Pentomino tiling
Pentomino tiling is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
A pentomino is a polyomino that consists of 5 squares. There are 12 pentomino shapes, if you don't count rotations and reflections. Most pentominoes can form their own mirror image through rotation, but some of them have to be flipped over.
I
I L N Y
FF I L NN PP TTT V W X YY ZZ
FF I L N PP T U U V WW XXX Y Z
F I LL N P T UUU VVV WW X Y ZZ
A Pentomino tiling is an example of an exact cover problem and can take on many forms.
A traditional tiling presents an 8 by 8 grid, where 4 cells are left uncovered. The other cells are covered
by the 12 pentomino shapes, without overlaps, with every shape only used once.
The 4 uncovered cells should be chosen at random. Note that not all configurations are solvable.
- Task
Create an 8 by 8 tiling and print the result.
- Example
F I I I I I L N F F F L L L L N W F - X Z Z N N W W X X X Z N V T W W X - Z Z V T T T P P V V V T Y - P P U U U Y Y Y Y P U - U
- Related tasks
C#
<lang csharp>using System; using System.Linq;
namespace PentominoTiling {
class Program
{
static readonly char[] symbols = "FILNPTUVWXYZ-".ToCharArray();
static readonly int nRows = 8;
static readonly int nCols = 8;
static readonly int target = 12;
static readonly int blank = 12;
static int[][] grid = new int[nRows][];
static bool[] placed = new bool[target];
static void Main(string[] args)
{
var rand = new Random();
for (int r = 0; r < nRows; r++)
grid[r] = Enumerable.Repeat(-1, nCols).ToArray();
for (int i = 0; i < 4; i++)
{
int randRow, randCol;
do
{
randRow = rand.Next(nRows);
randCol = rand.Next(nCols);
}
while (grid[randRow][randCol] == blank);
grid[randRow][randCol] = blank;
}
if (Solve(0, 0))
{
PrintResult();
}
else
{
Console.WriteLine("no solution");
}
Console.ReadKey();
}
private static void PrintResult()
{
foreach (int[] r in grid)
{
foreach (int i in r)
Console.Write("{0} ", symbols[i]);
Console.WriteLine();
}
}
private static bool Solve(int pos, int numPlaced)
{
if (numPlaced == target)
return true;
int row = pos / nCols;
int col = pos % nCols;
if (grid[row][col] != -1)
return Solve(pos + 1, numPlaced);
for (int i = 0; i < shapes.Length; i++)
{
if (!placed[i])
{
foreach (int[] orientation in shapes[i])
{
if (!TryPlaceOrientation(orientation, row, col, i))
continue;
placed[i] = true;
if (Solve(pos + 1, numPlaced + 1))
return true;
RemoveOrientation(orientation, row, col);
placed[i] = false;
}
}
}
return false;
}
private static void RemoveOrientation(int[] orientation, int row, int col)
{
grid[row][col] = -1;
for (int i = 0; i < orientation.Length; i += 2)
grid[row + orientation[i]][col + orientation[i + 1]] = -1;
}
private static bool TryPlaceOrientation(int[] orientation, int row, int col, int shapeIndex)
{
for (int i = 0; i < orientation.Length; i += 2)
{
int x = col + orientation[i + 1];
int y = row + orientation[i];
if (x < 0 || x >= nCols || y < 0 || y >= nRows || grid[y][x] != -1)
return false;
}
grid[row][col] = shapeIndex;
for (int i = 0; i < orientation.Length; i += 2)
grid[row + orientation[i]][col + orientation[i + 1]] = shapeIndex;
return true;
}
// four (x, y) pairs are listed, (0,0) not included
static readonly int[][] F = {
new int[] {1, -1, 1, 0, 1, 1, 2, 1}, new int[] {0, 1, 1, -1, 1, 0, 2, 0},
new int[] {1, 0, 1, 1, 1, 2, 2, 1}, new int[] {1, 0, 1, 1, 2, -1, 2, 0},
new int[] {1, -2, 1, -1, 1, 0, 2, -1}, new int[] {0, 1, 1, 1, 1, 2, 2, 1},
new int[] {1, -1, 1, 0, 1, 1, 2, -1}, new int[] {1, -1, 1, 0, 2, 0, 2, 1}};
static readonly int[][] I = {
new int[] { 0, 1, 0, 2, 0, 3, 0, 4 }, new int[] { 1, 0, 2, 0, 3, 0, 4, 0 } };
static readonly int[][] L = {
new int[] {1, 0, 1, 1, 1, 2, 1, 3}, new int[] {1, 0, 2, 0, 3, -1, 3, 0},
new int[] {0, 1, 0, 2, 0, 3, 1, 3}, new int[] {0, 1, 1, 0, 2, 0, 3, 0},
new int[] {0, 1, 1, 1, 2, 1, 3, 1}, new int[] {0, 1, 0, 2, 0, 3, 1, 0},
new int[] {1, 0, 2, 0, 3, 0, 3, 1}, new int[] {1, -3, 1, -2, 1, -1, 1, 0}};
static readonly int[][] N = {
new int[] {0, 1, 1, -2, 1, -1, 1, 0}, new int[] {1, 0, 1, 1, 2, 1, 3, 1},
new int[] {0, 1, 0, 2, 1, -1, 1, 0}, new int[] {1, 0, 2, 0, 2, 1, 3, 1},
new int[] {0, 1, 1, 1, 1, 2, 1, 3}, new int[] {1, 0, 2, -1, 2, 0, 3, -1},
new int[] {0, 1, 0, 2, 1, 2, 1, 3}, new int[] {1, -1, 1, 0, 2, -1, 3, -1}};
static readonly int[][] P = {
new int[] {0, 1, 1, 0, 1, 1, 2, 1}, new int[] {0, 1, 0, 2, 1, 0, 1, 1},
new int[] {1, 0, 1, 1, 2, 0, 2, 1}, new int[] {0, 1, 1, -1, 1, 0, 1, 1},
