<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 n = 2, m = 3;

    vector<vector<int>> goal = {{1, 2, 3}, {4, 5, 0}};

    bool checkGoal(vector<vector<int>> &board){
        for(int i =0; i<n; i++) for(int j = 0; j<m; j++) if(board[i][j] != goal[i][j]) return false;
        return true;
    };

    int slidingPuzzle(vector<vector<int>>& board) {
        int n = board.size(), m = board[0].size();

        queue<vector<vector<int>>> q;
        q.push(board);
        set<vector<vector<int>>> vis;
        vis.insert(board);

        queue<int> distQ;
        distQ.push(0);
        
        if(checkGoal(board))
            return 0;

        auto getNeigs = [&](vector<vector<int>> &currGrid){
            vector<vector<int>> dirs = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};

            vector<vector<vector<int>>> neigs;

            //find 0 and swap with neig if not present the add to neigs 
            int x0 = -1, y0 = -1;
            for(int i = 0; i < n && x0==-1; i++){
                for(int j = 0; j < m; j++){
                    if(currGrid[i][j] == 0){
                        x0 = i;
                        y0 = j;
                        break;
                    }
                }
            }
            
            for(auto dir: dirs){
                int x = x0 + dir[0], y = y0 + dir[1];
                if(min(x, y) < 0 || x==n || y == m)
                    continue;
                swap(currGrid[x][y] , currGrid[x0][y0]);
                if(!vis.count(currGrid)){
                    neigs.push_back(currGrid);
                }
                swap(currGrid[x][y] , currGrid[x0][y0]);
            }
            return neigs;
        };

        while(!q.empty()){
            vector<vector<int>> front = q.front();
            q.pop();
            int currDist = distQ.front();

            distQ.pop();
            //get unvisited neigbors
            vector<vector<vector<int>>> neigs = getNeigs(front);

            for(vector<vector<int>> &neig: neigs){
                if(checkGoal(neig))
                    return currDist + 1;
                distQ.push(currDist + 1);
                vis.insert(neig);
                q.push(neig);
            }
        }
        return -1;
    }
};










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