[Question]
  [
In the game of Flood Paint, the goal of the game is to get the entire board to be the same colour in as few turns as possible.
The game starts with a board that looks something like this:
```
3 3 5 4 1 3 4 1 5
5 1 3 4 1 1 5 2 1
6 5 2 3 4 3 3 4 3
4 4 4 5 5 5 4 1 4
6 2 5 3[3]1 1 6 6
5 5 1 2 5 2 6 6 3
6 1 1 5 3 6 2 3 6
1 2 2 4 5 3 5 1 2
3 6 6 1 5 1 3 2 4
```
Currently, the number (representing a colour) at the center of the board is 3. Each turn, the square at the center will change colour, and all the squares of the same colour that are reachable from the center by moving horizontally or vertically (i.e. in the flood region of the center square) will change colours with it. So if the center square changes colour to 5:
```
3 3 5 4 1 3 4 1 5
5 1 3 4 1 1 5 2 1
6 5 2 3 4 3 3 4 3
4 4 4 5 5 5 4 1 4
6 2 5 5[5]1 1 6 6
5 5 1 2 5 2 6 6 3
6 1 1 5 3 6 2 3 6
1 2 2 4 5 3 5 1 2
3 6 6 1 5 1 3 2 4
```
then the 3 that was to the left of the center 3 will also change colour. Now there are a total of seven 5's reachable from the center one, and so if we then change colour to 4:
```
3 3 5 4 1 3 4 1 5
5 1 3 4 1 1 5 2 1
6 5 2 3 4 3 3 4 3
4 4 4 4 4 4 4 1 4
6 2 4 4[4]1 1 6 6
5 5 1 2 4 2 6 6 3
6 1 1 5 3 6 2 3 6
1 2 2 4 5 3 5 1 2
3 6 6 1 5 1 3 2 4
```
the painted region again increases in size dramatically.
Your task is to create a program that will take a 19-by-19 grid of colours from 1 to 6 as input, in whatever form you choose:
```
4 5 1 1 2 2 1 6 2 6 3 4 2 3 2 3 1 6 3
4 2 6 3 4 4 5 6 4 4 5 3 3 3 3 5 4 3 4
2 3 5 2 2 5 5 1 2 6 2 6 6 2 1 6 6 1 2
4 6 5 5 5 5 4 1 6 6 3 2 6 4 2 6 3 6 6
1 6 4 4 4 4 6 4 2 5 5 3 2 2 4 1 5 2 5
1 6 2 1 5 1 6 4 4 1 5 1 3 4 5 2 3 4 1
3 3 5 3 2 2 2 4 2 1 6 6 6 6 1 4 5 2 5
1 6 1 3 2 4 1 3 3 4 6 5 1 5 5 3 4 3 3
4 4 1 5 5 1 4 6 3 3 4 5 5 6 1 6 2 6 4
1 4 2 5 6 5 5 3 2 5 5 5 3 6 1 4 4 6 6
4 6 6 2 6 6 2 4 2 6 1 5 6 2 3 3 4 3 6
6 1 3 6 3 5 5 3 6 1 3 4 4 5 1 2 6 4 3
2 6 1 3 2 4 2 6 1 1 5 2 6 6 6 6 3 3 3
3 4 5 4 6 6 3 3 4 1 1 6 4 5 1 3 4 1 2
4 2 6 4 1 5 3 6 4 3 4 5 4 2 1 1 4 1 1
4 2 4 1 5 2 2 3 6 6 6 5 2 5 4 5 4 5 1
5 6 2 3 4 6 5 4 1 3 2 3 2 1 3 6 2 2 4
6 5 4 1 3 2 2 1 1 1 6 1 2 6 2 5 6 4 5
5 1 1 4 2 6 2 5 6 1 3 3 4 1 6 1 2 1 2
```
and return a sequence of colours that the center square will change to each turn, again in the format of your choosing:
```
263142421236425431645152623645465646213545631465
```
At the end of each sequence of moves, the squares in the 19-by-19 grid must all be the same colour.
Your program must be entirely deterministic; pseudorandom solutions are allowed, but the program must generate the same output for the same test case every time.
The winning program will take the fewest total number of steps to solve all 100,000 test cases found in [this file](https://github.com/joezeng/pcg-se-files/raw/master/floodtest.tar.gz) (zipped text file, 14.23 MB). If two solutions take the same number of steps (e.g. if they both found the optimal strategy), the shorter program will win.
---
BurntPizza has written a program in Java to verify the test results. To use this program, run your submission and pipe the output to a file called `steps.txt`. Then, run this program with `steps.txt` and the `floodtest` file in the same directory. If your entry is valid and produces correct solutions for all the files, it should pass all the tests and return `All boards solved successfully.`
```
import java.io.*;
import java.util.*;
public class PainterVerifier {
    public static void main(String[] args) throws FileNotFoundException {
        char[] board = new char[361];
        Scanner s = new Scanner(new File("steps.txt"));
        Scanner b = new Scanner(new File("floodtest"));
        int lineNum = 0;
        caseloop: while (b.hasNextLine()) {
            for (int l = 0; l < 19; l++) {
                String lineb = b.nextLine();
                if (lineb.isEmpty())
                    continue caseloop;
                System.arraycopy(lineb.toCharArray(), 0, board, l * 19, 19);
            }
            String line = s.nextLine();
            if (line.isEmpty())
                continue;
            char[] steps = line.toCharArray();
            Stack<Integer> nodes = new Stack<Integer>();
            for (char c : steps) {
                char targetColor = board[180];
                char replacementColor = c;
                nodes.push(180);
                while (!nodes.empty()) {
                    int n = nodes.pop();
                    if (n < 0 || n > 360)
                        continue;
                    if (board[n] == targetColor) {
                        board[n] = replacementColor;
                        if (n % 19 > 0)
                            nodes.push(n - 1);
                        if (n % 19 < 18)
                            nodes.push(n + 1);
                        if (n / 19 > 0)
                            nodes.push(n - 19);
                        if (n / 19 < 18)
                            nodes.push(n + 19);
                    }
                }
            }
            char center = board[180];
            for (char c : board)
                if (c != center) {
                    s.close();
                    b.close();
                    System.out.println("\nIncomplete board found!\n\tOn line " + lineNum + " of steps.txt");
                    System.exit(0);
                }
            if (lineNum % 5000 == 0)
                System.out.printf("Verification %d%c complete...\n", lineNum * 100 / 100000, '%');
            lineNum++;
        }
        s.close();
        b.close();
        System.out.println("All boards solved successfully.");
    }
}
```
---
Also, a scoreboard, since the results aren't actually sorted by score and here it actually matters a lot:
1. [1,985,078](https://codegolf.stackexchange.com/a/158273/7110) - smack42, Java
2. [2,075,452](https://codegolf.stackexchange.com/a/114172/18957) - user1502040, C
3. [2,098,382](https://codegolf.stackexchange.com/a/26917/7110) - tigrou, C#
4. [2,155,834](https://codegolf.stackexchange.com/a/26608/7110) - CoderTao, C#
5. [2,201,995](https://codegolf.stackexchange.com/a/26368/7110) - MrBackend, Java
6. [2,383,569](https://codegolf.stackexchange.com/a/26455/7110) - CoderTao, C#
7. [2,384,020](https://codegolf.stackexchange.com/a/26373/7110) - Herjan, C
8. [2,403,189](https://codegolf.stackexchange.com/a/26534/7110) - Origineil, Java
9. [2,445,761](https://codegolf.stackexchange.com/a/26373/7110) - Herjan, C
10. [2,475,056](https://codegolf.stackexchange.com/a/26341/7110) - Jeremy List, Haskell
11. [2,480,714](https://codegolf.stackexchange.com/a/26255/7110) - SteelTermite, C (2,395 bytes)
12. [2,480,714](https://codegolf.stackexchange.com/a/26244/7110) - Herjan, Java (4,702 bytes)
13. [2,588,847](https://codegolf.stackexchange.com/a/26331/7110) - BurntPizza, Java (2,748 bytes)
14. [2,588,847](https://codegolf.stackexchange.com/a/26795/7110) - Gero3, node.js (4,641 bytes)
15. [2,979,145](https://codegolf.stackexchange.com/a/26813/7110) - Teun Pronk, Delphi XE3
16. [4,780,841](https://codegolf.stackexchange.com/a/26313/7110) - BurntPizza, Java
17. [10,800,000](https://codegolf.stackexchange.com/a/26233/7110) - Joe Z., Python
  
[Answer]
# C# - 2,098,382 steps
I try many things, most of them fail and just didn't work at all, until recently. I got something interesting enough to post an answer. 
There is certainly ways to improve this further more. I think going under the 2M steps might be possible.
It took approx `7 hours` to generate results. Here is a txt file with all solutions, in case someone want to check them : [results.zip](https://anonfiles.com/file/25e29d3ec19b03fac9c1f8997a5596fc)
```
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Threading.Tasks;
namespace FloodPaintAI
{
    class Node
    {   
        public byte Value;             //1-6
        public int Index;              //unique identifier, used for easily deepcopying the graph
        public List<Node> Neighbours;  
        public List<Tuple<int, int>> NeighboursPositions; //used by BuildGraph() 
        public int Depth;    //used by GetSumDistances() 
        public bool Checked; // 
        public Node(byte value, int index)
        {
            Value = value;      
            Index = index;          
        }
        public Node(Node node)
        {           
            Value = node.Value; 
            Index = node.Index;                     
        }
    }
    class Board
    {
        private const int SIZE = 19;
        private const int STARTPOSITION = 9;
        public Node Root;         //root of graph. each node is a set of contiguous, same color square
        public List<Node> Nodes;  //all nodes in the graph, used for deep copying
        public int EstimatedCost; //estimated cost, used by A* Pathfinding
        public List<byte> Solution;
        public Board(StreamReader input)
        {                   
            byte[,] board = new byte[SIZE, SIZE];
            for(int j = 0 ; j < SIZE ; j++)
            {
                string line = input.ReadLine();
                for(int i = 0 ; i < SIZE ; i++)         
                {                                       
                    board[j, i] = byte.Parse(line[i].ToString());
                }               
            }
            Solution = new List<byte>();
            BuildGraph(board);  
        }
        public Board(Board boardToCopy)
        {               
            //copy the graph            
            Nodes = new List<Node>(boardToCopy.Nodes.Count);
            foreach(Node nodeToCopy in boardToCopy.Nodes)
            {
                Node node = new Node(nodeToCopy);
                Nodes.Add(node);
            }
            //copy "Neighbours" property
            for(int i = 0 ; i < boardToCopy.Nodes.Count ; i++)
            {
                Node node = Nodes[i];
                Node nodeToCopy = boardToCopy.Nodes[i];
                node.Neighbours = new List<Node>(nodeToCopy.Neighbours.Count);
                foreach(Node neighbour in nodeToCopy.Neighbours)
                {
                    node.Neighbours.Add(Nodes[neighbour.Index]);
                }
            }
            Root = Nodes[boardToCopy.Root.Index];
            EstimatedCost = boardToCopy.EstimatedCost;          
            Solution = new List<byte>(boardToCopy.Solution);            
        }
        private void BuildGraph(byte[,] board)
        {                       
            int[,] nodeIndexes = new int[SIZE, SIZE];
            Nodes = new List<Node>();
            //check how much sets we have (1st pass)
            for(int j = 0 ; j < SIZE ; j++)
            {
                for(int i = 0 ; i < SIZE ; i++)         
                {               
                    if(nodeIndexes[j, i] == 0) //not already visited                    
                    {
                        Node newNode = new Node(board[j, i], Nodes.Count);                      
                        newNode.NeighboursPositions = new List<Tuple<int, int>>();
                        Nodes.Add(newNode);
                        BuildGraphFloodFill(board, nodeIndexes, newNode, i, j, board[j, i]);
                    }
                }       
            }
            //set neighbours and root (2nd pass)
            foreach(Node node in Nodes)
            {
                node.Neighbours = new List<Node>();
                node.Neighbours.AddRange(node.NeighboursPositions.Select(x => nodeIndexes[x.Item2, x.Item1]).Distinct().Select(x => Nodes[x - 1]));
                node.NeighboursPositions = null;                
            }
            Root = Nodes[nodeIndexes[STARTPOSITION, STARTPOSITION] - 1];            
        }
        private void BuildGraphFloodFill(byte[,] board, int[,] nodeIndexes, Node node, int startx, int starty, byte floodvalue)
        {
            Queue<Tuple<int, int>> queue = new Queue<Tuple<int, int>>();
            queue.Enqueue(new Tuple<int, int>(startx, starty));
            while(queue.Count > 0)
            {
                Tuple<int, int> position = queue.Dequeue();
                int x = position.Item1;
                int y = position.Item2;
                if(x >= 0 && x < SIZE && y >= 0 && y < SIZE)
                {
                    if(nodeIndexes[y, x] == 0 && board[y, x] == floodvalue)
                    {
                        nodeIndexes[y, x] = node.Index + 1;
                        queue.Enqueue(new Tuple<int, int>(x + 1, y));
                        queue.Enqueue(new Tuple<int, int>(x - 1, y));
                        queue.Enqueue(new Tuple<int, int>(x, y + 1));
                        queue.Enqueue(new Tuple<int, int>(x, y - 1));                                           
                    }               
                    if(board[y, x] != floodvalue)
                        node.NeighboursPositions.Add(position);                         
                }       
            }
        }
        public int GetEstimatedCost()
        {       
            Board current = this;
            //copy current board and play the best color until the end.
