<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 isValid(string& s) {
        for(int i=0; i<5; i++) {
            if(i + 1 != s[i] - '0')
                return false; 
        }

        return true;
    }
    string genNextString(int x, int y, int nx, int ny, string& s) {
        string res = s;
        vector<vector<int>> board(2, vector<int>(3));

        for(int i=0; i<6; i++)
            board[i / 3][i % 3] = s[i] - '0';

        swap(board[x][y], board[nx][ny]);

        return stringify(board);
    }
    string stringify(vector<vector<int>>& board) {
        string res = "";
        for(int i=0; i<6; i++) {
            res += '0' + board[i / 3][i % 3];
        }

        return res;
    }
    int slidingPuzzle(vector<vector<int>>& board) {
        int n = 2, m = 3;

        unordered_map<string, bool> states;
        queue<pair<int, pair<int, string>>> q;

        for(int i=0; i<n; i++) {
            for(int j=0; j<m; j++) {
                if(board[i][j] == 0) {
                    string s = stringify(board);
                    if(isValid(s)) return 0;
                    q.push({i, {j, s}});
                    states[s] = true;
                    break;
                }
            }
        }

        int ans = 0;
        vector<pair<int, int>> dr = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
        while(!q.empty()) {
            ans++;
            int sz = q.size();

            while(sz--) {
                int x = q.front().first, y = q.front().second.first;
                string s = q.front().second.second;
                q.pop();

                for(auto [i, j]: dr) {
                    int nx = i + x, ny = j + y;

                    if(nx < 0 || nx >= n || ny < 0 || ny >= m) 
                        continue;

                    string nextString = genNextString(x, y, nx, ny, s);

                    if(states.find(nextString) != states.end())
                        continue;

                    q.push({nx, {ny, nextString}});

                    if(isValid(nextString)) return ans;

                    states[nextString] = true;
                }
            }
        }

        return -1;
    }
};
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