<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 {
    int dr[4] = {-1,0,1,0};
    int dc[4] = {0,1,0,-1};

    bool isGood(vector<vector<int>>&g)
    {
        return g[0][0]==1 && g[0][1]==2 && g[0][2]==3 && g[1][0]==4 && g[1][1]==5;
    }

public:
    int slidingPuzzle(vector<vector<int>>& board) {
        int ans = 1e9;
        int r,c;
        for(int i=0; i<2; i++)
        {
            for(int j=0; j<3; j++)
            {
                if(board[i][j] == 0)
                {
                    r = i; c = j;
                    break;
                }
            }
        }
        // cout<<r<<" "<<c;
        set<vector<vector<int>>>vis;
        vis.insert(board);
        queue<pair<vector<int>,vector<vector<int>>>>q;
        q.push({{r,c},board});
        int level = 0;
        while(!q.empty())
        {
            int sz = q.size();
            while(sz--)
            {
                auto p = q.front(); q.pop();
                if(isGood(p.second) == true) return level;
                for(int j=0; j<4; j++)
                {
                    r = p.first[0]; c = p.first[1];
                    int nr = r + dr[j], nc = c + dc[j];
                    if(nr>=0 && nr<2 && nc>=0 && nc<3)
                    {
                        swap(p.second[r][c], p.second[nr][nc]);
                        if(vis.find(p.second) == vis.end())
                        {
                            vis.insert(p.second);
                            q.push({{nr,nc},p.second});
                        }
                        swap(p.second[r][c], p.second[nr][nc]);
                    }
                }
            }
            level++;
        }
        return -1;
    }
};
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