<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:
    string TARGET;
    vector<int>STEPS;
    bool inRange(int zi,int i) {
        if (zi == 3 && i == -1)return false;
        if (zi == 2 && i == 1)return false;
        return (i+zi >= 0 && i+zi < 6);
    }
    int slidingPuzzle(vector<vector<int>>& board) {
        TARGET = "123450";
        STEPS = { 1,-1,3,-3 };
        string CUR;
        int zeroI = -1;
        for (int i = 0; i < 2; i++) {
            for (int j = 0; j < 3; j++) {
                CUR.push_back('0' + board[i][j]);
                if (CUR.back() == '0')
                {
                    zeroI = CUR.size() - 1;
                }
            }
        }
        queue<pair<string,int>>q;
        unordered_set<string>visited;
        q.push({ CUR ,0});
        visited.insert(CUR);
        int level = 0, lvlsz = 1;
        while (!q.empty())
        {
            while (lvlsz--)
            {
                CUR = q.front().first;
                level = q.front().second;
                q.pop();
                if (CUR == TARGET)return level;
                for (int i = 0; i < 6; i++)
                    if (CUR[i] == '0') zeroI = i;
                for (int i = 0; i < 4; i++)
                {
                    if (inRange(zeroI , STEPS[i]))
                    {
                        string nextState = CUR;
                        swap(nextState[zeroI], nextState[zeroI + STEPS[i]]);
                        if (!visited.count(nextState))
                        {
                            q.push({ nextState,level +1 });
                            visited.insert(CUR);
                        }
                    }
                }

            }
            level++;
            lvlsz = q.size();
        }
        return -1;
    }
};
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