<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:
    int slidingPuzzle(vector<vector<int>>& board) {
        unordered_map<string, int> distance;
        queue<string> q;

        string startNode = "123450";
        q.push(startNode);
        distance[startNode] = 0;

        while (!q.empty())
        {
            string node = q.front(); q.pop();
            if (equalNodes(node, board))
                return distance[node];

            for (auto neighbour: getNodeNeighbours(node))
            {
                if (!distance.count(neighbour))
                {
                    distance[neighbour] = distance[node] + 1;
                    q.push(neighbour);
                }
            }
        }

        return -1;
    }

private:
    vector<string> getNodeNeighbours(string node)
    {
        vector<string> neighbours;
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
                if (node[getCharIdx(i, j)] != '0')
                    continue;

                if (i + 1 < n)
                {
                    string neighbour = node;
                    swap(neighbour[getCharIdx(i, j)], neighbour[getCharIdx(i + 1, j)]);
                    neighbours.push_back(neighbour);
                }
                if (i - 1 >= 0)
                {
                    string neighbour = node;
                    swap(neighbour[getCharIdx(i, j)], neighbour[getCharIdx(i - 1, j)]);
                    neighbours.push_back(neighbour);
                }
                if (j + 1 < m)
                {
                    string neighbour = node;
                    swap(neighbour[getCharIdx(i, j)], neighbour[getCharIdx(i, j + 1)]);
                    neighbours.push_back(neighbour);
                }
                if (j - 1 >= 0)
                {
                    string neighbour = node;
                    swap(neighbour[getCharIdx(i, j)], neighbour[getCharIdx(i, j - 1)]);
                    neighbours.push_back(neighbour);
                }
                break;
            }
        }
        return neighbours;
    }

    bool equalNodes(string& nodeStr, vector<vector<int>>& nodeVec)
    {
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
                if (nodeStr[getCharIdx(i, j)] - '0' != nodeVec[i][j])
                    return false;
            }
        }
        return true;
    }

    inline int getCharIdx(int i, int j) 
    {
        return i * m + j;
    }

private:
    int n = 2;
    int m = 3;
};
15084