# Fillomino Solver

Fillomino is a puzzle where you fill a grid with polyominoes. Each polyomino is an area of contiguous cells. The grid representation shows what size polyomino is covering each cell. For example, a pentomino(5) would be shown as 5 in each of five contiguous cells (see below). Two polyominoes of the same size cannot share a border, but may border diagonally.

For each puzzle, you're started with a number of givens and must fill in the remaining cells. An easy example puzzle and solution:

Your task: Given a square puzzle, solve it and output the answer. Input may be via stdin, a single command line argument, or text file. Input will be given as an integer n, followed by n lines of n digits each. Empty cells will be given as periods(.). For the example puzzle above, it would be:

5
3..66
5.4.6
.54.6
.1.6.
..312


Output is the solved puzzle, given on n lines of n digits, to console or text file:

33366
55446
55466
51462
33312


If the puzzle is not valid, output 0. A puzzle could be invalid if the input is malformed or there is no solution. If there are multiple solutions, you may output any one or all of them.

Since each cell is represented by a single digit, all puzzles will consist of polyominoes size 9 and under only. If it is not possible to solve without larger polyominoes, consider it invalid.

Valid answers will solve any given puzzle, not simply output solutions to test cases. No external resources, be it online or local. If there happens to be a language with a built-in fillomino solving function, you can't use it. In short, play fair.

Test Case:

Input:

9
..21.3..5
.5...5..5
.1.44.334
...53.4..
2.3.3..5.
1.15.5.15
..45..1..
.24.53.53
....2....


Output (a possible solution):

322133315
355445555
315443334
235531444
233135551
141535515
344553155
324553553
321223133


Remember that some polyominoes have no given numbers, and some have more than one. There is not a one-to-one relationship between the number of givens and the number of polyominoes.

Score is standard code-golf, size of the program in bytes.

• Is a recursive approach a valid answer if it works for a 9x9 board but will run out of memory for some larger size board? Jul 4, 2015 at 23:36
• Yes.I don't expect you to be able to feasibly run a 31x31 or anything. Just so that you can actually run both the 5x5 and 9x9 above(to give output for the test cases), and would theoretically work for larger with the same algorithm (given a crap-ton of resources). Jul 5, 2015 at 2:22