new int[] {0, 1, 1, 0, 1, 1, 1, 2}, new int[] {1, -1, 1, 0, 2, -1, 2, 0},
new int[] {0, 1, 0, 2, 1, 1, 1, 2}, new int[] {0, 1, 1, 0, 1, 1, 2, 0}};
static readonly int[][] T = {
new int[] {0, 1, 0, 2, 1, 1, 2, 1}, new int[] {1, -2, 1, -1, 1, 0, 2, 0},
new int[] {1, 0, 2, -1, 2, 0, 2, 1}, new int[] {1, 0, 1, 1, 1, 2, 2, 0}};
static readonly int[][] U = {
new int[] {0, 1, 0, 2, 1, 0, 1, 2}, new int[] {0, 1, 1, 1, 2, 0, 2, 1},
new int[] {0, 2, 1, 0, 1, 1, 1, 2}, new int[] {0, 1, 1, 0, 2, 0, 2, 1}};
static readonly int[][] V = {
new int[] {1, 0, 2, 0, 2, 1, 2, 2}, new int[] {0, 1, 0, 2, 1, 0, 2, 0},
new int[] {1, 0, 2, -2, 2, -1, 2, 0}, new int[] {0, 1, 0, 2, 1, 2, 2, 2}};
static readonly int[][] W = {
new int[] {1, 0, 1, 1, 2, 1, 2, 2}, new int[] {1, -1, 1, 0, 2, -2, 2, -1},
new int[] {0, 1, 1, 1, 1, 2, 2, 2}, new int[] {0, 1, 1, -1, 1, 0, 2, -1}};
static readonly int[][] X = { new int[] { 1, -1, 1, 0, 1, 1, 2, 0 } };
static readonly int[][] Y = {
new int[] {1, -2, 1, -1, 1, 0, 1, 1}, new int[] {1, -1, 1, 0, 2, 0, 3, 0},
new int[] {0, 1, 0, 2, 0, 3, 1, 1}, new int[] {1, 0, 2, 0, 2, 1, 3, 0},
new int[] {0, 1, 0, 2, 0, 3, 1, 2}, new int[] {1, 0, 1, 1, 2, 0, 3, 0},
new int[] {1, -1, 1, 0, 1, 1, 1, 2}, new int[] {1, 0, 2, -1, 2, 0, 3, 0}};
static readonly int[][] Z = {
new int[] {0, 1, 1, 0, 2, -1, 2, 0}, new int[] {1, 0, 1, 1, 1, 2, 2, 2},
new int[] {0, 1, 1, 1, 2, 1, 2, 2}, new int[] {1, -2, 1, -1, 1, 0, 2, -2}};
static readonly int[][][] shapes = { F, I, L, N, P, T, U, V, W, X, Y, Z };
}
}</lang>
I N F F - - L L I N N F F P P L I - N F W P P L I Y N W W X P L I Y W W X X X - Y Y T T T X Z V U Y U T Z Z Z V U U U T Z V V V
Go
<lang go>package main
import (
"fmt" "math/rand" "time"
)
var F = [][]int{
{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},
}
var I = [][]int{{0, 1, 0, 2, 0, 3, 0, 4}, {1, 0, 2, 0, 3, 0, 4, 0}}
var L = [][]int{
{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},
}
var N = [][]int{
{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},
}
var P = [][]int{
{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},
}
var T = [][]int{
{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},
}
var U = [][]int{
{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},
}
var V = [][]int{
{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},
}
var W = [][]int{
{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},
}
var X = [][]intTemplate:1, -1, 1, 0, 1, 1, 2, 0
var Y = [][]int{
{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},
}
var Z = [][]int{
{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},
}
var shapes = [][][]int{F, I, L, N, P, T, U, V, W, X, Y, Z}
var symbols = []byte("FILNPTUVWXYZ-")
const (
nRows = 8 nCols = 8 blank = 12
)
var grid [nRows][nCols]int var placed [12]bool
func tryPlaceOrientation(o []int, r, c, shapeIndex int) bool {
for i := 0; i < len(o); i += 2 {
x := c + o[i+1]
y := r + o[i]
if x < 0 || x >= nCols || y < 0 || y >= nRows || grid[y][x] != -1 {
return false
}
}
grid[r][c] = shapeIndex
for i := 0; i < len(o); i += 2 {
grid[r+o[i]][c+o[i+1]] = shapeIndex
}
return true
}
func removeOrientation(o []int, r, c int) {
grid[r][c] = -1
for i := 0; i < len(o); i += 2 {
grid[r+o[i]][c+o[i+1]] = -1
}
}
func solve(pos, numPlaced int) bool {
if numPlaced == len(shapes) {
return true
}
row := pos / nCols
col := pos % nCols
if grid[row][col] != -1 {
return solve(pos+1, numPlaced)
}
for i := range shapes {
if !placed[i] {
for _, orientation := range shapes[i] {
if !tryPlaceOrientation(orientation, row, col, i) {
continue
}
placed[i] = true
if solve(pos+1, numPlaced+1) {
return true
}
removeOrientation(orientation, row, col)
placed[i] = false
}
}
}
return false
}
func shuffleShapes() {
rand.Shuffle(len(shapes), func(i, j int) {
shapes[i], shapes[j] = shapes[j], shapes[i]
symbols[i], symbols[j] = symbols[j], symbols[i]
})
}
func printResult() {
for _, r := range grid {
for _, i := range r {
fmt.Printf("%c ", symbols[i])
}
fmt.Println()
}
}
func main() {
rand.Seed(time.Now().UnixNano())
shuffleShapes()
for r := 0; r < nRows; r++ {
for i := range grid[r] {
grid[r][i] = -1
}
}
for i := 0; i < 4; i++ {
var randRow, randCol int
for {
randRow = rand.Intn(nRows)
randCol = rand.Intn(nCols)
if grid[randRow][randCol] != blank {
break
}
}
grid[randRow][randCol] = blank
}
if solve(0, 0) {
printResult()
} else {
fmt.Println("No solution")
}
}</lang>
- Output:
Sample output:
Z I I I I I - Y Z Z Z V - F Y Y U U Z V - F F Y U V V V F F X Y U U P P W X X X T P P P W W X - T T T N N W W L T N N N L L L L