            //number of moves required to go the end is the heuristic
            //estimated cost = current cost + heuristic
            while(!current.IsSolved())
            {
                int minSumDistance = int.MaxValue;
                Board minBoard = null;
                //find color which give the minimum sum of distance from root to each other node
                foreach(byte i in current.Root.Neighbours.Select(x => x.Value).Distinct())
                {
                    Board copy = new Board(current);
                    copy.Play(i);                   
                    int distance = copy.GetSumDistances();                  
                    if(distance < minSumDistance)
                    {
                        minSumDistance = distance;
                        minBoard = copy;
                    }
                }
                current = minBoard;
            }           
            return current.Solution.Count;
        }
        public int GetSumDistances()
        {
            //get sum of distances from root to each other node, using BFS
            int sumDistances = 0;           
            //reset marker
            foreach(Node n in Nodes)
            {
                n.Checked = false;                                  
            }
            Queue<Node> queue = new Queue<Node>();
            Root.Checked = true;
            Root.Depth = 0; 
            queue.Enqueue(Root);
            while(queue.Count > 0)
            {
                Node current = queue.Dequeue();                             
                foreach(Node n in current.Neighbours)
                {
                    if(!n.Checked)          
                    {                                   
                        n.Checked = true;                                               
                        n.Depth = current.Depth + 1;
                        sumDistances += n.Depth;            
                        queue.Enqueue(n);   
                    }               
                }
            }
            return sumDistances;
        }       
        public void Play(byte value)            
        {
            //merge root node with other neighbours nodes, if color is matching
            Root.Value = value;
            List<Node> neighboursToRemove = Root.Neighbours.Where(x => x.Value == value).ToList();
            List<Node> neighboursToAdd = neighboursToRemove.SelectMany(x => x.Neighbours).Except((new Node[] { Root }).Concat(Root.Neighbours)).ToList();
            foreach(Node n in neighboursToRemove)
            {
                foreach(Node m in n.Neighbours)
                {
                    m.Neighbours.Remove(n);
                }
                Nodes.Remove(n);
            }   
            foreach(Node n in neighboursToAdd)
            {
                Root.Neighbours.Add(n);         
                n.Neighbours.Add(Root); 
            }           
            //re-synchronize node index
            for(int i = 0 ; i < Nodes.Count ; i++)
            {
                Nodes[i].Index = i;
            }           
            Solution.Add(value);
        }
        public bool IsSolved()
        {           
            //return Nodes.Count == 1;
            return Root.Neighbours.Count == 0;  
        }           
    }
    class Program
    {       
        public static List<byte> Solve(Board input)
        {
            //A* Pathfinding            
            LinkedList<Board> open = new LinkedList<Board>();       
            input.EstimatedCost = input.GetEstimatedCost();
            open.AddLast(input);            
            while(open.Count > 0)
            {                       
                Board current = open.First.Value;
                open.RemoveFirst();
                if(current.IsSolved())
                {
                    return current.Solution;                
                }
                else
                {
                    //play all neighbours nodes colors
                    foreach(byte i in current.Root.Neighbours.Select(x => x.Value).Distinct())
                    {                       
                        Board newBoard = new Board(current);
                        newBoard.Play(i);           
                        newBoard.EstimatedCost = newBoard.GetEstimatedCost();   
                        //insert board to open list
                        bool inserted = false;
                        for(LinkedListNode<Board> node = open.First ; node != null ; node = node.Next)
                        {                               
                            if(node.Value.EstimatedCost > newBoard.EstimatedCost)
                            {
                                open.AddBefore(node, newBoard);
                                inserted = true;
                                break;
                            }
                        }       
                        if(!inserted)
                            open.AddLast(newBoard);                                                 
                    }   
                }   
            }
            throw new Exception(); //no solution found, impossible
        }   
        public static void Main(string[] args)
        {                   
            using (StreamReader sr = new StreamReader("floodtest"))
            {   
                while(!sr.EndOfStream)
                {                               
                    List<Board> boards = new List<Board>();
                    while(!sr.EndOfStream && boards.Count < 100)
                    {
                        Board board = new Board(sr);                        
                        sr.ReadLine(); //skip empty line
                        boards.Add(board);
                    }                                           
                    List<byte>[] solutions = new List<byte>[boards.Count];                                          
                    Parallel.For(0, boards.Count, i => 
                    {                               
                        solutions[i] = Solve(boards[i]); 
                    });                                         
                    foreach(List<byte> solution in solutions)
                    {
                        Console.WriteLine(string.Join(string.Empty, solution));                                             
                    }       
                }               
            }
        }
    }
}
```
More details about how it works : 
It use [A\* Pathfinding](http://en.wikipedia.org/wiki/A*_search_algorithm) algorithm.
What is difficult is to find a good `heuristic`. If the `heuristic` it underestimate the cost, it will perform like almost like [Dijkstra](http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) algorithm and because of complexity of a 19x19 board with 6 colors it will run forever. If it overestimate the cost it will converge quickly to a solution but won't give good ones at all (something like 26 moves were 19 was possible). Finding the perfect `heuristic` that give the exact remaining amount of steps to reach solution would be the best (it would be fast and would give best possible solution). It is (unless i'm wrong) impossible. It actually require to solve the board itself first, while this is what you are actually trying to do (chicken and egg problem)
I tried many things, here is what worked for the `heuristic`:
* I build a [graph](http://en.wikipedia.org/wiki/Graph_%28data_structure%29) of current board to evaluate. Each `node` represent a set of contiguous, same colored squares. Using that `graph`, I can easily calculate the exact minimal distance from center to any other node. For example distance from center to top left would be 10, because at minimum 10 colors separate them.
* For calculating `heuristic` : I play the current board until the end. For each step, I choose the color which will minimize the sum of distances from root to all other nodes.
* Number of moves needed to reach that end is the `heuristic`.
* `Estimated cost` (used by A\*) = `moves so far` + `heuristic`
It is not perfect as it slightly overestimate the cost (thus non optimal solution is found). Anyway it is fast to calculate and give good results.
I was able to get huge speed improvment by using graph to perform all operations. At begining I had a `2-dimension` array. I flood it and recalculate graph when needed (eg : to calculate the heuristic). Now everything is done using the graph, which calculated only at the beginning. To simulate steps, flood fill is no more needed, I merge nodes instead. This is a lot faster.
[Answer]
# Python – 10,800,000 steps
As a last-place reference solution, consider this sequence:
```
print "123456" * 18
```
Cycling through all the colours `n` times means that every square `n` steps away will be guaranteed to be of the same colour as the center square. Every square is at most 18 steps away from the center, so 18 cycles will guarantee all the squares being the same colour. Most likely it will finish in less than that, but the program is not required to stop as soon as all squares are the same colour; it's just much more beneficial to do so. This constant procedure is 108 steps per test case, for a total of 10,800,000.
[Answer]
# Java - 2,480,714 steps
I made a little mistake before (I put one crucial sentence before a loop instead of in the loop:
```
import java.io.*;
public class HerjanPaintAI {
    BufferedReader r;
    String[] map = new String[19];
    char[][] colors = new char[19][19];
    boolean[][] reached = new boolean[19][19], checked = new boolean[19][19];
    int[] colorCounter = new int[6];
    String answer = "";
    int mapCount = 0, moveCount = 0;
    public HerjanPaintAI(){
        nextMap();
        while(true){
            int bestMove = nextRound();
            answer += bestMove;
            char t = Character.forDigit(bestMove, 10);
            for(int x = 0; x < 19; x++){
                for(int y = 0; y < 19; y++){
                    if(reached[x][y]){
                        colors[x][y] = t;
                    }else if(checked[x][y]){
                        if(colors[x][y] == t){
                            reached[x][y] = true;
                        }
                    }
                }
            }
            boolean gameOver = true;
            for(int x = 0; x < 19; x++){
                for(int y = 0; y < 19; y++){
                    if(!reached[x][y]){
                        gameOver = false;
                        break;
                    }
                }
            }
            for(int x = 0; x < 19; x++){
                for(int y = 0; y < 19; y++){
                    checked[x][y] = false;
                }
            }
            for(int i = 0; i < 6; i++)
                colorCounter[i] = 0;
            if(gameOver)
                nextMap();
        }
    }
    int nextRound(){
        for(int x = 0; x < 19; x++){
            for(int y = 0; y < 19; y++){
                if(reached[x][y]){//check what numbers are next to the reached numbers...
                    check(x, y);
                }
            }
        }
        int[] totalColorCount = new int[6];
        for(int x = 0; x < 19; x++){
            for(int y = 0; y < 19; y++){
                totalColorCount[Character.getNumericValue(colors[x][y])-1]++;
            }
        }
        for(int i = 0; i < 6; i++){
            if(totalColorCount[i] != 0 && totalColorCount[i] == colorCounter[i]){//all of this color can be reached
                return i+1;
            }
        }
        int index = -1, number = 0;
        for(int i = 0; i < 6; i++){
            if(colorCounter[i] > number){
                index = i;
                number = colorCounter[i];
            }
        }
        return index+1;
    }
    void check(int x, int y){
        if(x<18)
            handle(x+1, y, x, y);
        if(x>0)
            handle(x-1, y, x, y);
        if(y<18)
            handle(x, y+1, x, y);
        if(y>0)
            handle(x, y-1, x, y);
    }
    void handle(int x2, int y2, int x, int y){
        if(!reached[x2][y2] && !checked[x2][y2]){
            checked[x2][y2] = true;
            if(colors[x2][y2] == colors[x][y]){
                reached[x2][y2] = true;
                check(x2, y2);
            }else{
                colorCounter[Character.getNumericValue(colors[x2][y2])-1]++;
                checkAround(x2, y2);
            }
        }
    }
    void checkAround(int x2, int y2){
        if(x2<18)
            handleAround(x2+1, y2, x2, y2);
        if(x2>0)
            handleAround(x2-1, y2, x2, y2);
        if(y2<18)
            handleAround(x2, y2+1, x2, y2);
        if(y2>0)
            handleAround(x2, y2-1, x2, y2);
    }
    void handleAround(int x2, int y2, int x, int y){
        if(!reached[x2][y2] && !checked[x2][y2]){
            if(colors[x2][y2] == colors[x][y]){
                checked[x2][y2] = true;
                colorCounter[Character.getNumericValue(colors[x2][y2])-1]++;
                checkAround(x2, y2);
            }
        }
    }
    void nextMap(){
        moveCount += answer.length();
        System.out.println(answer);
        answer = "";
        for(int x = 0; x < 19; x++){
            for(int y = 0; y < 19; y++){
                reached[x][y] = false;
            }
        }
        reached[9][9] = true;
        try {
            if(r == null)
                r = new BufferedReader(new FileReader("floodtest"));
            for(int i = 0; i < 19; i++){
                map[i] = r.readLine();
            }
            r.readLine();//empty line
            if(map[0] == null){
                System.out.println("Maps solved: " + mapCount + " Steps: " + moveCount);
                r.close();
                System.exit(0);
            }
        } catch (Exception e) {e.printStackTrace();}
        mapCount++;
        for(int x = 0; x < 19; x++){
            colors[x] = map[x].toCharArray();
        }
    }
    public static void main(String[] a){
        new HerjanPaintAI();
    }
}
```
[Answer]
# Java - 1,985,078 steps
<https://github.com/smack42/ColorFill>
Another late entry. The result file containing the 1,985,078 steps can be found [here](https://github.com/smack42/ColorFill/raw/master/codegolf26232/steps.txt).
**Some background info:**
I discovered this challenge some years ago, when I started programming my own clone of the game Flood-it.
**"best-of incomplete" DFS and A\* algorithm**  
From the beginning, I wanted to create a good solver algorithm for this game. Over time, I could improve my solver by including several strategies that did different incomplete searches (similar to the ones used in the other programs here) and by using the best result of those strategies for each solution. I even re-implemented [tigrou's A\* algorithm](https://codegolf.stackexchange.com/a/26917/7110) in Java and added it to my solver to achieve overall better solutions than tigrou's result.
**exhaustive DFS algorithm**  
Then I focused on an algorithm that always finds the optimal solutions. I spent a lot of effort to optimize my exhaustive depth-first search strategy. To speed up the search, I included a hashmap that stores all explored states, so that the search can avoid exploring them again. While this algorithm works fine and solves all 14x14 puzzles quickly enough, it uses too much memory and runs very slowly with the 19x19 puzzles in this code challenge.
**Puchert A\* algorithm**  
A few months ago I was contacted to look at the [Flood-It solver by Aaron and Simon Puchert](https://github.com/aaronpuchert/floodit). That program uses an A\*-type algorithm with an admissible heuristic (in contrast to tigrou's) and move pruning similar to Jump-Point Search. I quickly noticed that this program is **very fast** and finds the **optimal solutions**!
Of course, I had to re-implement this great algorithm and added it to my program. I made an effort to optimize my Java program to run about as fast as the original C++ program by the Puchert brothers. Then I decided to make an attempt at the 100,000 test cases of this challenge. On my machine the program ran for more than 120 hours to find the 1,985,078 steps, using my implementation of the **Puchert A\* algorithm**.
This is to be the **best possible solution** to this challenge, unless there are some bugs in the program that would result in sub-optimal solutions. Any feedback is welcome!
edit: added relevant parts of the code here:
class *AStarPuchertStrategy*
```
/**
 * a specific strategy for the AStar (A*) solver.
