, I, L, N, P, T, U, V, W, X, Y, Z];
+
+def symbols: "FILNPTUVWXYZ-" | split("");
+
+def nRows:  8;
+def nCols:  8;
+def blank: 12;
+
+def printResult:
+  .symbols as $symbols
+  | .grid[] as $row
+  | reduce $row[] as $i (""; . + $symbols[$i]);
+
+# Input: {grid}
+def placeOrientation($o; $r; $c; $shapeIndex):
+  .grid[$r][$c] = $shapeIndex
+   | reduce range(0; $o|length; 2) as $io (.;
+      .grid[$r + $o[$io]][$c + $o[$io + 1]] = $shapeIndex);
+
+# Input and output: {grid}
+# If the placement is feasible, call placeOrientation/3
+def tryPlaceOrientation($o; $r; $c; $shapeIndex):
+  .grid as $grid
+  | if any( range(0; $o|length; 2);
+         . as $io
+         | ($c + $o[$io + 1]) as $x
+         | ($r + $o[$io] ) as $y
+         | $x < 0 or $x >= nCols or $y < 0 or $y >= nRows or $grid[$y][$x] != -1 )
+    then empty
+    else placeOrientation($o; $r; $c; $shapeIndex)
+  end
+  ;
+
+# Input: {grid, placed, shapes}
+def solve($pos; $numPlaced):
+  if $numPlaced == (.shapes|length)
+  then .
+  else (($pos / nCols)|floor) as $row
+  | ($pos % nCols ) as $col
+  | if .grid[$row][$col] != -1
+    then solve($pos + 1; $numPlaced)
+    else .emit = false
+    | foreach range(0; .shapes|length) as $i (.;
+         if .placed[$i] then .
+         else foreach .shapes[$i][] as $orientation (.;
+                (tryPlaceOrientation($orientation; $row; $col; $i)
+                 | .placed[$i] = true
+                 | solve($pos + 1; $numPlaced + 1)
+                 | .emit = true)
+               // .)
+         end )
+     | select(.emit)
+    end
+  end;
+
+# input: {shapes, symbols}
+def shuffleShapes:
+  (.shapes|length) as $n
+  | reduce range(0; $n) as $i (.;
+      ($n | prn) as $r
+      | .shapes |= array_swap($r; $i)
+      | .symbols |= array_swap($r; $i) )
+;
+
+def task:
+  def grid:
+    0 | array(nCols) | array(nRows);
+  def placed:
+    false | array(symbols|length - 1);
+
+  { shapes: shapes,
+    symbols: symbols,
+    grid: grid,
+    placed: placed}
+  | shuffleShapes
+  | reduce range(0; nRows) as $r (.;
+      reduce range(0; .grid[$r]|length) as $c (.;
+         .grid[$r][$c] = -1))
+  | reduce range(0; 4) as $i (.;
+      .done = false
+      | until(.done;
+            .randRow = (nRows | prn)
+          | .randCol = (nCols | prn)
+          | .done = (.grid[.randRow][.randCol] != blank) )
+      | .grid[.randRow][.randCol] = blank
+    )
+  | first(solve(0; 0))
+  | printResult
+  // "No solution"
+;
+task