Java
<lang java>package pentominotiling;
import java.util.*;
public class PentominoTiling {
static final char[] symbols = "FILNPTUVWXYZ-".toCharArray(); static final Random rand = new Random();
static final int nRows = 8; static final int nCols = 8; static final int blank = 12;
static int[][] grid = new int[nRows][nCols]; static boolean[] placed = new boolean[symbols.length - 1];
public static void main(String[] args) {
shuffleShapes();
for (int r = 0; r < nRows; r++)
Arrays.fill(grid[r], -1);
for (int i = 0; i < 4; i++) {
int randRow, randCol;
do {
randRow = rand.nextInt(nRows);
randCol = rand.nextInt(nCols);
} while (grid[randRow][randCol] == blank);
grid[randRow][randCol] = blank;
}
if (solve(0, 0)) {
printResult();
} else {
System.out.println("no solution");
}
}
static void shuffleShapes() {
int n = shapes.length;
while (n > 1) {
int r = rand.nextInt(n--);
int[][] tmp = shapes[r];
shapes[r] = shapes[n];
shapes[n] = tmp;
char tmpSymbol = symbols[r];
symbols[r] = symbols[n];
symbols[n] = tmpSymbol;
}
}
static void printResult() {
for (int[] r : grid) {
for (int i : r)
System.out.printf("%c ", symbols[i]);
System.out.println();
}
}
static boolean tryPlaceOrientation(int[] o, int r, int c, int shapeIndex) {
for (int i = 0; i < o.length; i += 2) {
int x = c + o[i + 1];
int y = r + o[i];
if (x < 0 || x >= nCols || y < 0 || y >= nRows || grid[y][x] != -1)
return false;
}
grid[r][c] = shapeIndex;
for (int i = 0; i < o.length; i += 2)
grid[r + o[i]][c + o[i + 1]] = shapeIndex;
return true; }
static void removeOrientation(int[] o, int r, int c) {
grid[r][c] = -1;
for (int i = 0; i < o.length; i += 2)
grid[r + o[i]][c + o[i + 1]] = -1;
}
static boolean solve(int pos, int numPlaced) {
if (numPlaced == shapes.length)
return true;
int row = pos / nCols;
int col = pos % nCols;
if (grid[row][col] != -1)
return solve(pos + 1, numPlaced);
for (int i = 0; i < shapes.length; i++) {
if (!placed[i]) {
for (int[] orientation : shapes[i]) {
if (!tryPlaceOrientation(orientation, row, col, i))
continue;
placed[i] = true;
if (solve(pos + 1, numPlaced + 1))
return true;
removeOrientation(orientation, row, col);
placed[i] = false;
}
}
}
return false;
}
static final int[][] 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}};
static final int[][] I = {{0, 1, 0, 2, 0, 3, 0, 4}, {1, 0, 2, 0, 3, 0, 4, 0}};
static final int[][] 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}};
static final int[][] 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}};
static final int[][] 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}};
static final int[][] 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}};
static final int[][] 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}};
static final int[][] 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}};
static final int[][] 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}};
static final int[][] X = Template:1, -1, 1, 0, 1, 1, 2, 0;
static final int[][] 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}};
static final int[][] 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}};
static final int[][][] shapes = {F, I, L, N, P, T, U, V, W, X, Y, Z};
}</lang>
F I I I I I L L F F F P P V L - Z F P P P V L N Z Z Z V V V L N - X Z - W W N N X X X W W - N T U X U W Y T T T U U U Y Y Y Y T
Kotlin
<lang scala>// Version 1.1.4-3
import java.util.Random
val F = arrayOf(
intArrayOf(1, -1, 1, 0, 1, 1, 2, 1), intArrayOf(0, 1, 1, -1, 1, 0, 2, 0), intArrayOf(1, 0, 1, 1, 1, 2, 2, 1), intArrayOf(1, 0, 1, 1, 2, -1, 2, 0), intArrayOf(1, -2, 1, -1, 1, 0, 2, -1), intArrayOf(0, 1, 1, 1, 1, 2, 2, 1), intArrayOf(1, -1, 1, 0, 1, 1, 2, -1), intArrayOf(1, -1, 1, 0, 2, 0, 2, 1)
)
val I = arrayOf(
intArrayOf(0, 1, 0, 2, 0, 3, 0, 4), intArrayOf(1, 0, 2, 0, 3, 0, 4, 0)
)
val L = arrayOf(
intArrayOf(1, 0, 1, 1, 1, 2, 1, 3), intArrayOf(1, 0, 2, 0, 3, -1, 3, 0), intArrayOf(0, 1, 0, 2, 0, 3, 1, 3), intArrayOf(0, 1, 1, 0, 2, 0, 3, 0), intArrayOf(0, 1, 1, 1, 2, 1, 3, 1), intArrayOf(0, 1, 0, 2, 0, 3, 1, 0), intArrayOf(1, 0, 2, 0, 3, 0, 3, 1), intArrayOf(1, -3, 1, -2, 1, -1, 1, 0)
)
val N = arrayOf(
intArrayOf(0, 1, 1, -2, 1, -1, 1, 0), intArrayOf(1, 0, 1, 1, 2, 1, 3, 1), intArrayOf(0, 1, 0, 2, 1, -1, 1, 0), intArrayOf(1, 0, 2, 0, 2, 1, 3, 1), intArrayOf(0, 1, 1, 1, 1, 2, 1, 3), intArrayOf(1, 0, 2, -1, 2, 0, 3, -1), intArrayOf(0, 1, 0, 2, 1, 2, 1, 3), intArrayOf(1, -1, 1, 0, 2, -1, 3, -1)
)