 * <p>
 * the idea is taken from the program "floodit" by Aaron and Simon Puchert,
 * which can be found at <a>https://github.com/aaronpuchert/floodit</a>
 */
public class AStarPuchertStrategy implements AStarStrategy {
    private final Board board;
    private final ColorAreaSet visited;
    private ColorAreaSet current, next;
    private final short[] numCaNotFilledInitial;
    private final short[] numCaNotFilled;
    public AStarPuchertStrategy(final Board board) {
        this.board = board;
        this.visited = new ColorAreaSet(board);
        this.current = new ColorAreaSet(board);
        this.next = new ColorAreaSet(board);
        this.numCaNotFilledInitial = new short[board.getNumColors()];
        for (final ColorArea ca : board.getColorAreasArray()) {
            ++this.numCaNotFilledInitial[ca.getColor()];
        }
        this.numCaNotFilled = new short[board.getNumColors()];
    }
    /* (non-Javadoc)
     * @see colorfill.solver.AStarStrategy#setEstimatedCost(colorfill.solver.AStarNode)
     */
    @Override
    public void setEstimatedCost(final AStarNode node) {
        // quote from floodit.cpp: int State::computeValuation()
        // (in branch "performance")
        //
        // We compute an admissible heuristic recursively: If there are no nodes
        // left, return 0. Furthermore, if a color can be eliminated in one move
        // from the current position, that move is an optimal move and we can
        // simply use it. Otherwise, all moves fill a subset of the neighbors of
        // the filled nodes. Thus, filling that layer gets us at least one step
        // closer to the end.
        node.copyFloodedTo(this.visited);
        System.arraycopy(this.numCaNotFilledInitial, 0, this.numCaNotFilled, 0, this.numCaNotFilledInitial.length);
        {
            final ColorAreaSet.FastIteratorColorAreaId iter = this.visited.fastIteratorColorAreaId();
            int nextId;
            while ((nextId = iter.nextOrNegative()) >= 0) {
                --this.numCaNotFilled[this.board.getColor4Id(nextId)];
            }
        }
        // visit the first layer of neighbors, which is never empty, i.e. the puzzle is not solved yet
        node.copyNeighborsTo(this.current);
        this.visited.addAll(this.current);
        int completedColors = 0;
        {
            final ColorAreaSet.FastIteratorColorAreaId iter = this.current.fastIteratorColorAreaId();
            int nextId;
            while ((nextId = iter.nextOrNegative()) >= 0) {
                final byte nextColor = this.board.getColor4Id(nextId);
                if (--this.numCaNotFilled[nextColor] == 0) {
                    completedColors |= 1 << nextColor;
                }
            }
        }
        int distance = 1;
        while(!this.current.isEmpty()) {
            this.next.clear();
            final ColorAreaSet.FastIteratorColorAreaId iter = this.current.fastIteratorColorAreaId();
            int thisCaId;
            if (0 != completedColors) {
                // We can eliminate colors. Do just that.
                // We also combine all these elimination moves.
                distance += Integer.bitCount(completedColors);
                final int prevCompletedColors = completedColors;
                completedColors = 0;
                while ((thisCaId = iter.nextOrNegative()) >= 0) {
                    final ColorArea thisCa = this.board.getColorArea4Id(thisCaId);
                    if ((prevCompletedColors & (1 << thisCa.getColor())) != 0) {
                        // completed color
                        // expandNode()
                        for (final int nextCaId : thisCa.getNeighborsIdArray()) {
                            if (!this.visited.contains(nextCaId)) {
                                this.visited.add(nextCaId);
                                this.next.add(nextCaId);
                                final byte nextColor = this.board.getColor4Id(nextCaId);
                                if (--this.numCaNotFilled[nextColor] == 0) {
                                    completedColors |= 1 << nextColor;
                                }
                            }
                        }
                    } else {
                        // non-completed color
                        // move node to next layer
                        this.next.add(thisCaId);
                    }
                }
            } else {
                // Nothing found, do the color-blind pseudo-move
                // Expand current layer of nodes.
                ++distance;
                while ((thisCaId = iter.nextOrNegative()) >= 0) {
                    final ColorArea thisCa = this.board.getColorArea4Id(thisCaId);
                    // expandNode()
                    for (final int nextCaId : thisCa.getNeighborsIdArray()) {
                        if (!this.visited.contains(nextCaId)) {
                            this.visited.add(nextCaId);
                            this.next.add(nextCaId);
                            final byte nextColor = this.board.getColor4Id(nextCaId);
                            if (--this.numCaNotFilled[nextColor] == 0) {
                                completedColors |= 1 << nextColor;
                            }
                        }
                    }
                }
            }
            // Move the next layer into the current.
            final ColorAreaSet tmp = this.current;
            this.current = this.next;
            this.next = tmp;
        }
        node.setEstimatedCost(node.getSolutionSize() + distance);
    }
}
```
part of class *AStarSolver*
```
private void executeInternalPuchert(final ColorArea startCa) throws InterruptedException {
    final Queue<AStarNode> open = new PriorityQueue<AStarNode>(AStarNode.strongerComparator());
    open.offer(new AStarNode(this.board, startCa));
    AStarNode recycleNode = null;
    while (open.size() > 0) {
        if (Thread.interrupted()) { throw new InterruptedException(); }
        final AStarNode currentNode = open.poll();
        if (currentNode.isSolved()) {
            this.addSolution(currentNode.getSolution());
            return;
        } else {
            // play all possible colors
            int nextColors = currentNode.getNeighborColors(this.board);
            while (0 != nextColors) {
                final int l1b = nextColors & -nextColors; // Integer.lowestOneBit()
                final int clz = Integer.numberOfLeadingZeros(l1b); // hopefully an intrinsic function using instruction BSR / LZCNT / CLZ
                nextColors ^= l1b; // clear lowest one bit
                final byte color = (byte)(31 - clz);
                final AStarNode nextNode = currentNode.copyAndPlay(color, recycleNode, this.board);
                if (null != nextNode) {
                    recycleNode = null;
                    this.strategy.setEstimatedCost(nextNode);
                    open.offer(nextNode);
                }
            }
        }
        recycleNode = currentNode;
    }
}
```
part of class *AStarNode*
```
/**
 * check if this color can be played. (avoid duplicate moves)
 * the idea is taken from the program "floodit" by Aaron and Simon Puchert,
 * which can be found at <a>https://github.com/aaronpuchert/floodit</a>
 * @param nextColor
 * @return
 */
private boolean canPlay(final byte nextColor, final List<ColorArea> nextColorNeighbors) {
    final byte currColor = this.solution[this.solutionSize];
    // did the previous move add any new "nextColor" neighbors?
    boolean newNext = false;
next:   for (final ColorArea nextColorNeighbor : nextColorNeighbors) {
        for (final ColorArea prevNeighbor : nextColorNeighbor.getNeighborsArray()) {
            if ((prevNeighbor.getColor() != currColor) && this.flooded.contains(prevNeighbor)) {
                continue next;
            }
        }
        newNext = true;
        break next;
    }
    if (!newNext) {
        if (nextColor < currColor) {
            return false;
        } else {
            // should nextColor have been played before currColor?
            for (final ColorArea nextColorNeighbor : nextColorNeighbors) {
                for (final ColorArea prevNeighbor : nextColorNeighbor.getNeighborsArray()) {
                    if ((prevNeighbor.getColor() == currColor) && !this.flooded.contains(prevNeighbor)) {
                        return false;
                    }
                }
            }
            return true;
        }
    } else {
        return true;
    }
}
/**
 * try to re-use the given node or create a new one
 * and then play the given color in the result node.
 * @param nextColor
 * @param recycleNode
 * @return
 */
public AStarNode copyAndPlay(final byte nextColor, final AStarNode recycleNode, final Board board) {
    final List<ColorArea> nextColorNeighbors = new ArrayList<ColorArea>(128);  // constant, arbitrary initial capacity
    final ColorAreaSet.FastIteratorColorAreaId iter = this.neighbors.fastIteratorColorAreaId();
    int nextId;
    while ((nextId = iter.nextOrNegative()) >= 0) {
        final ColorArea nextColorNeighbor = board.getColorArea4Id(nextId);
        if (nextColorNeighbor.getColor() == nextColor) {
            nextColorNeighbors.add(nextColorNeighbor);
        }
    }
    if (!this.canPlay(nextColor, nextColorNeighbors)) {
        return null;
    } else {
        final AStarNode result;
        if (null == recycleNode) {
            result = new AStarNode(this);
        } else {
            // copy - compare copy constructor
            result = recycleNode;
            result.flooded.copyFrom(this.flooded);
            result.neighbors.copyFrom(this.neighbors);
            System.arraycopy(this.solution, 0, result.solution, 0, this.solutionSize + 1);
            result.solutionSize = this.solutionSize;
            //result.estimatedCost = this.estimatedCost;  // not necessary to copy
        }
        // play - compare method play()
        for (final ColorArea nextColorNeighbor : nextColorNeighbors) {
            result.flooded.add(nextColorNeighbor);
            result.neighbors.addAll(nextColorNeighbor.getNeighborsIdArray());
        }
        result.neighbors.removeAll(result.flooded);
        result.solution[++result.solutionSize] = nextColor;
        return result;
    }
}
```
[Answer]
**C - 2,075,452**
I know I'm extremely late to the party, but I saw this challenge and wanted to have a go.
```
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdint.h>
#include <stdbool.h>
#include <stdlib.h>
#include <string.h>
uint64_t rand_state;
uint64_t rand_u64(void) {
    return (rand_state = rand_state * 6364136223846793005ULL + 1442695040888963407ULL);
}
uint64_t better_rand_u64(void) {
    uint64_t r = rand_u64();
    r ^= ((r >> 32) >> (r >> 60));
    return r + 1442695040888963407ULL;
}
uint32_t rand_u32(void) {return rand_u64() >> 32;}
float normal(float mu, float sigma) {
    uint64_t t = 0;
    for (int i = 0; i < 6; i++) {
        uint64_t r = rand_u64();
        uint32_t a = r;
        uint32_t b = r >> 32;
        t += a;
        t += b;
    }
    return ((float)t / (float)UINT32_MAX - 6) * sigma + mu;
}
typedef struct {
    uint8_t x;
    uint8_t y;
} Position;
#define ncolors 6
#define len 19
#define cells (len * len)
#define max_steps (len * (ncolors - 1))
#define center_x 9
#define center_y 9
#define center ((Position){center_x, center_y})
uint64_t zobrist_table[len][len];
void init_zobrist() {
    for (int y = 0; y < len; y++) {
        for (int x = 0; x < len; x++) {
            zobrist_table[y][x] = better_rand_u64();
        }
    }
}
typedef struct {
    uint64_t hash;
    uint8_t grid[len][len];
    bool interior[len][len];
    int boundary_size;
    Position boundary[cells];
} Grid;
void transition(Grid* grid, uint8_t color, int* surrounding_counts) {
    int i = 0;
    while (i < grid->boundary_size) {
        Position p = grid->boundary[i];
        uint8_t x = p.x;
        uint8_t y = p.y;
        bool still_boundary = false;
        for (int dx = -1; dx <= 1; dx++) {
            for (int dy = -1; dy <= 1; dy++) {
                if (!(dx == 0 || dy == 0)) {
                    continue;
                }
                int8_t x1 = x + dx;
                if (!(0 <= x1 && x1 < len)) {
                    continue;
                }
                int8_t y1 = y + dy;
                if (!(0 <= y1 && y1 < len)) {
                    continue;
                }
                if (grid->interior[y1][x1]) {
                    continue;
                }
                uint8_t color1 = grid->grid[y1][x1];
                if (color1 == color) {
                    grid->boundary[grid->boundary_size++] = (Position){x1, y1};
                    grid->interior[y1][x1] = true;
                    grid->hash ^= zobrist_table[y1][x1];
                } else {
                    surrounding_counts[color1]++;
                    still_boundary = true;
                }
            }
        }
        if (still_boundary) {
            i += 1;
        } else {
            grid->boundary[i] = grid->boundary[--grid->boundary_size]; 
        }
    }
}
void reset_grid(Grid* grid, int* surrounding_counts) {
    grid->hash = 0;
    memset(surrounding_counts, 0, ncolors * sizeof(int)); 
    memset(&grid->interior, 0, sizeof(grid->interior));
    grid->interior[center_y][center_x] = true;
    grid->boundary_size = 0;
    grid->boundary[grid->boundary_size++] = center; 
    transition(grid, grid->grid[center_y][center_x], surrounding_counts);
}
bool load_grid(FILE* fp, Grid* grid) {
    memset(grid, 0, sizeof(*grid));
    char buf[19 + 2];
    size_t row = 0;
    while ((fgets(buf, sizeof(buf), fp)) && row < 19) {
        if (strlen(buf) != 20) {
            break;
        }
        for (int i = 0; i < 19; i++) {
            if (!('1' <= buf[i] && buf[i] <= '6')) {
                return false;
            }
            grid->grid[row][i] = buf[i] - '1';
        }
        row++;
    }
    return row == 19;
}
typedef struct Node Node;
struct Node {
    uint64_t hash;
    float visit_counts[ncolors];
    float mean_cost[ncolors];
    float sse[ncolors];
};
#define iters 15000
#define pool_size 32768
#define pool_nodes (pool_size + 100)
#define pool_mask (pool_size - 1)
Node pool[pool_nodes];
void init_node(Node* node, uint64_t hash, int* surrounding_counts) {
    node->hash = hash;
    for (int i = 0; i < ncolors; i++) {
        if (surrounding_counts[i]) {
            node->visit_counts[i] = 1;
            node->mean_cost[i] = 20;
            node->sse[i] = 400;
        }
    }
}
Node* lookup_node(uint64_t hash) {
    size_t index = hash & pool_mask;
    for (int i = index;; i++) {
        uint64_t h = pool[i].hash;
        if (h == hash || !h) {
            return pool + i;
        }
    }
}
int rollout(Grid* grid, int* surrounding_counts, char* solution) {
    for (int i = 0;; i++) {
        int nonzero = 0;
        uint8_t colors[6];
        for (int i = 0; i < ncolors; i++) {
            if (surrounding_counts[i]) {
                colors[nonzero++] = i;
            }
        }
        if (!nonzero) {
            return i;
        }
        uint8_t color = colors[rand_u32() % nonzero]; 
        *(solution++) = color;
        assert(grid->boundary_size);
        memset(surrounding_counts, 0, 6 * sizeof(int));
        transition(grid, color, surrounding_counts);
    }
}
int simulate(Node* node, Grid* grid, int depth, char* solution) {
    float best_cost = INFINITY;
    uint8_t best_color = 255;
    for (int color = 0; color < ncolors; color++) {
        float n = node->visit_counts[color];
        if (node->visit_counts[color] == 0) {
            continue;
        }
        float sigma = sqrt(node->sse[color] / (n * n));
        float cost = node->mean_cost[color];
        cost = normal(cost, sigma);
        if (cost < best_cost) {
            best_color = color;
            best_cost = cost;
        }
    }
    if (best_color == 255) {
        return 0;
    }
    *solution++ = best_color;
    int score;
    int surrounding_counts[ncolors] = {0};
    transition(grid, best_color, surrounding_counts);
    Node* child = lookup_node(grid->hash);
    if (!child->hash) {
        init_node(child, grid->hash, surrounding_counts);
        score = rollout(grid, surrounding_counts, solution);
    } else {
        score = simulate(child, grid, depth + 1, solution);
    }
    score++;
    float n1 = ++node->visit_counts[best_color];
    float u0 = node->mean_cost[best_color];
    float u1 = node->mean_cost[best_color] = u0 + (score - u0) / n1;
    node->sse[best_color] += (score - u0) * (score - u1);
    return score;
}
int main(void) {
    FILE* fp;
    if (!(fp = fopen("floodtest", "r"))) {
        return 1;
    }
    Grid grid;
    init_zobrist();
    while (load_grid(fp, &grid)) {
        memset(pool, 0, sizeof(pool));
        int surrounding_counts[ncolors] = {0};
        reset_grid(&grid, surrounding_counts);
        Node root = {0};
        init_node(&root, grid.hash, surrounding_counts);
        char solution[max_steps] = {0};
        char best_solution[max_steps] = {0};
        int min_score = INT_MAX;
        uint64_t prev_hash = 0;
        uint64_t hash = 0;
        int same_count = 0;
        for (int iter = 0; iter < iters; iter++) {
            reset_grid(&grid, surrounding_counts);
            int score = simulate(&root, &grid, 1, solution);
            if (score < min_score) {
                min_score = score;
                memcpy(best_solution, solution, score);
            }
            hash = 0;
            for (int i = 0; i < score; i++) {
                hash ^= zobrist_table[i%len][(int)solution[i]];
            }
            if (hash == prev_hash) {
                same_count++;
                if (same_count >= 10) {
                    break;
                }
            } else {
                same_count = 0;
                prev_hash = hash;
            }
        }
        int i;
        for (i = 0; i < min_score; i++) {
            best_solution[i] += '1';
        }
        best_solution[i++] = '\n';
        best_solution[i++] = '\0';
        printf(best_solution);
        fflush(stdout);
    }
    return 0;
}
```
The algorithm is based on Monte-Carlo Tree Search with Thompson sampling, and a transposition table to reduce the search space. It takes about 12 hours on my machine. If you want to check the results, you can find them at <https://dropfile.to/pvjYDMV>.