import java.util.*;import java.awt.Point;public class G{public static void main(String[]args){new G();}Scanner z=new Scanner(System.in);public G(){s=z.nextInt();z.nextLine();int g[][]=new int[s][s];for(int i=0;i<s;i++)Arrays.fill(g[i],-1);for(int i=0;i<s;i++){String line=z.nextLine();for(int j=0;j<s;j++)if(line.charAt(j)!='.')g[i][j]=Integer.parseInt(Character.toString(line.charAt(j)));}System.out.println();if(y(g)){for(int i=0;i<s;i++)for(int j=0;j<s;j++)System.out.print(g[i][j]);System.out.println();}else System.out.println(0);}private boolean x(Collection<Point>c,int[][]d){if(c.size()==0)return true;int j=0;for(Iterator<Point>k=c.iterator();k.hasNext();k.next(),j++){for(int sol=9;sol>=0;sol--){int[][]a=new int[s][s];for(int i=0;i<s;i++)a[i]=Arrays.copyOf(d[i],s);List<Point>b=new ArrayList<Point>();for(Point p:c)if(!b.contains(p))b.add(new Point(p));a[b.get(j).x][b.get(j).y]=sol;if(w(a,b.get(j))){if(x(b,a)){for(int i=0;i<s;i++)d[i]=Arrays.copyOf(a[i],s);c.clear();c.addAll(b);return true;}}}}return false;}int s;private boolean y(int[][]d){int[][] a=new int[s][s];for (int i = 0; i<s;i++)a[i]=Arrays.copyOf(d[i],s);List<Point> incomplete=new ArrayList<Point>();if(r(a)&&s(a)){a(a);System.exit(0);}else if(!r(a)){q("INVALID FROM MAIN, ",12);return false;}for(int i=0;i<s;i++)for(int j=0;j<s;j++){if(a[i][j]!=-1)if(t(new Point(i,j),a,null,a[i][j]).size()!=a[i][j]){if(w(a,new Point(i,j))){a(a);if(y(a)){for(int i=0;i<s;i++)d[i]=Arrays.copyOf(a[i],s);return true;}else return false;}else return false;}}for(int i=0;i<s;i++)for(int j=0;j<s;j++)if(a[i][j]==-1){Set<Point>c=t(new Point(i,j),a,null,-1);if(x(c,a)){if(y(a)){for(int i=0;i<s;i++)d[i] = Arrays.copyOf(a[i], s);return true;}else return false;}else return false;}q("How did you get here",1);return false;}private boolean w(int[][]d,Point b){List<Point>c;Set<Point>a;a=t(b,d,null,d[b.x][b.y]);c=new ArrayList<Point>(u(b,d,null,d[b.x][b.y]));int h=d[b.x][b.y];int g=h-a.size();if(c.size()<g){return false;}else if(v(c,h,h,new ArrayList<Point>(a),0,d))return true;else return false;}private boolean v(List<Point>c,int h,int g,List<Point>e,int f,int[][]d){if(e==null)e=new ArrayList<Point>();int[][]a=new int[s][s];for(int i=0;i<s;i++)for(int k=0;k<s;k++)a[i][k]=d[i][k];if(f<g&&e.size()<g){for(int i=0;i<c.size();i++){if(!e.contains(c.get(i))){if(d[c.get(i).x][c.get(i).y]==h){for(Point c:e){a[c.x][c.y]=h;}Set<Point> u=t(e.get(0),a,null,h);Set<Point>v=t(c.get(i),a,null,h);if(!Collections.disjoint(u,v)){u.addAll(v);List<Point>uList=new ArrayList<Point>(u);if(v(c,h,g,uList,f+1,a)){q("this e sucess",2);if(y(d)){e.addAll(uList);return true;}}else;}for(int l=0;l<s;l++)for(int k=0;k<s;k++)a[l][k]=d[l][k];}else if(e.add(c.get(i))){if(v(c,h,g,e,f+1,d)){q("this e sucess",2);if(y(d))return true;}}if(e.contains(c.get(i)))e.remove(c.get(i));}}return false;}else if(f>g||e.size()>g){if(f>g){q("Your over the g. ");return false;}else return false;}else{for(Point c:e){a[c.x][c.y]=h;}if(r(a)){if(y(a)){for(int i=0;i<s;i++)d[i]=Arrays.copyOf(a[i],s);q("complete(a) is true, ",4);return true;}else{return false;}}else{return false;}}}private void q(String out,int i){System.err.println(out+". exit code: "+i);System.exit(i);}private void q(String a){q(a,0);}private boolean r(int[][] d){for(int i=0;i<s;i++)for(int j=0;j<s;j++)if(d[i][j]!=-1){Set<Point>same=t(new Point(i,j),d,null,d[i][j]);if(same.size()>d[i][j]){return false;}Set<Point>fae=u(new Point(i,j),d,null,d[i][j]);if(u(new Point(i,j),d,null,d[i][j]).size()<d[i][j]){return false;}}return true;}private Set<Point> u(Point p,int[][]d,Set<Point>u,int i){u=(u==null)?new HashSet<Point>():u;if(d[p.x][p.y]==i||d[p.x][p.y]==-1)u.add(p);int x=p.x,y=p.y;Point t=new Point();if(x+1<s&&(d[x+1][y]==i||d[x+1][y]==-1)){if(u.add(new Point(x+1,y)))u=u(new Point(x+1,y),d,u,i);}if(y+1<s&&(d[x][y+1]==i||d[x][y+1]==-1)){if(u.add(new Point(x,y+1)))u=u(new Point(x,y+1),d,u,i);}if(x-1>=0&&(d[x-1][y]==i||d[x-1][y]==-1)){if(u.add(new Point(x-1,y)))u=u(new Point(x-1,y),d,u,i);}if(y-1>=0&&(d[x][y-1]==i||d[x][y-1]==-1)){if(u.add(new Point(x,y-1)))u=u(new Point(x,y-1),d,u,i);}return u;}private Set<Point> t(Point p,int[][]d,Set<Point>u,int i){u=(u==null)?new HashSet<Point>():u;if(d[p.x][p.y]==i)u.add(p);int x=p.x,y=p.y;Point t=new Point(p);if(x+1<s&&d[x+1][y]==i){if(u.add(new Point(x+1,y)))u=t(new Point(x+1,y),d,u,i);}if(y+1<s&&d[x][y+1]==i){if(u.add(new Point(x,y+1)))u=t(new Point(x,y+1),d,u,i);}if(x-1>=0&&d[x-1][y]==i){if(u.add(new Point(x-1,y)))u=t(new Point(x-1,y),d,u,i);}if(y-1>=0&&d[x][y-1]==i){if(u.add(new Point(x,y-1)))u=t(new Point(x,y-1),d,u,i);}return u;}private boolean s(int[][]d){for(int i=0;i<s;i++)for(int j=0;j<s;j++)if(t(new Point(i,j),d,null,d[i][j]).size()!=d[i][j])return false;return true;}private void a(int[][]d){for(int i=0;i<s;i++){for(int j=0;j<s;j++){System.out.printf("%1s",d[i][j]==-1?".":Integer.toString(d[i][j]));}System.out.println("");}}}