<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:
    map<vector<vector<int>>,int>mp;
    bool check(vector<int>&temp,vector<vector<int>>&board)
    {
        int c=0;int m=2;int n=3;
        for(int i=0;i<m;i++)
        {
            for(int j=0;j<n;j++)
            {
              if(board[i][j]==temp[c])
              {
                c++;
              }
            }
        }
        return(c==6);
    }
    int bfs(queue<pair<vector<vector<int>>,int>>&q) 
    {   int m=2;
        int n=3 ;vector<int>ref={1,2,3,4,5,0};
        int ans=INT_MAX;
        while(!q.empty())
        {       int moves=q.front().second;
                vector<vector<int>>temp=q.front().first;
                if(check(ref,temp))
                {    for(int i=0;i<m;i++)
                {
                    for(int j=0;j<n;j++)
                    {
                        cout<<temp[i][j]<<" ";
                    }cout<<endl;
                }
                     ans=min(ans,moves);
                }
                q.pop();
                int cx=-1;int cy=-1;
                for(int i=0;i<m;i++)
                {
                    for(int j=0;j<n;j++)
                    {
                      if(temp[i][j]==0)
                      {
                        cx=i;cy=j;break;
                      }
                    }
                }
                vector<int>rows={0,1,-1,0};
                vector<int>cols={-1,0,0,1};

                for(int i=0;i<4;i++)
                {
                    int nx=cx+rows[i];
                    int ny=cy+cols[i];

                    if(!(nx<0||ny>=n||nx>=m||ny<0))
                    {
                        vector<vector<int>>help=temp;
                        swap(help[cx][cy],help[nx][ny]);
                        if(mp[help]==1)
                        {
                        continue;
                        }
                        mp[help]=1;
                        q.push({help,moves+1});
                    }
                }

        }
        return ans;
    }
    int slidingPuzzle(vector<vector<int>>& board)
    { mp[board]=1;
        int m=board.size();
        int n=board[0].size();
        vector<int>temp={1,2,3,4,5,0};
        if(check(temp,board))return 0;

        queue<pair<vector<vector<int>>,int>>q;
        q.push({board,0});
        mp[board]=1;
        int ans=bfs(q);
        if(ans==INT_MAX)return -1;
        return ans;
    }
};
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