val P = arrayOf(
intArrayOf(0, 1, 1, 0, 1, 1, 2, 1), intArrayOf(0, 1, 0, 2, 1, 0, 1, 1), intArrayOf(1, 0, 1, 1, 2, 0, 2, 1), intArrayOf(0, 1, 1, -1, 1, 0, 1, 1), intArrayOf(0, 1, 1, 0, 1, 1, 1, 2), intArrayOf(1, -1, 1, 0, 2, -1, 2, 0), intArrayOf(0, 1, 0, 2, 1, 1, 1, 2), intArrayOf(0, 1, 1, 0, 1, 1, 2, 0)
)
val T = arrayOf(
intArrayOf(0, 1, 0, 2, 1, 1, 2, 1), intArrayOf(1, -2, 1, -1, 1, 0, 2, 0), intArrayOf(1, 0, 2, -1, 2, 0, 2, 1), intArrayOf(1, 0, 1, 1, 1, 2, 2, 0)
)
val U = arrayOf(
intArrayOf(0, 1, 0, 2, 1, 0, 1, 2), intArrayOf(0, 1, 1, 1, 2, 0, 2, 1), intArrayOf(0, 2, 1, 0, 1, 1, 1, 2), intArrayOf(0, 1, 1, 0, 2, 0, 2, 1)
)
val V = arrayOf(
intArrayOf(1, 0, 2, 0, 2, 1, 2, 2), intArrayOf(0, 1, 0, 2, 1, 0, 2, 0), intArrayOf(1, 0, 2, -2, 2, -1, 2, 0), intArrayOf(0, 1, 0, 2, 1, 2, 2, 2)
)
val W = arrayOf(
intArrayOf(1, 0, 1, 1, 2, 1, 2, 2), intArrayOf(1, -1, 1, 0, 2, -2, 2, -1), intArrayOf(0, 1, 1, 1, 1, 2, 2, 2), intArrayOf(0, 1, 1, -1, 1, 0, 2, -1)
)
val X = arrayOf(intArrayOf(1, -1, 1, 0, 1, 1, 2, 0))
val Y = arrayOf(
intArrayOf(1, -2, 1, -1, 1, 0, 1, 1), intArrayOf(1, -1, 1, 0, 2, 0, 3, 0), intArrayOf(0, 1, 0, 2, 0, 3, 1, 1), intArrayOf(1, 0, 2, 0, 2, 1, 3, 0), intArrayOf(0, 1, 0, 2, 0, 3, 1, 2), intArrayOf(1, 0, 1, 1, 2, 0, 3, 0), intArrayOf(1, -1, 1, 0, 1, 1, 1, 2), intArrayOf(1, 0, 2, -1, 2, 0, 3, 0)
)
val Z = arrayOf(
intArrayOf(0, 1, 1, 0, 2, -1, 2, 0), intArrayOf(1, 0, 1, 1, 1, 2, 2, 2), intArrayOf(0, 1, 1, 1, 2, 1, 2, 2), intArrayOf(1, -2, 1, -1, 1, 0, 2, -2)
)
val shapes = arrayOf(F, I, L, N, P, T, U, V, W, X, Y, Z) val rand = Random()
val symbols = "FILNPTUVWXYZ-".toCharArray()
val nRows = 8 val nCols = 8 val blank = 12
val grid = Array(nRows) { IntArray(nCols) } val placed = BooleanArray(symbols.size - 1)
fun tryPlaceOrientation(o: IntArray, r: Int, c: Int, shapeIndex: Int): Boolean {
for (i in 0 until o.size step 2) {
val x = c + o[i + 1]
val y = r + o[i]
if (x !in (0 until nCols) || y !in (0 until nRows) || grid[y][x] != - 1) return false
}
grid[r][c] = shapeIndex
for (i in 0 until o.size step 2) grid[r + o[i]][c + o[i + 1]] = shapeIndex
return true
}
fun removeOrientation(o: IntArray, r: Int, c: Int) {
grid[r][c] = -1 for (i in 0 until o.size step 2) grid[r + o[i]][c + o[i + 1]] = -1
}
fun solve(pos: Int, numPlaced: Int): Boolean {
if (numPlaced == shapes.size) return true val row = pos / nCols val col = pos % nCols if (grid[row][col] != -1) return solve(pos + 1, numPlaced)
for (i in 0 until shapes.size) {
if (!placed[i]) {
for (orientation in shapes[i]) {
if (!tryPlaceOrientation(orientation, row, col, i)) continue
placed[i] = true
if (solve(pos + 1, numPlaced + 1)) return true
removeOrientation(orientation, row, col)
placed[i] = false
}
}
}
return false
}
fun shuffleShapes() {
var n = shapes.size
while (n > 1) {
val r = rand.nextInt(n--)
val tmp = shapes[r]
shapes[r] = shapes[n]
shapes[n] = tmp
val tmpSymbol= symbols[r]
symbols[r] = symbols[n]
symbols[n] = tmpSymbol
}
}
fun printResult() {
for (r in grid) {
for (i in r) print("${symbols[i]} ")
println()
}
}
fun main(args: Array<String>) {
shuffleShapes()
for (r in 0 until nRows) grid[r].fill(-1)
for (i in 0..3) {
var randRow: Int
var randCol: Int
do {
randRow = rand.nextInt(nRows)
randCol = rand.nextInt(nCols)
}
while (grid[randRow][randCol] == blank)
grid[randRow][randCol] = blank
}
if (solve(0, 0)) printResult()
else println("No solution")
}</lang>
Sample output:
I I I I I F - W N N N F F F W W U U N N F W W - - U V L L L L T U U V L Z T T T V V V X Z Z Z T P P X X X Y Z - P P P X Y Y Y Y
Phix
Apart from the shape table creation, the solving part is a translation of Go.
I also added a fast unsolveable() check routine, not that it desperately needed it.
<lang Phix>constant pentominoes = split("""
......I................................................................
......I.....L......N.........................................Y.........
.FF...I.....L.....NN....PP....TTT...........V.....W....X....YY.....ZZ..
FF....I.....L.....N.....PP.....T....U.U.....V....WW...XXX....Y.....Z...
.F....I.....LL....N.....P......T....UUU...VVV...WW.....X.....Y....ZZ...""",'\n')
----- ----- ----- ----- ----- ----- ----- ----- ----- ----- -----
function get_shapes()
sequence res = {}
for offset=0 to length(pentominoes[1]) by 6 do
--
-- scan left/right, and up/down, both ways, to give 8 orientations
-- (computes the equivalent of those hard-coded tables in
-- other examples, albeit in a slightly different order.)