[Answer]
# Java - 2,434,108 2,588,847 steps
Currently winning (~46K ahead of Herjan) as of 4/26
Welp, so not only did MrBackend beat me, but I found a bug which produced a deceptively good score. It's fixed now (was also in the verifier! Ack), but unfortunately I don't have any time at the moment to try and take back the crown. Will attempt later.
This is based off of my other solution, but instead of painting with the color most common to the fill edges, it paints with the color that will result in exposing edges that have many adjacent squares of the same color. Call it LookAheadPainter. I'll golf it later if necessary.
```
import java.io.*;
import java.util.*;
public class LookAheadPainter {
    static final boolean PRINT_FULL_OUTPUT = true;
    public static void main(String[] a) throws IOException {
        int totalSteps = 0, numSolved = 0;
        char[] board = new char[361];
        Scanner s = new Scanner(new File("floodtest"));
        long startTime = System.nanoTime();
        caseloop: while (s.hasNextLine()) {
            for (int l = 0; l < 19; l++) {
                String line = s.nextLine();
                if (line.isEmpty())
                    continue caseloop;
                System.arraycopy(line.toCharArray(), 0, board, l * 19, 19);
            }
            List<Character> colorsUsed = new ArrayList<>();
            for (;;) {
                FillResult fill = new FillResult(board, board[180], (char) 48, null);
                if (fill.nodesFilled.size() == 361)
                    break;
                int[] branchSizes = new int[7];
                for (int i = 1; i < 7; i++) {
                    List<Integer> seeds = new ArrayList<>();
                    for (Integer seed : fill.edges)
                        if (board[seed] == i + 48)
                            seeds.add(seed);
                    branchSizes[i] = new FillResult(fill.filledBoard, (char) (i + 48), (char) 48, seeds).nodesFilled.size();
                }
                int maxSize = 0;
                char bestColor = 0;
                for (int i = 1; i < 7; i++)
                    if (branchSizes[i] > maxSize) {
                        maxSize = branchSizes[i];
                        bestColor = (char) (i + 48);
                    }
                for (int i : fill.nodesFilled)
                    board[i] = bestColor;
                colorsUsed.add(bestColor);
                totalSteps++;
            }
            numSolved++;
            if (PRINT_FULL_OUTPUT) {
                if (numSolved % 1000 == 0)
                    System.out.println("Solved: " + numSolved); // So you know it's working
                String out = "";
                for (Character c : colorsUsed)
                    out += c;
                System.out.println(out);
            }
        }
        s.close();
        System.out.println("\nTotal steps to solve all cases: " + totalSteps);
        System.out.printf("\nSolved %d test cases in %.2f seconds", numSolved, (System.nanoTime() - startTime) / 1000000000.);
    }
    private static class FillResult {
        Set<Integer> nodesFilled, edges;
        char[] filledBoard;
        FillResult(char[] board, char target, char replacement, List<Integer> seeds) {
            Stack<Integer> nodes = new Stack<>();
            nodesFilled = new HashSet<>();
            edges = new HashSet<>();
            if (seeds == null)
                nodes.push(180);
            else
                for (int i : seeds)
                    nodes.push(i);
            filledBoard = new char[361];
            System.arraycopy(board, 0, filledBoard, 0, 361);
            while (!nodes.empty()) {
                int n = nodes.pop();
                if (n < 0 || n > 360)
                    continue;
                if (filledBoard[n] == target) {
                    filledBoard[n] = replacement;
                    nodesFilled.add(n);
                    if (n % 19 > 0)
                        nodes.push(n - 1);
                    if (n % 19 < 18)
                        nodes.push(n + 1);
                    if (n / 19 > 0)
                        nodes.push(n - 19);
                    if (n / 19 < 18)
                        nodes.push(n + 19);
                } else
                    edges.add(n);
            }
        }
    }
}
```
EDIT: I wrote a verifier, feel free to use, it expects a steps.txt file containing the steps your program outputs as well as the floodtest file: Edit-Edit: (See OP)
If anyone finds a problem, please report it to me!
[Answer]
# C - 2,480,714 steps
Still not optimal, but it is now faster and scores better.
```
#include <stdio.h>
#include <string.h>
#include <stdbool.h>
char map[19][19], reach[19][19];
int reachsum[6], totalsum[6];
bool loadmap(FILE *fp)
{
    char buf[19 + 2];
    size_t row = 0;
    while (fgets(buf, sizeof buf, fp) && row < 19) {
        if (strlen(buf) != 20)
            break;
        memcpy(map[row++], buf, 19);
    }
    return row == 19;
}
void calcreach(bool first, size_t row, size_t col);
void check(char c, bool first, size_t row, size_t col)
{
    if (map[row][col] == c)
        calcreach(first, row, col);
    else if (first)
        calcreach(false, row, col);
}
void calcreach(bool first, size_t row, size_t col)
{
    char c = map[row][col];
    reach[row][col] = c;
    reachsum[c - '1']++;
    if (row < 18 && !reach[row + 1][col])
        check(c, first, row + 1, col);
    if (col < 18 && !reach[row][col + 1])
        check(c, first, row, col + 1);
    if (row > 0 && !reach[row - 1][col])
        check(c, first, row - 1, col);
    if (col > 0 && !reach[row][col - 1])
        check(c, first, row, col - 1);
}
void calctotal()
{
    size_t row, col;
    for (row = 0; row < 19; row++)
        for (col = 0; col < 19; col++)
            totalsum[map[row][col] - '1']++;
}
void apply(char c)
{
    char d = map[9][9];
    size_t row, col;
    for (row = 0; row < 19; row++)
        for (col = 0; col < 19; col++)
            if (reach[row][col] == d)
                map[row][col] = c;
}
int main()
{
    char c, best;
    size_t steps = 0;
    FILE *fp;
    if (!(fp = fopen("floodtest", "r")))
        return 1;
    while (loadmap(fp)) {
        do {
            memset(reach, 0, sizeof reach);
            memset(reachsum, 0, sizeof reachsum);
            calcreach(true, 9, 9);
            if (reachsum[map[9][9] - '1'] == 361)
                break;
            memset(totalsum, 0, sizeof totalsum);
            calctotal();
            reachsum[map[9][9] - '1'] = 0;
            for (best = 0, c = 0; c < 6; c++) {
                if (!reachsum[c])
                    continue;
                if (reachsum[c] == totalsum[c]) {
                    best = c;
                    break;
                } else if (reachsum[c] > reachsum[best]) {
                    best = c;
                }
            }
            apply(best + '1');
        } while (++steps);
    }
    fclose(fp);
    printf("steps: %zu\n", steps);
    return 0;
}
```
[Answer]
# Java - ~~2,245,529~~ 2,201,995 steps
Parallel & caching tree search at depth 5, minimizing the number of "islands". Since the improvement from depth 4 to depth 5 was so small, I don't think there is much point in improving it much more. But if it were to need improvement, my gut feeling says to work with calculating the number of islands as a diff between two states, instead of recalculating everything.
Currently outputs to stdout, until I know the verifier's input format.
