<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>

class Solution {
public:

bool isSolvable(vector<vector<int>> & board)
{
    int inversions = 0;
    vector<int> arr;
    for(int i = 0;i<2;i++)
    {
        for(int j = 0;j<3;j++)
        {
            arr.push_back(board[i][j]);
        }
    }
    for(int i = 0;i<arr.size();i++)
    {
        if(arr[i]!=0)
        for(int j = 0;j<i;j++)
        {
            if(arr[j]>arr[i]) inversions++;
        }
    }
    cout<<inversions<<endl;
    return !(inversions%2);
}

bool isValid(vector<vector<int>> &board)
{
    if(board == vector<vector<int>>{{1,2,3},{4,5,0}}) return true;
    return false;
}

int bfs(vector<vector<int>> board)
{
    set<vector<vector<int>>> dp;
    queue <pair<vector<vector<int>>,int>> q;
    q.push({board,0});
    
    int retval = INT_MAX;

    while(q.size())
    {
        pair<vector<vector<int>>, int> a;
        a = q.front();
        q.pop();
        if(isValid(a.first)) retval = min(retval, a.second);
        else if(dp.find(a.first) == dp.end() && a.second<retval)
        {
            int r, c;
            for(r = 0;r<2;r++)
            {
                for(c = 0;c<3;c++)
                {
                    if(a.first[r][c] == 0) break;
                }
                if(c!=3) break;
            }
            //cout<<endl<<r<<c;
            if(c>0)
            {
                swap(a.first[r][c-1], a.first[r][c]);
                q.push({a.first,a.second+1});
                swap(a.first[r][c-1], a.first[r][c]);
            }
            if(c<2)
            {
                swap(a.first[r][c+1], a.first[r][c]);
                q.push({a.first,a.second+1});
                swap(a.first[r][c+1], a.first[r][c]);
            }
            if(r>0)
            {
                swap(a.first[r-1][c], a.first[r][c]);
                q.push({a.first,a.second+1});
                swap(a.first[r-1][c], a.first[r][c]);
            }
            if(r<1)
            {
                swap(a.first[r+1][c], a.first[r][c]);
                q.push({a.first,a.second+1});
                swap(a.first[r+1][c], a.first[r][c]);
            }
        }
        dp.insert(a.first);
    }
    if(retval == INT_MAX) return -1;
    return retval;
    
    // return 0;
}

int slidingPuzzle(vector<vector<int>>& board) 
{
    if(!isSolvable(board)) return -1;
    return bfs(board);
} 
};
14696