--
sequence shape = {}
integer letter
for orientation=0 to 7 do
sequence this = {}
bool found = false
integer fr, fc
for r=1 to 5 do
for c=1 to 5 do
integer rr = iff(and_bits(orientation,#01)?6-r:r),
cc = iff(and_bits(orientation,#02)?6-c:c)
if and_bits(orientation,#04) then {rr,cc} = {cc,rr} end if
integer ch = pentominoes[rr,offset+cc]
if ch!='.' then
if not found then
{found,fr,fc,letter} = {true,r,c,ch}
else
this &= {r-fr,c-fc}
end if
end if
end for
end for
if not find(this,shape) then
shape = append(shape,this)
end if
end for
res = append(res,{letter&"",shape})
end for
return res
end function
constant shapes = get_shapes(),
nRows = 8,
nCols = 8
sequence grid = repeat(repeat(' ',nCols),nRows),
placed = repeat(false,length(shapes))
function can_place(sequence o, integer r, c, ch)
for i=1 to length(o) by 2 do
integer x := c + o[i+1],
y := r + o[i]
if x<1 or x>nCols
or y<1 or y>nRows
or grid[y][x]!=' ' then
return false
end if
end for
grid[r][c] = ch
for i=1 to length(o) by 2 do
grid[r+o[i]][c+o[i+1]] = ch
end for
return true
end function
procedure un_place(sequence o, integer r, c)
grid[r][c] = ' '
for i=1 to length(o) by 2 do
grid[r+o[i]][c+o[i+1]] = ' '
end for
end procedure
function solve(integer pos=0, numPlaced=0)
if numPlaced == length(shapes) then
return true
end if
integer row = floor(pos/8)+1,
col = mod(pos,8)+1
if grid[row][col]!=' ' then
return solve(pos+1, numPlaced)
end if
for i=1 to length(shapes) do
if not placed[i] then
integer ch = shapes[i][1][1]
for j=1 to length(shapes[i][2]) do
sequence o = shapes[i][2][j]
if can_place(o, row, col, ch) then
placed[i] = true
if solve(pos+1, numPlaced+1) then
return true
end if
un_place(o, row, col)
placed[i] = false
end if
end for
end if
end for
return false
end function
function unsolveable() -- -- The only unsolvable grids seen have -- -.- or -..- or -... at edge/corner, -- - -- --- - -- or somewhere in the middle a -.- -- - -- -- Simply place all shapes at all positions/orientations, -- all the while checking for any untouchable cells. --
sequence griddled = grid
for r=1 to 8 do
for c=1 to 8 do
if grid[r][c]=' ' then
for i=1 to length(shapes) do
integer ch = shapes[i][1][1]
for j=1 to length(shapes[i][2]) do
sequence o = shapes[i][2][j]
if can_place(o, r, c, ch) then
grid[r][c] = ' '
griddled[r][c] = '-'
for k=1 to length(o) by 2 do
grid[r+o[k]][c+o[k+1]] = ' '
griddled[r+o[k]][c+o[k+1]] = '-'
end for
end if
end for
end for
if griddled[r][c]!='-' then return true end if
end if
end for
end for
return false
end function
procedure add_four_randomly()
integer count = 0
while count<4 do
integer r = rand(8),
c = rand(8)
if grid[r][c]=' ' then
grid[r][c] = '-'
count += 1
end if
end while
end procedure
procedure main()
add_four_randomly()
if unsolveable() then
puts(1,"No solution\n")
else
if not solve() then ?9/0 end if
end if
puts(1,join(grid,"\n")&"\n")
end procedure main()</lang>
- Output:
FFPPPVVV YFFPPX-V YFUUXXXV YYU-ZX-I YTUUZZZI -TTTWWZI LTNNNWWI LLLLNNWI
Visual Basic .NET
via
Instead of having a large declaration for each rotation of each pentomino, a small array of encoded positions is supplied (seeds), and it is expanded into the set of 63 possible orientations. However, the additional expansion routines code does take up about 2/3 of the space that would have been taken by the elaborate Integer array definitions. <lang vbnet>Module Module1
Dim symbols As Char() = "XYPFTVNLUZWI█".ToCharArray(),
nRows As Integer = 8, nCols As Integer = 8,
target As Integer = 12, blank As Integer = 12,
grid As Integer()() = New Integer(nRows - 1)() {},
placed As Boolean() = New Boolean(target - 1) {},
pens As List(Of List(Of Integer())), rand As Random,
seeds As Integer() = {291, 292, 293, 295, 297, 329, 330, 332, 333, 335, 378, 586}
Sub Main()
Unpack(seeds) : rand = New Random() : ShuffleShapes(2)
For r As Integer = 0 To nRows - 1
grid(r) = Enumerable.Repeat(-1, nCols).ToArray() : Next
For i As Integer = 0 To 3
Dim rRow, rCol As Integer : Do : rRow = rand.Next(nRows) : rCol = rand.Next(nCols)
Loop While grid(rRow)(rCol) = blank : grid(rRow)(rCol) = blank
Next
If Solve(0, 0) Then
PrintResult()
Else
Console.WriteLine("no solution for this configuration:") : PrintResult()
End If
If System.Diagnostics.Debugger.IsAttached Then Console.ReadKey()
End Sub
Sub ShuffleShapes(count As Integer) ' changes order of the pieces for a more random solution
For i As Integer = 0 To count : For j = 0 To pens.Count - 1
Dim r As Integer : Do : r = rand.Next(pens.Count) : Loop Until r <> j
Dim tmp As List(Of Integer()) = pens(r) : pens(r) = pens(j) : pens(j) = tmp
Dim ch As Char = symbols(r) : symbols(r) = symbols(j) : symbols(j) = ch
Next : Next
End Sub
Sub PrintResult() ' display results
For Each r As Integer() In grid : For Each i As Integer In r
Console.Write("{0} ", If(i < 0, ".", symbols(i)))
Next : Console.WriteLine() : Next
End Sub
' returns first found solution only
Function Solve(ByVal pos As Integer, ByVal numPlaced As Integer) As Boolean
If numPlaced = target Then Return True
Dim row As Integer = pos \ nCols, col As Integer = pos Mod nCols
If grid(row)(col) <> -1 Then Return Solve(pos + 1, numPlaced)
For i As Integer = 0 To pens.Count - 1 : If Not placed(i) Then
For Each orientation As Integer() In pens(i)
If Not TPO(orientation, row, col, i) Then Continue For
placed(i) = True : If Solve(pos + 1, numPlaced + 1) Then Return True
RmvO(orientation, row, col) : placed(i) = False
Next : End If : Next : Return False
End Function
' removes a placed orientation
Sub RmvO(ByVal ori As Integer(), ByVal row As Integer, ByVal col As Integer)
grid(row)(col) = -1 : For i As Integer = 0 To ori.Length - 1 Step 2
grid(row + ori(i))(col + ori(i + 1)) = -1 : Next
End Sub
' checks an orientation, if possible it is placed, else returns false
Function TPO(ByVal ori As Integer(), ByVal row As Integer, ByVal col As Integer,
ByVal sIdx As Integer) As Boolean
For i As Integer = 0 To ori.Length - 1 Step 2
Dim x As Integer = col + ori(i + 1), y As Integer = row + ori(i)
If x < 0 OrElse x >= nCols OrElse y < 0 OrElse y >= nRows OrElse
grid(y)(x) <> -1 Then Return False
Next : grid(row)(col) = sIdx
For i As Integer = 0 To ori.Length - 1 Step 2
grid(row + ori(i))(col + ori(i + 1)) = sIdx
Next : Return True
End Function
'!' the following routines expand the seed values into the 63 orientation arrays. ' source code space savings comparison: ' around 2000 chars for the expansion code, verses about 3000 chars for the integer array defs. ' perhaps not worth the savings?