```
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.util.AbstractList;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collection;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.concurrent.ExecutionException;
import java.util.concurrent.ForkJoinPool;
import java.util.concurrent.RecursiveTask;
import java.util.concurrent.locks.ReadWriteLock;
import java.util.concurrent.locks.ReentrantReadWriteLock;
public class FloodPaint {
    private static final ForkJoinPool FORK_JOIN_POOL = new ForkJoinPool();
    public static void main(String[] arg) throws IOException, InterruptedException, ExecutionException {
        try (BufferedReader reader = new BufferedReader(new FileReader("floodtest"))) {
            int sum = 0;
            State initState = readNextInitState(reader);
            while (initState != null) {
                List<Integer> solution = generateSolution(initState);
                System.out.println(solution);
                sum += solution.size();
                initState = readNextInitState(reader);
            }
            System.out.println(sum);
        }
    }
    private static State readNextInitState(BufferedReader reader) throws IOException {
        int[] initGrid = new int[State.DIM * State.DIM];
        String line = reader.readLine();
        while ((line != null) && line.isEmpty()) {
            line = reader.readLine();
        }
        if (line == null) {
            return null;
        }
        for (int rowNo = 0; rowNo < State.DIM; ++rowNo) {
            for (int colNo = 0; colNo < State.DIM; ++colNo) {
                initGrid[(State.DIM * rowNo) + colNo] = line.charAt(colNo) - '0';
            }
            line = reader.readLine();
        }
        return new State(initGrid);
    }
    private static List<Integer> generateSolution(State initState) throws InterruptedException, ExecutionException {
        List<Integer> solution = new LinkedList<>();
        StateFactory stateFactory = new StateFactory();
        State state = initState;
        while (!state.isSolved()) {
            int num = findGoodNum(state, stateFactory);
            solution.add(num);
            state = state.getNextState(num, stateFactory);
        }
        return solution;
    }
    private static int findGoodNum(State state, StateFactory stateFactory) throws InterruptedException, ExecutionException {
        SolverTask task = new SolverTask(state, stateFactory);
        FORK_JOIN_POOL.invoke(task);
        return task.get();
    }
}
class SolverTask extends RecursiveTask<Integer> {
    private static final int DEPTH = 5;
    private final State state;
    private final StateFactory stateFactory;
    SolverTask(State state, StateFactory stateFactory) {
        this.state = state;
        this.stateFactory = stateFactory;
    }
    @Override
    protected Integer compute() {
        try {
            Map<Integer,AnalyzerTask> tasks = new HashMap<>();
            for (int num = 1; num <= 6; ++num) {
                if (num != state.getCenterNum()) {
                    State nextState = state.getNextState(num, stateFactory);
                    AnalyzerTask task = new AnalyzerTask(nextState, DEPTH - 1, stateFactory);
                    tasks.put(num, task);
                }
            }
            invokeAll(tasks.values());
            int bestValue = Integer.MAX_VALUE;
            int bestNum = -1;
            for (Map.Entry<Integer,AnalyzerTask> taskEntry : tasks.entrySet()) {
                int value = taskEntry.getValue().get();
                if (value < bestValue) {
                    bestValue = value;
                    bestNum = taskEntry.getKey();
                }
            }
            return bestNum;
        } catch (InterruptedException | ExecutionException ex) {
            throw new RuntimeException(ex);
        }
    }
}
class AnalyzerTask extends RecursiveTask<Integer> {
    private static final int DEPTH_THRESHOLD = 3;
    private final State state;
    private final int depth;
    private final StateFactory stateFactory;
    AnalyzerTask(State state, int depth, StateFactory stateFactory) {
        this.state = state;
        this.depth = depth;
        this.stateFactory = stateFactory;
    }
    @Override
    protected Integer compute() {
        return (depth < DEPTH_THRESHOLD) ? analyze() : split();
    }
    private int analyze() {
        return analyze(state, depth);
    }
    private int analyze(State state, int depth) {
        if (state.isSolved()) {
            return -depth;
        }
        if (depth == 0) {
            return state.getNumIslands();
        }
        int bestValue = Integer.MAX_VALUE;
        for (int num = 1; num <= 6; ++num) {
            if (num != state.getCenterNum()) {
                State nextState = state.getNextState(num, stateFactory);
                int nextValue = analyze(nextState, depth - 1);
                bestValue = Math.min(bestValue, nextValue);
            }
        }
        return bestValue;
    }
    private int split() {
        try {
            if (state.isSolved()) {
                return -depth;
            }
            Collection<AnalyzerTask> tasks = new ArrayList<>(5);
            for (int num = 1; num <= 6; ++num) {
                State nextState = state.getNextState(num, stateFactory);
                AnalyzerTask task = new AnalyzerTask(nextState, depth - 1, stateFactory);
                tasks.add(task);
            }
            invokeAll(tasks);
            int bestValue = Integer.MAX_VALUE;
            for (AnalyzerTask task : tasks) {
                int nextValue = task.get();
                bestValue = Math.min(bestValue, nextValue);
            }
            return bestValue;
        } catch (InterruptedException | ExecutionException ex) {
            throw new RuntimeException(ex);
        }
    }
}
class StateFactory {
    private static final int INIT_CAPACITY = 40000;
    private static final float LOAD_FACTOR = 0.9f;
    private final ReadWriteLock cacheLock = new ReentrantReadWriteLock();
    private final Map<List<Integer>,State> cache = new HashMap<>(INIT_CAPACITY, LOAD_FACTOR);
    State get(int[] grid) {
        List<Integer> stateKey = new IntList(grid);
        State state;
        cacheLock.readLock().lock();
        try {
            state = cache.get(stateKey);
        } finally {
            cacheLock.readLock().unlock();
        }
        if (state == null) {
            cacheLock.writeLock().lock();
            try {
                state = cache.get(stateKey);
                if (state == null) {
                    state = new State(grid);
                    cache.put(stateKey, state);
                }
            } finally {
                cacheLock.writeLock().unlock();
            }
        }
        return state;
    }
}
class State {
    static final int DIM = 19;
    private static final int CENTER_INDEX = ((DIM * DIM) - 1) / 2;
    private final int[] grid;
    private int numIslands;
    State(int[] grid) {
        this.grid = grid;
        numIslands = calcNumIslands(grid);
    }
    private static int calcNumIslands(int[] grid) {
        int numIslands = 0;
        BitSet uncounted = new BitSet(DIM * DIM);
        uncounted.set(0, DIM * DIM);
        int index = -1;
        while (!uncounted.isEmpty()) {
            index = uncounted.nextSetBit(index + 1);
            BitSet island = new BitSet(DIM * DIM);
            generateIsland(grid, index, grid[index], island);
            ++numIslands;
            uncounted.andNot(island);
        }
        return numIslands;
    }
    private static void generateIsland(int[] grid, int index, int num, BitSet island) {
        if ((grid[index] == num) && !island.get(index)) {
            island.set(index);
            if ((index % DIM) > 0) {
                generateIsland(grid, index - 1, num, island);
            }
            if ((index % DIM) < (DIM - 1)) {
                generateIsland(grid, index + 1, num, island);
            }
            if ((index / DIM) > 0) {
                generateIsland(grid, index - DIM, num, island);
            }
            if ((index / DIM) < (DIM - 1)) {
                generateIsland(grid, index + DIM, num, island);
            }
        }
    }
    int getCenterNum() {
        return grid[CENTER_INDEX];
    }
    boolean isSolved() {
        return numIslands == 1;
    }
    int getNumIslands() {
        return numIslands;
    }
    State getNextState(int num, StateFactory stateFactory) {
        int[] nextGrid = grid.clone();
        if (num != getCenterNum()) {
            flood(nextGrid, CENTER_INDEX, getCenterNum(), num);
        }
        State nextState = stateFactory.get(nextGrid);
        return nextState;
    }
    private static void flood(int[] grid, int index, int fromNum, int toNum) {
        if (grid[index] == fromNum) {
            grid[index] = toNum;
            if ((index % 19) > 0) {
                flood(grid, index - 1, fromNum, toNum);
            }
            if ((index % 19) < (DIM - 1)) {
                flood(grid, index + 1, fromNum, toNum);
            }
            if ((index / 19) > 0) {
                flood(grid, index - DIM, fromNum, toNum);
            }
            if ((index / 19) < (DIM - 1)) {
                flood(grid, index + DIM, fromNum, toNum);
            }
        }
    }
}
class IntList extends AbstractList<Integer> implements List<Integer> {
    private final int[] arr;
    private int hashCode = -1;
    IntList(int[] arr) {
        this.arr = arr;
    }
    @Override
    public int size() {
        return arr.length;
    }
    @Override
    public Integer get(int index) {
        return arr[index];
    }
    @Override
    public Integer set(int index, Integer value) {
        int oldValue = arr[index];
        arr[index] = value;
        return oldValue;
    }
    @Override
    public boolean equals(Object obj) {
        if (this == obj) {
            return true;
        }
        if (obj instanceof IntList) {
            IntList arg = (IntList) obj;
            return Arrays.equals(arr, arg.arr);
        }
        return super.equals(obj);
    }
    @Override
    public int hashCode() {
        if (hashCode == -1) {
            hashCode = 1;
            for (int elem : arr) {
                hashCode = 31 * hashCode + elem;
            }
        }
        return hashCode;
    }
}
```
[Answer]
# My Last Entry: C - 2,384,020 steps
This time a 'check-all-possibilities' one...
This score is gained with Depth set on 3.
Depth at 5 should give ~2.1M steps... TOO SLOW.
Depth 20+ gives the least amount of steps possible (it just checks all matches and the shortest wins ofcourse)...
It has the least amount of steps, though I hate it since it only is a tiny bit better, but performance sucks. I prefer my other C entry, which is also in this post.
```
#include <stdio.h>
#include <string.h>
#include <stdbool.h>
char map[19][19], reach[19][19];
int reachsum[6], totalsum[6], mapCount = 0;
FILE *stepfile;
bool loadmap(FILE *fp)
{
    fprintf(stepfile, "%s", "\n");
    mapCount++;
    char buf[19 + 2];
    size_t row = 0;
    while (fgets(buf, sizeof buf, fp) && row < 19) {
        if (strlen(buf) != 20)
            break;
        memcpy(map[row++], buf, 19);
    }
    return row == 19;
}
void calcreach(bool first, size_t row, size_t col);
void check(char c, bool first, size_t row, size_t col)
{
    if (map[row][col] == c)
        calcreach(first, row, col);
    else if (first)
        calcreach(false, row, col);
}
void calcreach(bool first, size_t row, size_t col)
{
    char c = map[row][col];
    reach[row][col] = c;
    reachsum[c - '1']++;
    if (row < 18 && !reach[row + 1][col])
        check(c, first, row + 1, col);
    if (col < 18 && !reach[row][col + 1])
        check(c, first, row, col + 1);
    if (row > 0 && !reach[row - 1][col])
        check(c, first, row - 1, col);
    if (col > 0 && !reach[row][col - 1])
        check(c, first, row, col - 1);
}
void calctotal()
{
    size_t row, col;
    for (row = 0; row < 19; row++)
        for (col = 0; col < 19; col++)
            totalsum[map[row][col] - '1']++;
}
void apply(char c)
{
    char d = map[9][9];
    size_t row, col;
    for (row = 0; row < 19; row++)
        for (col = 0; col < 19; col++)
            if (reach[row][col] == d)
                map[row][col] = c;
}
int pown(int x, int y){
    int p = 1;
    for(int i = 0; i < y; i++){
        p = p * x;
    }
    return p;
}
int main()
{
    size_t steps = 0;
    FILE *fp;
    if (!(fp = fopen("floodtest", "r")))
        return 1;
    if(!(stepfile = fopen("steps.txt", "w")))
        return 1;
    const int depth = 5;
    char possibilities[pown(6, depth)][depth];
    int t = 0;
    for(int a = 0; a < 6; a++){
        for(int b = 0; b < 6; b++){
            for(int c = 0; c < 6; c++){
                for(int d = 0; d < 6; d++){
                    for(int e = 0; e < 6; e++){
                        possibilities[t][0] = (char)(a + '1');
                        possibilities[t][1] = (char)(b + '1');
                        possibilities[t][2] = (char)(c + '1');
                        possibilities[t][3] = (char)(d + '1');
                        possibilities[t++][4] = (char)(e + '1');
                    }
                }
            }
        }
    }
    poes:
    while (loadmap(fp)) {
        do {
            char map2[19][19];
            memcpy(map2, map, sizeof(map));
            memset(reach, 0, sizeof reach);
            memset(reachsum, 0, sizeof reachsum);
            calcreach(true, 9, 9);
            int best = 0, index = 0, end = depth;
            for(int i = 0; i < pown(6, depth); i++){
                for(int d = 0; d < end; d++){
                    apply(possibilities[i][d]);
                    memset(reach, 0, sizeof reach);
                    memset(reachsum, 0, sizeof reachsum);
                    calcreach(true, 9, 9);
                    if(reachsum[map[9][9] - '1'] == 361 && d < end){
                        end = d+1;
                        index = i;
                        break;
                    }
                }
                if(end == depth && best < reachsum[map[9][9] - '1']){
                    best = reachsum[map[9][9] - '1'];
                    index = i;
                }
                memcpy(map, map2, sizeof(map2));
                memset(reach, 0, sizeof reach);
                memset(reachsum, 0, sizeof reachsum);
                calcreach(true, 9, 9);
            }
            for(int d = 0; d < end; d++){
                apply(possibilities[index][d]);
                memset(reach, 0, sizeof reach);
                memset(reachsum, 0, sizeof reachsum);
                calcreach(true, 9, 9);
                fprintf(stepfile, "%c", possibilities[index][d]);
                steps++;
            }
            if(reachsum[map[9][9] - '1'] == 361)
                goto poes;
        } while (1);
    }
    fclose(fp);
    fclose(stepfile);
    printf("steps: %zu\n", steps);
    return 0;
}
```
# Another Improved AI written in C - 2,445,761 steps
Based on SteelTermite's:
```
#include <stdio.h>
#include <string.h>
#include <stdbool.h>
char map[19][19], reach[19][19];
int reachsum[6], totalsum[6], mapCount = 0;
FILE *stepfile;
bool loadmap(FILE *fp)
{
    fprintf(stepfile, "%s", "\n");
    if(mapCount % 1000 == 0)
        printf("mapCount = %d\n", mapCount);
    mapCount++;
    char buf[19 + 2];
    size_t row = 0;
    while (fgets(buf, sizeof buf, fp) && row < 19) {
        if (strlen(buf) != 20)
            break;
        memcpy(map[row++], buf, 19);
    }
    return row == 19;
}
void calcreach(bool first, size_t row, size_t col);
void check(char c, bool first, size_t row, size_t col)
{
    if (map[row][col] == c)
        calcreach(first, row, col);
    else if (first)
        calcreach(false, row, col);
}
void calcreach(bool first, size_t row, size_t col)
{
    char c = map[row][col];
    reach[row][col] = c;
    reachsum[c - '1']++;
    if (row < 18 && !reach[row + 1][col])
        check(c, first, row + 1, col);
    if (col < 18 && !reach[row][col + 1])
        check(c, first, row, col + 1);
    if (row > 0 && !reach[row - 1][col])
        check(c, first, row - 1, col);
    if (col > 0 && !reach[row][col - 1])
        check(c, first, row, col - 1);
}
void calctotal()
{
    size_t row, col;
    for (row = 0; row < 19; row++)
        for (col = 0; col < 19; col++)
            totalsum[map[row][col] - '1']++;
}
void apply(char c)
{
    char d = map[9][9];
    size_t row, col;
    for (row = 0; row < 19; row++)
        for (col = 0; col < 19; col++)
            if (reach[row][col] == d)
                map[row][col] = c;
}
int main()
{
    char c, best, answer;
    size_t steps = 0;
    FILE *fp;
    if (!(fp = fopen("floodtest", "r")))
        return 1;
    if(!(stepfile = fopen("steps.txt", "w")))
            return 1;
    while (loadmap(fp)) {
        do {
            memset(reach, 0, sizeof reach);
            memset(reachsum, 0, sizeof reachsum);
            calcreach(true, 9, 9);
            if (reachsum[map[9][9] - '1'] == 361)
                break;
            memset(totalsum, 0, sizeof totalsum);
            calctotal();
            reachsum[map[9][9] - '1'] = 0;
            for (best = 0, c = 0; c < 6; c++) {
                if (!reachsum[c])
                    continue;
                if (reachsum[c] == totalsum[c]) {
                    best = c;
                    goto outLoop;
                } else if (reachsum[c] > reachsum[best]) {
                    best = c;
                }
            }
            char map2[19][19];
            memcpy(map2, map, sizeof(map));
            int temp = best;
            for(c = 0; c < 6; c++){
                if(c != best){
                    apply(c + '1');
                    memset(reach, 0, sizeof reach);
                    memset(reachsum, 0, sizeof reachsum);
                    calcreach(true, 9, 9);
                    if (reachsum[best] == totalsum[best]) {
                        memcpy(map, map2, sizeof(map2));
                        memset(reach, 0, sizeof reach);
                        memset(reachsum, 0, sizeof reachsum);
                        calcreach(true, 9, 9);
                        if(temp == -1)
                            temp = c;
                        else if(reachsum[c] > reachsum[temp])
                            temp = c;
                    }
                    memcpy(map, map2, sizeof(map2));
                    memset(reach, 0, sizeof reach);
                    memset(reachsum, 0, sizeof reachsum);
                    calcreach(true, 9, 9);
                }
            }
outLoop:    answer = (char)(temp + '1');
            fprintf(stepfile, "%c", answer);
            apply(answer);
        } while (++steps);
    }
    fclose(fp);
    fclose(stepfile);
    printf("steps: %zu\n", steps);
    return 0;
}
```
[Answer]
# Java - 2,610,797 4,780,841 steps
(Fill-Bug fixed, score is now dramatically worse -\_- )
This is my basic reference algorithm submission, simply makes a histogram of the squares on the edges of the painted area, and paints with the most common color. Runs the 100k in a couple minutes.
