<p>On an <code>2 x 3</code> board, there are five tiles labeled from <code>1</code> to <code>5</code>, and an empty square represented by <code>0</code>. A <strong>move</strong> consists of choosing <code>0</code> and a 4-directionally adjacent number and swapping it.</p>

<p>The state of the board is solved if and only if the board is <code>[[1,2,3],[4,5,0]]</code>.</p>

<p>Given the puzzle board <code>board</code>, return <em>the least number of moves required so that the state of the board is solved</em>. If it is impossible for the state of the board to be solved, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide1-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[1,2,3],[4,0,5]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> Swap the 0 and the 5 in one move.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide2-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[1,2,3],[5,4,0]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> No number of moves will make the board solved.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide3-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[4,1,2],[5,0,3]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> 5 is the smallest number of moves that solves the board.
An example path:
After move 0: [[4,1,2],[5,0,3]]
After move 1: [[4,1,2],[0,5,3]]
After move 2: [[0,1,2],[4,5,3]]
After move 3: [[1,0,2],[4,5,3]]
After move 4: [[1,2,0],[4,5,3]]
After move 5: [[1,2,3],[4,5,0]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>board.length == 2</code></li>
	<li><code>board[i].length == 3</code></li>
	<li><code>0 &lt;= board[i][j] &lt;= 5</code></li>
	<li>Each value <code>board[i][j]</code> is <strong>unique</strong>.</li>
</ul>

#define INF 10000

class Solution {
public:

    int fact(int n)
{
    if(n == 0)
        return 1;
    return n * fact(n - 1);
}

int configtoindex(vector<vector<int>>& board)
{
    int val = 0, c;
    int arr[] = {-1,-1,-1,-1,-1,-1};
    for(int i = 0; i <= 1 ; i++)
        for(int j = 0 ; j <= 2 ; j++)
        {
            c = 0;
            for(int k = 0 ; k < board[i][j] ; k++)
                c += (arr[k] == -1);
            val += fact(5 - 3 * i - j) * c;
            arr[board[i][j]] = 0; 
        }
    return val;
}

int indextoconfig(int idx)
{
    int arr[6] = {-1, -1, -1, -1, -1 ,-1}, c, j, val = 0, f;
    for(int i = 0 ; i < 6 ; i++)
    {
        f = fact(5 - i);
        c = idx/f + 1;
        j = 0;
        while(1)
        {
            c -= (arr[j] == -1);
            if(c == 0)
                break;
            j++;
        }
        val = 10 * val + j;
        arr[j] = 0;
        idx %= f;
    }
    return val;
}


    int slidingPuzzle(vector<vector<int>>& board) 
    {
        int idx = configtoindex(board), flag = 1, mindist, minidx, i, j, rowzero, colzero, nbidx, inter, endq = 0, empty = 1;
    vector dist(720, INF), queue(720, 0);
    dist[idx] = 0;
    while(1)
    {
        //cout << "Np" << endl;
        mindist = INF + 1; minidx = -1;
        empty = 0;
        for(i = 0 ; i < 720 ; i++)
            if(queue[i] == -1)
                continue;
            else
            {
                empty++;
                if(dist[i] < mindist)
                {
                    mindist = dist[i];
                    minidx = i;
                }
            }

        if(mindist == INF || empty == 0)
            break;

        //Extract the vertex with the minimum distance
        inter = indextoconfig(minidx);
        for(i = 1 ; i >= 0 ; i--)
            for(j = 2 ; j >= 0 ; j--)
            {
                board[i][j] = inter % 10;
                inter /= 10;
                if(board[i][j] == 0)
                {
                    rowzero = i;
                    colzero = j;
                }
            }

        //Now update the neighbours of this vertex
        if(rowzero > 0)
        {
            swap(board[rowzero - 1][colzero], board[rowzero][colzero]);
            nbidx = configtoindex(board);
            swap(board[rowzero - 1][colzero], board[rowzero][colzero]);
            if(queue[nbidx] == 0 && dist[nbidx] > mindist + 1)
                dist[nbidx] = mindist + 1;
        }

        if(rowzero == 0)
        {
            swap(board[rowzero + 1][colzero], board[rowzero][colzero]);
            nbidx = configtoindex(board);
            swap(board[rowzero + 1][colzero], board[rowzero][colzero]);
            if(queue[nbidx] == 0 && dist[nbidx] > mindist + 1)
                dist[nbidx] = mindist + 1;
        }

        if(colzero > 0)
        {
            swap(board[rowzero][colzero - 1], board[rowzero][colzero]);
            nbidx = configtoindex(board);
            swap(board[rowzero][colzero - 1], board[rowzero][colzero]);
            if(queue[nbidx] == 0 && dist[nbidx] > mindist + 1)
                dist[nbidx] = mindist + 1;
        }

        if(colzero < 2)
        {
            swap(board[rowzero][colzero + 1], board[rowzero][colzero]);
            nbidx = configtoindex(board);
            swap(board[rowzero][colzero + 1], board[rowzero][colzero]);
            if(queue[nbidx] == 0 && dist[nbidx] > mindist + 1)
                dist[nbidx] = mindist + 1;
        }
        queue[minidx] = -1;
    }

    if(dist[153] == INF)
        return -1;
    else
        return dist[153];
    }
};
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