Sub Unpack(sv As Integer()) ' unpacks a list of seed values into a set of 63 rotated pentominoes
pens = New List(Of List(Of Integer())) : For Each item In sv
Dim Gen As New List(Of Integer()), exi As List(Of Integer) = Expand(item),
fx As Integer() = ToP(exi) : Gen.Add(fx) : For i As Integer = 1 To 7
If i = 4 Then Mir(exi) Else Rot(exi)
fx = ToP(exi) : If Not Gen.Exists(Function(Red) TheSame(Red, fx)) Then Gen.Add(ToP(exi))
Next : pens.Add(Gen) : Next
End Sub
' expands an integer into a set of directions
Function Expand(i As Integer) As List(Of Integer)
Expand = {0}.ToList() : For j As Integer = 0 To 3 : Expand.Insert(1, i And 15) : i >>= 4 : Next
End Function
' converts a set of directions to an array of y, x pairs
Function ToP(p As List(Of Integer)) As Integer()
Dim tmp As List(Of Integer) = {0}.ToList() : For Each item As Integer In p.Skip(1)
tmp.Add(tmp.Item(item >> 2) + {1, 8, -1, -8}(item And 3)) : Next
tmp.Sort() : For i As Integer = tmp.Count - 1 To 0 Step -1 : tmp.Item(i) -= tmp.Item(0) : Next
Dim res As New List(Of Integer) : For Each item In tmp.Skip(1)
Dim adj = If((item And 7) > 4, 8, 0)
res.Add((adj + item) \ 8) : res.Add((item And 7) - adj)
Next : Return res.ToArray()
End Function
' compares integer arrays for equivalency
Function TheSame(a As Integer(), b As Integer()) As Boolean
For i As Integer = 0 To a.Count - 1 : If a(i) <> b(i) Then Return False
Next : Return True
End Function
Sub Rot(ByRef p As List(Of Integer)) ' rotates a set of directions by 90 degrees
For i As Integer = 0 To p.Count - 1 : p(i) = (p(i) And -4) Or ((p(i) + 1) And 3) : Next
End Sub
Sub Mir(ByRef p As List(Of Integer)) ' mirrors a set of directions
For i As Integer = 0 To p.Count - 1 : p(i) = (p(i) And -4) Or (((p(i) Xor 1) + 1) And 3) : Next
End Sub
End Module
</lang>
- Output:
Solution found result (typical output):
Y F F █ L L L L Y Y F F L P P P Y T F N N N P P Y T N N █ V V V T T T W W Z Z V U U X █ W W Z V U X X X █ W Z Z U U X I I I I I
Impossible to solve result (a somewhat rare occurrence):
no solution for this configuration: . █ . . . . . . █ . . █ . . . . . . . . . . . . . . . . █ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VB .Net alternative output (corner characters)
This output may appear better in a command window <lang vbnet>Module Module1
Dim symbols As Char() = "XYPFTVNLUZWI-".ToCharArray(),
nRows As Integer = 8, nCols As Integer = 8,
target As Integer = 12, blank As Integer = 12,
grid As Integer()() = New Integer(nRows - 1)() {},
placed As Boolean() = New Boolean(target - 1) {},
pens As List(Of List(Of Integer())), rand As Random,
seeds As Integer() = {291, 292, 293, 295, 297, 329, 330, 332, 333, 335, 378, 586}
Sub Main()
Unpack(seeds) : rand = New Random() : ShuffleShapes(2)
For r As Integer = 0 To nRows - 1
grid(r) = Enumerable.Repeat(-1, nCols).ToArray() : Next
For i As Integer = 0 To 3
Dim rRow, rCol As Integer : Do : rRow = rand.Next(nRows) : rCol = rand.Next(nCols)
Loop While grid(rRow)(rCol) = blank : grid(rRow)(rCol) = blank
Next
If Solve(0, 0) Then
PrintResult()
Else
Console.WriteLine("no solution for this configuration:") : PrintResult()
End If
If System.Diagnostics.Debugger.IsAttached Then Console.ReadKey()
End Sub
Sub ShuffleShapes(count As Integer) ' changes order of the pieces for a more random solution
For i As Integer = 0 To count : For j = 0 To pens.Count - 1
Dim r As Integer : Do : r = rand.Next(pens.Count) : Loop Until r <> j
Dim tmp As List(Of Integer()) = pens(r) : pens(r) = pens(j) : pens(j) = tmp
Dim ch As Char = symbols(r) : symbols(r) = symbols(j) : symbols(j) = ch
Next : Next
End Sub
Sub PrintPlainResult() ' display results
For Each r As Integer() In grid : For Each i As Integer In r
Console.Write("{0} ", If(i < 0, ".", symbols(i)))
Next : Console.WriteLine() : Next
End Sub
Sub PrintResult() ' display fancy results
Dim res As String = String.Empty
For Each r As Integer() In grid : For Each i As Integer In r
res &= String.Format("{0}", If(i < 0, ".", symbols(i)))
Next : res &= " " & vbLf : Next
Console.WriteLine(Cornered(DW(res)))
End Sub