Obviously won't win, but it's certainly not last. I'll probably make another submission for clever stuff. Feel free to use this algorithm as a starting point.
Un-comment the commented lines for the full output. Defaults to printing the # of steps taken.
```
import java.io.*;
import java.util.*;
public class PainterAI {
    public static void main(String[] args) throws IOException {
        int totalSteps = 0, numSolved = 0;
        char[] board = new char[361];
        Scanner s = new Scanner(new File("floodtest"));
        long startTime = System.nanoTime();
        caseloop: while (s.hasNextLine()) {
            for (int l = 0; l < 19; l++) {
                String line = s.nextLine();
                if (line.isEmpty())
                    continue caseloop;
                System.arraycopy(line.toCharArray(), 0, board, l * 19, 19);
            }
            List<Character> colorsUsed = new ArrayList<>();
            Stack<Integer> nodes = new Stack<>();
            for (;; totalSteps++) {
                char p = board[180];
                int[] occurrences = new int[7];
                nodes.add(180);
                int numToPaint = 0;
                while (!nodes.empty()) {
                    int n = nodes.pop();
                    if (n < 0 || n > 360)
                        continue;
                    if (board[n] == p) {
                        board[n] = 48;
                        numToPaint++;
                        if (n % 19 > 0)
                            nodes.push(n - 1);
                        if(n%19<18)
                            nodes.push(n + 1);
                        if(n/19>0)
                            nodes.push(n - 19);
                        if(n/19<18)
                            nodes.push(n + 19);
                    } else
                        occurrences[board[n] - 48]++;
                }
                if (numToPaint == 361)
                    break;
                char mostFrequent = 0;
                int times = -1;
                for (int i = 1; i < 7; i++)
                    if (occurrences[i] > times) {
                        times = occurrences[i];
                        mostFrequent = (char) (i + 48);
                    }
                for (int i = 0; i < 361; i++)
                    if (board[i] == 48)
                        board[i] = mostFrequent;
                //colorsUsed.add(mostFrequent);
            }
            numSolved++;
            /*String out = "";
            for (Character c : colorsUsed)
                out += c;
            System.out.println(out); //print output*/
        }
        s.close();
        System.out.println("Total steps to solve all cases: " + totalSteps);
        System.out.printf("\nSolved %d test cases in %.2f seconds", numSolved, (System.nanoTime() - startTime) / 1000000000.);
    }
}
```
Golfs to 860 chars (not including the newlines for formatting), but could be shrunk more if I felt like trying:
```
import java.io.*;import java.util.*;class P{
public static void main(String[]a)throws Exception{int t=0;char[]b=new char[361];
Scanner s=new Scanner(new File("floodtest"));c:while(s.hasNextLine()){
for(int l=0;l<19;l++){String L=s.nextLine();if(L.isEmpty())continue c;
System.arraycopy(L.toCharArray(),0,b,l*19,19);}List<Character>u=new ArrayList<>();
Stack<Integer>q=new Stack<>();for(int[]o=new int[7];;t++){char p=b[180];q.add(180);
int m=0;while(!q.empty()){int n=q.pop();if(n<0|n>360)continue;if(b[n]==p){b[n]=48;m++;
if(n%19>0)q.add(n-1);if(n%19<18)q.add(n+1);if(n/19>0)q.add(n-19);if(n/19<18)
q.add(n+19);}else o[b[n]-48]++;}if(m==361)break;
char f=0;int h=0;for(int i=1;i<7;i++)if(o[i]>h){h=o[i];f=(char)(i+48);}
for(int i=0;i<361;i++)if(b[i]==48)b[i]=f;u.add(f);}String y="";for(char c:u)y+=c;
System.out.println(y);}s.close();System.out.println("Steps: "+t);}}
```
[Answer]
# Haskell - 2,475,056 steps
Algorithm is similar to the one suggested by MrBackend in the comments. The difference is: his suggestion finds the cheapest path to the highest cost square, mine greedily reduces the graph eccentricity at every step.
```
import Data.Array
import qualified Data.Map as M
import Data.Word
import Data.List
import Data.Maybe
import Data.Function (on)
import Data.Monoid
import Control.Arrow
import Control.Monad (liftM)
import System.IO
import System.Environment
import Control.Parallel.Strategies
import Control.DeepSeq
type Grid v = Array (Word8,Word8) v
main = do
  (ifn:_) <- getArgs
  hr <- openFile ifn ReadMode
  sp <- liftM parseFile $ hGetContents hr
  let (len,sol) = turns (map solve sp `using` parBuffer 3 (evalList rseq))
  putStrLn $ intercalate "\n" $ map (concatMap show) sol
  putStrLn $ "\n\nTotal turns: " ++ (show len)
turns :: [[a]] -> (Integer,[[a]])
turns l = rl' 0 l where
  rl' c [] = (c,[])
  rl' c (k:r) = let
   s = c + genericLength k
   (s',l') = s `seq` rl' s r
   in (s',k:l')
centrepoint :: Grid v -> (Word8,Word8)
centrepoint g = let
  ((x0,y0),(x1,y1)) = bounds g
  med l h = let t = l + h in t `div` 2 + t `mod` 2
  in (med x0 x1, med y0 y1)
neighbours :: Grid v -> (Word8,Word8) -> [(Word8,Word8)]
neighbours g (x,y) = filter
  (inRange $ bounds g)
  [(x,y+1),(x+1,y),(x,y-1),(x-1,y)]
areas :: Eq v => Grid v -> [[(Word8,Word8)]]
areas g = p $ indices g where
  p [] = []
  p (a:r) = f : p (r \\ f) where
    f = s g [a] []
s g [] _ = []
s g (h:o) v = let
  n = filter (((==) `on` (g !)) h) $ neighbours g h
  in h : s g ((n \\ (o ++ v)) ++ o) (h : v)
applyFill :: Eq v => v -> Grid v -> Grid v
applyFill c g = g // (zip fa $ repeat c) where
  fa = s g [centrepoint g] []
solve g = solve' gr' where
  aa = areas g
  cp = centrepoint g
  ca = head $ head $ filter (elem cp) aa
  gr' = M.fromList $ map (
    \r1 -> (head r1, map head $ filter (
      \r2 -> head r1 /= head r2 &&
        (not $ null $ intersect (concatMap (neighbours g) r1) r2)
     ) aa
    )
   ) aa
  solve' gr
    | null $ tail $ M.keys $ gr = []
    | otherwise = best : solve' ngr where
      djk _ [] = []
      djk v ((n,q):o) = (n,q) : djk (q:v) (
        o ++ zip (repeat (n+1))
        ((gr M.! q) \\ (v ++ map snd o))
       )
      dout = djk [] [(0,ca)]
      din = let
        m = maximum $ map fst dout
        s = filter ((== m) . fst) dout
        in djk [] s
      rc = filter (flip elem (gr M.! ca) . snd) din
      frc = let
        m = minimum $ map fst rc
        in map snd $ filter ((==m) . fst) rc
      msq = concat $ filter (flip elem frc . head) aa
      clr = map (length &&& head) $ group $ sort $ map (g !) msq
      best = snd $ maximumBy (compare `on` fst) clr
      ngr = let
        ssm = filter ((== best) . (g !)) $ map snd rc
        sml = (concatMap (gr M.!) ssm)
        ncl = ((gr M.! ca) ++ sml) \\ (ca : ssm)
        brk = M.insert ca ncl $ M.filterWithKey (\k _ ->
          (not . flip elem ssm) k
         ) gr
        in M.map 
          (\l -> nub $ map (\e -> if e `elem` ssm then ca else e) l)
          brk
parseFile :: String -> [Grid Word8]
parseFile f = map mk $ filter (not . null . head) $ groupBy ((==) `on` null) $
  map (map ((read :: String -> Word8) . (:[]))) $ lines f where
    mk :: [[Word8]] -> Grid Word8
    mk m = let
      w = fromIntegral (length $ head m) - 1
      h = fromIntegral (length m) - 1
      in array ((0,0),(w,h)) [ ((x,y),v) |
        (y,l) <- zip [h,h-1..] m,
        (x,v) <- zip [0..] l
       ]
showGrid :: Grid Word8 -> String
showGrid g = intercalate "\n" l where
  l = map sl $ groupBy ((==) `on` snd) $
    sortBy ((flip (compare `on` snd)) <> (compare `on` fst)) $
    indices g
  sl = intercalate " " . map (show . (g !))
testsolve = do
  hr <- openFile "floodtest" ReadMode
  sp <- liftM (head . parseFile) $ hGetContents hr
  let
   sol = solve sp
   a = snd $ mapAccumL (\g s -> let g' = applyFill s g in (g',g')) sp sol
  sequence_ $ map (\g -> putStrLn (showGrid g) >> putStrLn "\n") a
```
[Answer]
## C#- 2,383,569
It's a depth traversal of possible solutions that roughly chooses the path of best improvement (similar/same as Herjan's C entry), except I *cleverly* reversed the order of candidate solution generation after seeing Herjan posted the same numbers. Takes a good 12+ hours to run though.
```
class Solver
{
    static void Main()
    {
        int depth = 3;
        string text = File.ReadAllText(@"C:\TEMP\floodtest.txt");
        text = text.Replace("\n\n", ".").Replace("\n", "");
        int count = 0;
        string[] tests = text.Split(new char[] { '.' }, StringSplitOptions.RemoveEmptyEntries);
        for (int i = 0; i < tests.Length; i++)
        {
            Solver s = new Solver(tests[i]);
            string k1 = s.solve(depth);
            count += k1.Length;
            Console.WriteLine(((100 * i) / tests.Length) + " " + i + " " + k1.Length + " " + count + " " + k1);
        }
        Console.WriteLine(count);
    }
    public readonly int MAX_DIM;
    public char[] board;
    public Solver(string prob)
    {
        board = read(prob);
        MAX_DIM = (int)Math.Sqrt(board.Length);
    }
    public string solve(int d)
    {
        var sol = "";
        while (score(eval(copy(board), sol)) != board.Length)
        {
            char[] b = copy(board);
            eval(b, sol);
            var canidates = new List<string>();
            buildCanidates("", canidates, d);
            var best = canidates.Select(c => new {score = score(eval(copy(b), c)), sol = c}).ToList().OrderByDescending(t=>t.score).ThenBy(v => v.sol.Length).First();
            sol = sol + best.sol[0];
        }
        return sol;
    }
    public void buildCanidates(string b, List<string> r, int d)
    {
        if(b.Length>0)
            r.Add(b);
        if (d > 0)
        {
            r.Add(b);
            for (char i = '6'; i >= '1'; i--)
                if(b.Length == 0 || b[b.Length-1] != i)
                    buildCanidates(b + i, r, d - 1);
        }
    }
    public char[] read(string s)
    {
        return s.Where(c => c >= '0' && c <= '9').ToArray();
    }
    public void print(char[] b)
    {
        for (int i = 0; i < MAX_DIM; i++)
        {
            for(int j=0; j<MAX_DIM; j++)
                Console.Write(b[i*MAX_DIM+j]);
            Console.WriteLine();
        }
        Console.WriteLine();
    }
    public char[] copy(char[] b)
    {
        char[] n = new char[b.Length];
        for (int i = 0; i < b.Length; i++)
            n[i] = b[i];
        return n;
    }
    public char[] eval(char[] b, string sol)
    {
        foreach (char c in sol)
            eval(b, c);
        return b;
    }
    public void eval(char[] b, char c)
    {
        foreach (var l in flood(b))
            b[l] = c;
    }
    public int score(char[] b)
    {
        return flood(b).Count;
    }
    public List<int> flood(char[] b)
    {
        int start = (MAX_DIM * (MAX_DIM / 2)) + (MAX_DIM / 2);
        var check = new List<int>(MAX_DIM * MAX_DIM);
        bool[] seen = new bool[b.Length];
        var hits = new List<int>(MAX_DIM*MAX_DIM);
        check.Add(start);
        seen[start]=true;
        char target = b[start];
        int at = 0;
        while (at<check.Count)
        {
            int toCheck = check[at++];
            if (b[toCheck] == target)
            {
                addNeighbors(check, seen, toCheck);
                hits.Add(toCheck);
            }
        }
        return hits;
    }
    public void addNeighbors(List<int> check, bool[] seen, int loc)
    {
        int x = loc / MAX_DIM;
        int y = loc % MAX_DIM;
        addNeighbor(check, seen, x, y - 1);
        addNeighbor(check, seen, x, y + 1);
        addNeighbor(check, seen, x - 1, y);
        addNeighbor(check, seen, x + 1, y);
    }
    public void addNeighbor(List<int> check, bool[] seen, int x, int y)
    {
        if (x >= 0 && x < MAX_DIM && y >= 0 && y < MAX_DIM)
        {
            int l = (x * MAX_DIM) + y;
            if (!seen[l])
            {
                seen[l] = true;
                check.Add(l);
            }
        }
    }
}
```
[Answer]
## Java - 2,403,189
```
BUILD SUCCESSFUL (total time: 220 minutes 15 seconds)
```
This was supposed to be my attempt at a brute force. But! My first implementation of single-depth "best" choice yielded: 
```
2,589,328 - BUILD SUCCESSFUL (total time: 3 minutes 11 seconds)
```
The code used for both is the same with the brute force storing a "snapshot" of the other possible moves and running the algorithm over all of them. 