' returns first found solution only
Function Solve(ByVal pos As Integer, ByVal numPlaced As Integer) As Boolean
If numPlaced = target Then Return True
Dim row As Integer = pos \ nCols, col As Integer = pos Mod nCols
If grid(row)(col) <> -1 Then Return Solve(pos + 1, numPlaced)
For i As Integer = 0 To pens.Count - 1 : If Not placed(i) Then
For Each orientation As Integer() In pens(i)
If Not TPO(orientation, row, col, i) Then Continue For
placed(i) = True : If Solve(pos + 1, numPlaced + 1) Then Return True
RmvO(orientation, row, col) : placed(i) = False
Next : End If : Next : Return False
End Function
' removes a placed orientation
Sub RmvO(ByVal ori As Integer(), ByVal row As Integer, ByVal col As Integer)
grid(row)(col) = -1 : For i As Integer = 0 To ori.Length - 1 Step 2
grid(row + ori(i))(col + ori(i + 1)) = -1 : Next
End Sub
' checks an orientation, if possible it is placed, else returns false
Function TPO(ByVal ori As Integer(), ByVal row As Integer, ByVal col As Integer,
ByVal sIdx As Integer) As Boolean
For i As Integer = 0 To ori.Length - 1 Step 2
Dim x As Integer = col + ori(i + 1), y As Integer = row + ori(i)
If x < 0 OrElse x >= nCols OrElse y < 0 OrElse y >= nRows OrElse
grid(y)(x) <> -1 Then Return False
Next : grid(row)(col) = sIdx
For i As Integer = 0 To ori.Length - 1 Step 2
grid(row + ori(i))(col + ori(i + 1)) = sIdx
Next : Return True
End Function
'!' the following routines expand the seed values into the 63 orientation arrays. ' source code space savings comparison: ' around 2000 chars for the expansion code, verses about 3000 chars for the integer array defs. ' perhaps not worth the savings?
Sub Unpack(sv As Integer()) ' unpacks a list of seed values into a set of 63 rotated pentominoes
pens = New List(Of List(Of Integer())) : For Each item In sv
Dim Gen As New List(Of Integer()), exi As List(Of Integer) = Expand(item),
fx As Integer() = ToP(exi) : Gen.Add(fx) : For i As Integer = 1 To 7
If i = 4 Then Mir(exi) Else Rot(exi)
fx = ToP(exi) : If Not Gen.Exists(Function(Red) TheSame(Red, fx)) Then Gen.Add(ToP(exi))
Next : pens.Add(Gen) : Next
End Sub
' expands an integer into a set of directions
Function Expand(i As Integer) As List(Of Integer)
Expand = {0}.ToList() : For j As Integer = 0 To 3 : Expand.Insert(1, i And 15) : i >>= 4 : Next
End Function
' converts a set of directions to an array of y, x pairs
Function ToP(p As List(Of Integer)) As Integer()
Dim tmp As List(Of Integer) = {0}.ToList() : For Each item As Integer In p.Skip(1)
tmp.Add(tmp.Item(item >> 2) + {1, 8, -1, -8}(item And 3)) : Next
tmp.Sort() : For i As Integer = tmp.Count - 1 To 0 Step -1 : tmp.Item(i) -= tmp.Item(0) : Next
Dim res As New List(Of Integer) : For Each item In tmp.Skip(1)
Dim adj = If((item And 7) > 4, 8, 0)
res.Add((adj + item) \ 8) : res.Add((item And 7) - adj)
Next : Return res.ToArray()
End Function
' compares integer arrays for equivalency
Function TheSame(a As Integer(), b As Integer()) As Boolean
For i As Integer = 0 To a.Count - 1 : If a(i) <> b(i) Then Return False
Next : Return True
End Function
Sub Rot(ByRef p As List(Of Integer)) ' rotates a set of directions by 90 degrees
For i As Integer = 0 To p.Count - 1 : p(i) = (p(i) And -4) Or ((p(i) + 1) And 3) : Next
End Sub
Sub Mir(ByRef p As List(Of Integer)) ' mirrors a set of directions
For i As Integer = 0 To p.Count - 1 : p(i) = (p(i) And -4) Or (((p(i) Xor 1) + 1) And 3) : Next
End Sub
'!' routines for fancy output
Function DW(s As String) As String ' double every character in string except linefeeds
DW = String.Empty : For Each ch As Char In s : DW &= ch & If(ch = vbLf, "", ch) : Next
End Function
' converts double-width ascii text into a cornered version
Function Cornered(s As String) As String
Dim lines() As String = s.Split(vbLf)
Dim res As String = String.Empty
Dim line As String = New String(" ", lines(0).Length + 1), last
For i As Integer = 0 To lines.Length - 1
last = line : line = " " & lines(i) : res &= Puzzle(last, line) & vbLf
Next
Return res & Puzzle(line, New String(" ", lines.Last().Length + 1))
End Function