---
* Issues
If running with the "multi" pass approach random failures will occur. I setup the first 100 puzzle entries in a unit test and can achieve a 100% pass but not 100% of the time. To compensate, I just tracked the current puzzle number at fail time and started a new Thread picking up where the last one left off. Each thread wrote their respective results to a file. The file pool was then condensed into a single file. 
* Approach
`Node` represents a tile/square of the board and stores a reference to all of it's neighbors. Track three `Set<Node>` variables: `Remaining`, `Painted`, `Targets`. Each iteration looks at `Targets` to group all `candidate` nodes by value, selecting the `target value` by the number of "affected" nodes. These affected nodes then become the targets for the next iteration. 
The source is spread across many classes and snippets aren't very meaningful away from the context of the whole. My source can be browsed via [GitHub](http://github.com/origineil02/sandbox/tree/master/SandBox/src/main/java/stackexchange/codegolf/floodpaint). I also messed around with a [JSFiddle](http://jsfiddle.net/G8R8c/embedded/result/) demo for visualization.
Nevertheless, my workhorse method from `Solver.java`:
```
public void flood() {
 final Data data = new Data();
 consolidateCandidates(data, targets);
 input.add(data.getTarget());
 if(input.size() > SolutionRepository.getInstance().getThreshold()){
  //System.out.println("Exceeded threshold: " + input.toString());
  cancelled = true;
 }
 paintable.addAll(data.targets());
 remaining.removeAll(data.targets());
 if(!data.targets().isEmpty()){
  targets = data.potentialTargets(data.targets(), paintable);
  data.setPaintable(paintable);
  data.setRemaining(remaining);
  data.setInput(input);
  SolutionRepository.getInstance().addSnapshot(data, input);
 }
}
```
[Answer]
## C#- 2,196,462 2,155,834
This is effectively the same 'look for best descendant' approach as my other solver, but with a few optimizations that just barely, with parallelism, allow it go to depth 5 in a little under 10 hours. In the course of testing this I also found a bug in the original, such that the algorithm would occasionally take inefficient routes to the end state (it wasn't accounting for depth of states with score=64; discovered while toying with results of depth=7). 
The main difference between this and the previous solver is that it keeps the Flood Game States in memory, so it doesn't have to regenerate 6^5 states. Based on CPU use during running, I'm fairly certain this has moved from CPU bound to memory bandwidth bound. Great fun. So many sins. 
Edit: Because of reasons, the depth 5 algorithm doesn't always produce the best result. To improve performance, let's just do depth 5... and 4... and 3 and 2 and 1, and see which is best. Did shave off another 40k moves. Since depth 5 is the bulk of the time, adding 4 through 1 only increases runtime from ~10hrs to ~11hrs. Yay!
```
using System;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Collections.Generic;
public class Program
{
    static void Main()
    {
        int depth = 5;
        string text = File.ReadAllText(@"C:\TEMP\floodtest.txt");
        text = text.Replace("\n\n", ".").Replace("\n", "");
        int count = 0;
        string[] tests = text.Split(new [] { '.' }, StringSplitOptions.RemoveEmptyEntries);
        Stopwatch start = Stopwatch.StartNew();
        const int parChunk = 16*16;
        for (int i = 0; i < tests.Length; i += parChunk)
        {
            //did not know that parallel select didn't respect order
            string[] sols = tests.Skip(i).Take(parChunk).AsParallel().Select((t, idx) => new { s = new Solver2(t).solve(depth), idx}).ToList().OrderBy(v=>v.idx).Select(v=>v.s).ToArray();
            for (int j = 0; j < sols.Length; j++)
            {
                string k1 = sols[j];
                count += k1.Length;
                int k = i + j;
                int estimate = (int)((count*(long)tests.Length)/(k+1));
                Console.WriteLine(k + "\t" + start.Elapsed.TotalMinutes.ToString("F2") + "\t" + count + "\t" + estimate + "\t" + k1.Length + "\t" + k1);
            }
        }
        Console.WriteLine(count);
    }
}
public class Solver2
{
    public readonly int MAX_DIM;
    public char[] board;
    public Solver2(string prob)
    {
        board = read(prob);
        MAX_DIM = (int)Math.Sqrt(board.Length);
    }
    public string solve(int d)
    {
        string best = null;
        for (int k = d; k >= 1; k--)
        {
            string c = subSolve(k);
            if (best == null || c.Length < best.Length)
                best = c;
        }
        return best;
    }
    public string subSolve(int d)
    {
        State current = new State(copy(board), '\0', flood(board));
        var sol = "";
        while (current.score != board.Length)
        {
            State nextState = subSolve(current, d);
            sol = sol + nextState.key;
            current = nextState;
        }
        return sol;
    }
    public State subSolve(State baseState, int d)
    {
        if (d == 0)
            return baseState;
        if (!baseState.childrenGenerated)
        {
            for (int i = 0; i < baseState.children.Length; i++)
            {
                if (('1' + i) == baseState.key) continue; //no point in even eval'ing
                char[] board = copy(baseState.board);
                foreach(int idx in baseState.flood)
                    board[idx] = (char)('1' + i);
                List<int> f = flood(board);
                if (f.Count != baseState.score)
                    baseState.children[i] = new State(board, (char)('1' + i), f);
            }
            baseState.childrenGenerated = true;
        }
        State bestState = null;
        for (int i = 0; i < baseState.children.Length; i++)
            if (baseState.children[i] != null)
            {
                State bestChild = subSolve(baseState.children[i], d - 1);
                baseState.children[i].bestChildScore = bestChild.bestChildScore;
                if (bestState == null || bestState.bestChildScore < bestChild.bestChildScore)
                    bestState = baseState.children[i];
            }
        if (bestState == null || bestState.bestChildScore == baseState.score)
        {
            if (baseState.score == baseState.board.Length)
                baseState.bestChildScore = baseState.score*(d + 1);
            return baseState;
        }
        return bestState;
    }
    public char[] read(string s)
    {
        return s.Where(c => c >= '1' && c <= '6').ToArray();
    }
    public char[] copy(char[] b)
    {
        char[] n = new char[b.Length];
        for (int i = 0; i < b.Length; i++)
            n[i] = b[i];
        return n;
    }
    public List<int> flood(char[] b)
    {
        int start = (MAX_DIM * (MAX_DIM / 2)) + (MAX_DIM / 2);
        var check = new List<int>(MAX_DIM * MAX_DIM);
        bool[] seen = new bool[b.Length];
        var hits = new List<int>(MAX_DIM * MAX_DIM);
        check.Add(start);
        seen[start] = true;
        char target = b[start];
        int at = 0;
        while (at < check.Count)
        {
            int toCheck = check[at++];
            if (b[toCheck] == target)
            {
                addNeighbors(check, seen, toCheck);
                hits.Add(toCheck);
            }
        }
        return hits;
    }
    public void addNeighbors(List<int> check, bool[] seen, int loc)
    {
        //int x = loc / MAX_DIM;
        int y = loc % MAX_DIM;
        if(loc+MAX_DIM < seen.Length)
            addNeighbor(check, seen, loc+MAX_DIM);
        if(loc-MAX_DIM >= 0)
            addNeighbor(check, seen, loc-MAX_DIM);
        if(y<MAX_DIM-1)
            addNeighbor(check, seen, loc+1);
        if (y > 0)
            addNeighbor(check, seen, loc-1);
    }
    public void addNeighbor(List<int> check, bool[] seen, int l)
    {
        if (!seen[l])
        {
            seen[l] = true;
            check.Add(l);
        }
    }
}
public class State
{
    public readonly char[] board;
    public readonly char key;
    public readonly State[] children = new State[6];
    public readonly List<int> flood; 
    public readonly int score;
    public bool childrenGenerated;
    public int bestChildScore;
    public State(char[] board, char k, List<int> flood)
    {
        this.board = board;
        key = k;
        this.flood = flood;
        score = flood.Count;
        bestChildScore = score;
    }
}
```
[Answer]
# Delphi XE3 2,979,145 steps
Ok so this is my attempt. I call the changing part a blob, each turn it will make a copy of the array and test every possible color to see which color will give the biggest blob.
Runs all puzzles in 3 hours and 6 minutes
```
program Main;
{$APPTYPE CONSOLE}
{$R *.res}
uses
  SysUtils,
  Classes,
  Generics.Collections,
  math,
  stopwatch in 'stopwatch.pas';
type
  myArr=array[0..1]of integer;
const
  MaxSize=19;
  puzLoc='here is my file';
var
  L:TList<TList<integer>>;
  puzzles:TStringList;
  sc:TList<myArr>;
  a:array[0..MaxSize-1,0..MaxSize-1] of Integer;
  aTest:array[0..MaxSize-1,0..MaxSize-1] of Integer;
  turns,midCol,sX,sY,i:integer;
  currBlob,biggestBlob,ColorBigBlob:integer;
  sTurn:string='';
  GLC:integer=0;
procedure FillArrays;
var
  ln,x,y:integer;
  puzzle:TStringList;
begin
  sc:=TList<myArr>.Create;
  puzzle:=TStringList.Create;    
  while puzzle.Count<19 do
  begin
    if puzzles[GLC]='' then
    begin
      inc(GLC);
      continue
    end
    else
      puzzle.Add(puzzles[GLC]);
    inc(GLC)
  end;    
  for y:=0to MaxSize-1do
    for x:=0to MaxSize-1do
      a[y][x]:=Ord(puzzle[y][x+1])-48;
  puzzle.Free;
end;
function CreateArr(nx,ny:integer):myArr;
begin
  Result[1]:=nx;
  Result[0]:=ny;
end;
procedure CreateBlob;
var
  tst:myArr;
  n,tx,ty:integer;
  currColor:integer;
begin
  n:=0;
  sc.Clear;
  currColor:=a[sy][sx];
  sc.Add(CreateArr(sx,sy));
  repeat
    tx:=sc[n][1];
    ty:=sc[n][0];
    if tx>0 then
      if a[ty][tx-1]=currColor then
      begin
        tst:=CreateArr(tx-1,ty);
        if not sc.Contains(tst)then
          sc.Add(tst);
      end;
    if tx<MaxSize-1 then
      if a[ty][tx+1]=currColor then
      begin
        tst:=CreateArr(tx+1,ty);
        if not sc.Contains(tst)then
          sc.Add(tst);
      end;
    if ty>0 then
      if a[ty-1][tx]=currColor then
      begin
        tst:=CreateArr(tx,ty-1);
        if not sc.Contains(tst)then
          sc.Add(tst);
      end;
    if ty<MaxSize-1 then
      if a[ty+1][tx]=currColor then
      begin
        tst:=CreateArr(tx,ty+1);
        if not sc.Contains(tst)then
          sc.Add(tst);
      end;
    inc(n);
  until (n=sc.Count);
end;
function BlobSize:integer;
var
  L:TList<myArr>;
  tst:myArr;
  n,currColor,tx,ty:integer;
begin
  n:=0;
  L:=TList<myArr>.Create;
  currColor:=aTest[sy][sx];
  L.Add(CreateArr(sx,sy));
  repeat
    tx:=L[n][1];
    ty:=L[n][0];
    if tx>0then
      if aTest[ty][tx-1]=currColor then
      begin
        tst:=CreateArr(tx-1,ty);
        if not L.Contains(tst)then
          L.Add(tst);
      end;
    if tx<MaxSize-1then
      if aTest[ty][tx+1]=currColor then
      begin
        tst:=CreateArr(tx+1,ty);
        if not L.Contains(tst)then
          L.Add(tst);
      end;
    if ty>0then
      if aTest[ty-1][tx]=currColor then
      begin
        tst:=CreateArr(tx,ty-1);
        if not L.Contains(tst)then
          L.Add(tst);
      end;
    if ty<MaxSize-1then
      if aTest[ty+1][tx]=currColor then
      begin
        tst:=CreateArr(tx,ty+1);
        if not L.Contains(tst)then
          L.Add(tst);
      end;
    inc(n);
  until n=l.Count;
  Result:=L.Count;
  L.Free;
end;
function AllsameColor(c:integer):boolean;
var
  cy,cx:integer;
begin
  Result:=true;
  for cy:=0to MaxSize-1do
    for cx:=0to MaxSize-1do
      if a[cy][cx]=c then
        continue
      else
        exit(false);
end;
procedure ChangeColors(old,new:integer; testing:boolean=false);
var
  i,j:integer;
  tst:myArr;
begin
  if testing then
  begin
    for i:= 0to MaxSize-1do
      for j:= 0to MaxSize-1do
        aTest[i][j]:=a[i][j];    
    for I:=0to sc.Count-1do
    begin
      tst:=sc[i];
      aTest[tst[0]][tst[1]]:=new;
    end;
  end
  else
  begin
    for I:=0to sc.Count-1do
    begin
      tst:=sc[i];
      a[tst[0]][tst[1]]:=new;
    end;
  end;
end;
var
  sw, swTot:TStopWatch;
  solved:integer=0;
  solutions:TStringList;
  steps:integer;
  st:TDateTime;
begin          
  st:=Now;
  writeln(FormatDateTime('hh:nn:ss',st));
  solutions:=TStringList.Create;
  puzzles:=TStringList.Create;
  puzzles.LoadFromFile(puzLoc);
  swTot:=TStopWatch.Create(true);
  turns:=0;
  repeat
    sTurn:='';    
    FillArrays;
    sX:=Round(Sqrt(MaxSize))+1;
    sY:=sX;    
    repeat
      biggestBlob:=0;
      ColorBigBlob:=0;
      midCol:=a[sy][sx];
      CreateBlob;
      for I:=1to 6do
      begin
        if I=midCol then continue;    
        ChangeColors(midCol,I,true);
        currBlob:=BlobSize;
        if currBlob>biggestBlob then
        begin
          biggestBlob:=currBlob;
          ColorBigBlob:=i;
        end;
      end;
      ChangeColors(midCol,ColorBigBlob);
      inc(turns);
      if sTurn='' then
        sTurn:=IntToStr(ColorBigBlob)
      else
        sTurn:=sTurn+', '+IntToStr(ColorBigBlob);
    until AllsameColor(a[sy][sx]);
    solutions.Add(sTurn);
    inc(solved);
    if solved mod 100=0then
      writeln(Format('Solved %d puzzles || %s',[solved,FormatDateTime('hh:nn:ss',Now-st)]));    
  until GLC>=puzzles.Count-1;    
  swTot.Stop;
  WriteLn(Format('solving these puzzles took %d',[swTot.Elapsed]));
  writeln(Format('Total moves: %d',[turns]));
  solutions.SaveToFile('save solutions here');
  readln;
end.
```
Thinking about a bruteforce backtracing method too.  
Maybe fun for this weekend ^^
[Answer]
## Javascript/node.js - 2,588,847
Algoritm is a bit different then most here as it makes use of precalculated regions and diff states between calculations. It runs under 10 minutes here if you are worried about speed because of javascript.
```
var fs = require('fs')
var file = fs.readFileSync('floodtest','utf8');
var boards = file.split('\n\n');
var linelength  = boards[0].split('\n')[0].length;
var maxdim = linelength* linelength;
var board = function(info){
    this.info =[];
    this.sameNeighbors = [];
    this.differentNeighbors = [];
    this.samedifferentNeighbors = [];
    for (var i = 0;i <info.length;i++ ){
        this.info.push(info[i]|0);
    };
    this.getSameAndDifferentNeighbors();
}
board.prototype.getSameAndDifferentNeighbors = function(){
    var self = this;
    var info = self.info;
    function getSameNeighbors(i,value,sameneighbors,diffneighbors){
        var neighbors = self.getNeighbors(i);
        for(var j =0,nl = neighbors.length; j< nl;j++){
            var index = neighbors[j];
            if (info[index]  === value ){
                if( sameneighbors.indexOf(index) === -1){
                    sameneighbors.push(index);
                    getSameNeighbors(index,value,sameneighbors,diffneighbors);
                }
            }else if( diffneighbors.indexOf(index) === -1){
                    diffneighbors.push(index);
            }
        } 
    }
    var sneighbors = [];
    var dneighbors = [];
    var sdneighbors = [];
    for(var i= 0,l= maxdim;i<l;i++){
        if (sneighbors[i] === undefined){
            var sameneighbors = [i];
            var diffneighbors = [];
            getSameNeighbors(i,info[i],sameneighbors,diffneighbors);
            for (var j = 0; j<sameneighbors.length;j++){
                var k = sameneighbors[j];
                sneighbors[k] = sameneighbors;
                dneighbors[k] = diffneighbors;
            } 
        }
    }
    for(var i= 0,l= maxdim;i<l;i++){
        if (sdneighbors[i] === undefined){
            var value = [];
            var dni = dneighbors[i];
            for (var j = 0,dnil = dni.length; j<dnil;j++){
                var dnij = dni[j];
                var sdnij = sneighbors[dnij];
                for(var k = 0,sdnijl = sdnij.length;k<sdnijl;k++){
                    if (value.indexOf(sdnij[k])=== -1){
                        value.push(sdnij[k]);
                    }
                }
            };
            var sni = sneighbors[i];
            for (var j=0,snil = sni.length;j<snil;j++){
                sdneighbors[sni[j]] = value;
            };
        };
    }
    this.sameNeighbors = sneighbors;
    this.differentNeighbors =  dneighbors;
    this.samedifferentNeighbors =sdneighbors;
}
board.prototype.getNeighbors = function(i){
        var returnValue = [];
        var index = i-linelength;
        if (index >= 0){
            returnValue.push(index);
        }
        index = i+linelength;
        if (index < maxdim){
            returnValue.push(index);
        }
        index = i-1;
        if (index >= 0 && index/linelength >>> 0 === i/linelength  >>> 0){
            returnValue.push(index);
        }
        index = i+1;
        if (index/linelength >>> 0 === i/linelength >>> 0){
            returnValue.push(index);
        }
        if (returnValue.indexOf(-1) !== -1){
            console.log(i,parseInt(index/linelength,10),parseInt(i/linelength,10));
        } 
        return returnValue 
}
board.prototype.solve = function(){
    var i,j;
    var info = this.info;
    var sameNeighbors = this.sameNeighbors;
    var samedifferentNeighbors = this.samedifferentNeighbors;
    var middle = 9*19+9;
    var maxValues = [];
    var done = {};
    for (i=0; i<sameNeighbors[middle].length;i++){
        done[sameNeighbors[middle][i]] = true;
    }
    var usefullNeighbors = [[],[],[],[],[],[],[]];
    var diff = [];
    var count = [0];
    count[1] = 0;
    count[2] = 0;
    count[3] = 0;
    count[4] = 0;
    count[5] = 0;
    count[6] = 0;
    var addusefullNeighbors = function(index,diff){
        var indexsamedifferentNeighbors =samedifferentNeighbors[index];
        for (var i=0;i < indexsamedifferentNeighbors.length;i++){
            var is = indexsamedifferentNeighbors[i];
            var value = info[is];
            if (done[is] === undefined && usefullNeighbors[value].indexOf(is) === -1){
                usefullNeighbors[value].push(is);
                diff.push(value);
            }
        }
    }
    addusefullNeighbors(middle,diff);
    while(  usefullNeighbors[1].length > 0 || usefullNeighbors[2].length > 0 ||
            usefullNeighbors[3].length > 0 || usefullNeighbors[4].length > 0 ||
            usefullNeighbors[5].length > 0 || usefullNeighbors[6].length > 0 ){
        for (i=0;i < diff.length;i++){ 
            count[diff[i]]++;
        };
        var maxValue = count.indexOf(Math.max.apply(null, count));
        diff.length = 0;
        var used = usefullNeighbors[maxValue];
        for (var i=0,ul = used.length;i < ul;i++){
            var index = used[i];
            if (info[index] === maxValue){
                done[index] = true;
                addusefullNeighbors(index,diff);
            }
        }
        used.length = 0;
        count[maxValue] = 0;
        maxValues.push(maxValue);
    }
    return maxValues.join("");
};
var solved = [];
var start = Date.now();
for (var boardindex =0;boardindex < boards.length;boardindex++){ 
    var b = boards[boardindex].replace(/\n/g,'').split('');
    var board2 = new board(b);
    solved.push(board2.solve());
};
var diff = Date.now()-start;
console.log(diff,boards.length);
console.log(solved.join('').length);
console.log("end");
fs.writeFileSync('solution.txt',solved.join('\n'),'utf8');
```
[Answer]
C code that is guaranteed to find an optimal solution by simple brute force. Works for arbitrary size grids and all inputs. Takes a very, very long time to run on most grids.
The flood fill is extremely inefficient and relies on recursion. Might need to make your stack bigger if it is very small. The brute force system uses a string to hold the numbers and simple add-with-carry to cycle through all possible options. This is also extremely inefficient as it repeats most of the steps quadrillions of times.
Unfortunately I was unable to test it against all the test cases, since I'll die of old age before it finishes.
```
#include <stdio.h>
#include <string.h>
#define GRID_SIZE       19
char grid[GRID_SIZE][GRID_SIZE] = { {3,3,5,4,1,3,4,1,5,3,3,5,4,1,3,4,1,5},
                                    {5,1,3,4,1,1,5,2,1,3,3,5,4,1,3,4,1,5},
                                    {6,5,2,3,4,3,3,4,3,3,3,5,4,1,3,4,1,5},
                                    {4,4,4,5,5,5,4,1,4,3,3,5,4,1,3,4,1,5},
                                    {6,2,5,3,3,1,1,6,6,3,3,5,4,1,3,4,1,5},
                                    {5,5,1,2,5,2,6,6,3,3,3,5,4,1,3,4,1,5},
                                    {6,1,1,5,3,6,2,3,6,3,3,5,4,1,3,4,1,5},
                                    {1,2,2,4,5,3,5,1,2,3,3,5,4,1,3,4,1,5},
                                    {3,6,6,1,5,1,3,2,4,3,3,5,4,1,3,4,1,5} };
char grid_save[GRID_SIZE][GRID_SIZE];
char test_grids[6][GRID_SIZE][GRID_SIZE];
void flood_fill(char x, char y, char old_colour, char new_colour)
{
    if (grid[y][x] == new_colour)
        return;
    grid[y][x] = new_colour;
    if (y > 0)
    {
        if (grid[y-1][x] == old_colour)
            flood_fill(x, y-1, old_colour, new_colour);
    }
    if (y < GRID_SIZE - 1)
    {
        if (grid[y+1][x] == old_colour)
            flood_fill(x, y+1, old_colour, new_colour);
    }
    if (x > 0)
    {
        if (grid[y][x-1] == old_colour)
            flood_fill(x-1, y, old_colour, new_colour);
    }
    if (x < GRID_SIZE - 1)
    {
        if (grid[y][x+1] == old_colour)
            flood_fill(x+1, y, old_colour, new_colour);
    }
}
bool check_grid(void)
{
    for (char i = 0; i < 6; i++)
    {
        if (!memcmp(grid, &test_grids[i][0][0], sizeof(grid)))
            return(true);
    }
    return(false);
}
void inc_string_num(char *s)
{
    char *c;
    c = s + strlen(s) - 1;
    *c += 1;
    // carry
    while (*c > '6')
    {
        *c = '1';
        if (c == s) // first char
        {
            strcat(s, "1");
            return;
        }
        c--;
        *c += 1;
    }
}
void print_grid(void)
{
    char x, y;
    for (y = 0; y < GRID_SIZE; y++)
    {
        for (x = 0; x < GRID_SIZE; x++)
            printf("%d ", grid[y][x]);
        printf("\n");
    }
    printf("\n");
}
int main(int argc, char* argv[])
{
    // create test grids for comparisons
    for (char i = 0; i < 6; i++)
        memset(&test_grids[i][0][0], i+1, GRID_SIZE*GRID_SIZE);
    char s[256] = "0";
    //char s[256] = "123456123456123455";
    memcpy(grid_save, grid, sizeof(grid));
    print_grid();
    do
    {
        memcpy(grid, grid_save, sizeof(grid));
        inc_string_num(s);
        for (unsigned int i = 0; i < strlen(s); i++)
        {
            flood_fill(4, 4, grid[4][4], s[i] - '0');
        }
    } while(!check_grid());
    print_grid();
    printf("%s\n", s);
    return 0;
}
```
---
As far as I can tell this is the current winner. The competition requires that:
> 
> Your program must be entirely deterministic; pseudorandom solutions are allowed, but the program must generate the same output for the same test case every time.
> 
> 
> 
Check
> 
> The winning program will take the fewest total number of steps to solve all 100,000 test cases found in this file (zipped text file, 14.23 MB). If two solutions take the same number of steps (e.g. if they both found the optimal strategy), the shorter program will win.
> 
> 
> 
Since this always finds the lowest number of steps to complete every board and none of the others do, it is currently ahead. If someone can come up with a shorter program they could win, so I present the following size optimized version. Execution is a bit slower, but execution time isn't part of the winning conditions:
```
#include <stdio.h>
#include <string.h>
#define A 9
int g[A][A]={{3,3,5,4,1,3,4,1,5},{5,1,3,4,1,1,5,2,1},{6,5,2,3,4,3,3,4,3},{4,4,4,5,5,5,4,1,4},{6,2,5,3,3,1,1,6,6},{5,5,1,2,5,2,6,6,3},{6,1,1,5,3,6,2,3,6},{1,2,2,4,5,3,5,1,2},{3,6,6,1,5,1,3,2,4}};
int s[A][A];
int t[6][A][A];
void ff(int x,int y,int o,int n)
{if (g[y][x]==n)return;g[y][x]=n;if (y>0){if(g[y-1][x]==o)ff(x,y-1,o,n);}if(y<A-1){if(g[y+1][x]==o)ff(x,y+1,o,n);}if(x>0){if (g[y][x-1] == o)ff(x-1,y,o,n);}if(x<A-1){if(g[y][x+1]==o)ff(x+1,y,o,n);}}
bool check_g(void)
{for(int i=0;i<6;i++){if(!memcmp(g,&t[i][0][0],sizeof(g)))return(true);}return(0);}
void is(char*s){char*c;c=s+strlen(s)-1;*c+=1;while(*c>'6'){*c='1';if (c==s){strcat(s,"1");return;}c--;*c+=1;}}
void pr(void)
{int x, y;for(y=0;y<A;y++){for(x=0;x<A;x++)printf("%d ",g[y][x]);printf("\n");}printf("\n");}
int main(void)
{for(int i=0;i<6;i++)memset(&t[i][0][0],i+1,A*A);char s[256]="0";memcpy(s,g,sizeof(g));pr();do{memcpy(g,s,sizeof(g));is(s);for(int i=0;i<strlen(s);i++){ff(4,4,g[4][4],s[i]-'0');}}while(!check_g());
pr();printf("%s\n",s);return 0;}
```
]