' tests each intersection to determine the correct corner symbol
Function Puzzle(a As String, b As String)
Dim res As String = String.Empty
If (a.Length > b.Length) Then b &= New String(" ", a.Length - b.Length)
If (a.Length < b.Length) Then a &= New String(" ", b.Length - a.Length)
For i As Integer = 0 To a.Length - 2
res &= " 12└4┘─┴8│┌├┐┤┬┼"(If(a(i) = a(i + 1), 0, 1) +
If(b(i + 1) = a(i + 1), 0, 2) + If(a(i) = b(i), 0, 4) + If(b(i) = b(i + 1), 0, 8))
Next
Return res
End Function
End Module
</lang>
- Output:
Solution found result (typical output):
┌─────┬─────┬─┬─┐ │ ┌─┐ ├─┐ │ │ │ ├─┼─┴─┴─┴─┬─┘ │ │ │ └───┬─┐ │ ┌─┤ │ │ ┌───┼─┼─┴─┘ │ │ ├─┘ ┌─┘ └─┐ ┌─┼─┤ │ ┌─┼─┐ ┌─┴─┘ │ │ ├─┴─┘ └─┤ ┌───┘ │ └───────┴─┴─────┘
Impossible to solve result (a somewhat rare occurrence):
no solution for this configuration: ┌─┬─┬─┬─┬───────┐ │ └─┘ └─┘ │ │ ┌─┐ │ ├─┼─┘ │ ├─┘ │ │ │ │ │ │ │ └───────────────┘
zkl
<lang zkl>fcn printResult
{ foreach row in (grid){ row.apply(symbols.get).concat(" ").println() } }
fcn tryPlaceOrientation(o, R,C, shapeIndex){
foreach ro,co in (o){ r,c:=R+ro, C+co;
if(r<0 or r>=nRows or c<0 or c>=nCols or grid[r][c]!=-1) return(False);
}
grid[R][C]=shapeIndex; foreach ro,co in (o){ grid[R+ro][C+co]=shapeIndex }
True
} fcn removeOrientation(o, r,c)
{ grid[r][c]=-1; foreach ro,co in (o){ grid[r+ro][c+co]=-1 } }
fcn solve(pos,numPlaced){
if(numPlaced==target) return(True);
row,col:=pos.divr(nCols);
if(grid[row][col]!=-1) return(solve(pos+1,numPlaced));
foreach i in (shapes.len()){
if(not placed[i]){
foreach orientation in (shapes[i]){ if(not tryPlaceOrientation(orientation, row,col, i)) continue; placed[i]=True; if(solve(pos+1,numPlaced+1)) return(True); removeOrientation(orientation, row,col); placed[i]=False; }
} } False
}</lang> <lang zkl>reg [private] // the shapes are made of groups of 4 (r,c) pairs
_F=T(T(1,-1, 1,0, 1,1, 2,1), T(0,1, 1,-1, 1,0, 2,0),
T(1,0 , 1,1, 1,2, 2,1), T(1,0, 1,1, 2,-1, 2,0), T(1,-2, 1,-1, 1,0, 2,-1),
T(0,1, 1,1, 1,2, 2,1), T(1,-1, 1,0, 1,1, 2,-1), T(1,-1, 1,0, 2,0, 2,1)),
_I=T(T(0,1, 0,2, 0,3, 0,4), T(1,0, 2,0, 3,0, 4,0)),
_L=T(T(1,0, 1,1, 1,2, 1,3), T(1,0, 2,0, 3,-1, 3,0),
T(0,1, 0,2, 0,3, 1,3), T(0,1, 1,0, 2,0, 3,0), T(0,1, 1,1, 2,1, 3,1),
T(0,1, 0,2, 0,3, 1,0), T(1,0, 2,0, 3,0, 3,1), T(1,-3, 1,-2, 1,-1, 1,0)),
_N=T(T(0,1, 1,-2, 1,-1, 1,0), T(1,0, 1,1, 2,1, 3,1),
T(0,1, 0,2, 1,-1, 1,0), T(1,0, 2,0, 2,1, 3,1), T(0,1, 1,1, 1,2, 1,3),
T(1,0, 2,-1, 2,0, 3,-1),T(0,1, 0,2, 1,2, 1,3), T(1,-1, 1,0, 2,-1, 3,-1)),
_P=T(T(0,1, 1,0, 1,1, 2,1), T(0,1, 0,2, 1,0, 1,1),
T(1,0, 1,1, 2,0, 2,1), T(0,1, 1,-1, 1,0, 1,1), T(0,1, 1,0, 1,1, 1,2),
T(1,-1, 1,0, 2,-1, 2,0), T(0,1, 0,2, 1,1, 1,2), T(0,1, 1,0, 1,1, 2,0)),
_T=T(T(0,1, 0,2, 1,1, 2,1), T(1,-2, 1,-1, 1,0, 2,0),
T(1,0, 2,-1, 2,0, 2,1), T(1,0, 1,1, 1,2, 2,0)),
_U=T(T(0,1, 0,2, 1,0, 1,2), T(0,1, 1,1, 2,0, 2,1),
T(0,2, 1,0, 1,1, 1,2), T(0,1, 1,0, 2,0, 2,1)),
_V=T(T(1,0, 2,0, 2,1, 2,2), T(0,1, 0,2, 1,0, 2,0),
T(1,0, 2,-2, 2,-1, 2,0), T(0,1, 0,2, 1,2, 2,2)),
_W=T(T(1,0, 1,1, 2,1, 2,2), T(1,-1, 1,0, 2,-2, 2,-1),
T(0,1, 1,1, 1,2, 2,2), T(0,1, 1,-1, 1,0, 2,-1)),
_X=T(T(1,-1, 1,0, 1,1, 2,0)),
_Y=T(T(1,-2, 1,-1, 1,0, 1,1), T(1,-1, 1,0, 2,0, 3,0),
T(0,1, 0,2, 0,3, 1,1), T(1,0, 2,0, 2,1, 3,0), T(0,1, 0,2, 0,3, 1,2),
T(1,0, 1,1, 2,0, 3,0), T(1,-1, 1,0, 1,1, 1,2), T(1,0, 2,-1, 2,0, 3,0)),
_Z=T(T(0,1, 1,0, 2,-1, 2,0), T(1,0, 1,1, 1,2, 2,2),
T(0,1, 1,1, 2,1, 2,2), T(1,-2, 1,-1, 1,0, 2,-2));
const nRows=8, nCols=8, target=12, blank=12; var [const]
grid = nRows.pump(List(),nCols.pump(List(),-1).copy), placed = target.pump(List(),False),
symbols="FILNPTUVWXYZ-".split(""),
shapes=T(_F,_I,_L,_N,_P,_T,_U,_V,_W,_X,_Y,_Z) // ((a,b, c,d))-->(((a,b),(c,d)))
.pump(List,List("pump",List,List("pump",List,Void.Read,T.create)));</lang>
<lang zkl>foreach r,c in ([0..nRows-1].walk().shuffle().zip([0..nCols-1].walk().shuffle())[0,4])
{ grid[r][c]=blank } // make sure 4 unique random spots
if(solve(0,0)) printResult(); else println("No solution");</lang>
- Output:
F Y Y Y Y U U U F F F Y - U X U I F W W L X X X I W W N L - X T I W N N L T T T I V N L L Z Z T I V N P P P Z - - V V V P P Z Z