<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>

string ab = "";
class Solution {
    vector<pair<int,int>>dirs = {{-1,0},{0,1},{1,0},{0,-1}};
public:

 class Compare {
        public:
        
        //hash<string> hasher; 
        size_t operator() ( const vector<vector<int>>a ) const {

            for( int i=0; i<a.size(); i++ ){
                for( int j=0; j<a[i].size(); j++ ){
                    
                    ab = to_string(i);
                    ab += ",";
                    ab += to_string(j);
                    ab += ",";
                    ab += to_string(a[i][j]);
                    ab += "-";
                    
                }
            }
            return hash<string>()( ab );
        }
        
    };

    int slidingPuzzle(vector<vector<int>>& board) {
            int rows = board.size();
            int cols = board[0].size();

        unordered_set<vector<vector<int>>,Compare>mySet;
        list< pair<vector<vector<int>>,pair<int,int>>>myQ; // board and i and j of 0


        // result board
        vector<vector<int>>resultBoard( rows, vector<int>( cols, 0 ) );
        resultBoard[0][0] = 1;
        resultBoard[0][1] = 2;
        resultBoard[0][2] = 3;
        resultBoard[1][0] = 4;
        resultBoard[1][1] = 5;
        resultBoard[1][2] = 0;

        // find curr 0 pos and push
        int i = 0;
        int j = 0;
        for( i=0; i<board.size(); i++ ){
            for( j=0; j<board[i].size(); j++ ){
                if( board[i][j] == 0 ){
                    myQ.push_back( { board, { i, j } } );
                }
            }
        }
        mySet.insert( board );

        int count = 0;
        if( mySet.find( resultBoard ) != mySet.end() ){
            return count;
        }
        while( myQ.size() ){
            int size = myQ.size();
            count++;
            while( size ){
                pair<vector<vector<int>>,pair<int,int>> top = myQ.front();  
                myQ.pop_front();
                for( int k=0; k<dirs.size(); k++ ){
                    int newi = top.second.first + dirs[k].first;
                    int newj = top.second.second + dirs[k].second;

                    if( newi >=0 && newj >=0 && newi < rows && newj < cols ){
                        swap( top.first[top.second.first][top.second.second], top.first[newi][newj] );
                        if( mySet.find( top.first ) == mySet.end() ){
                            myQ.push_back( { top.first, { newi, newj } } );
                            mySet.insert( top.first );
                            if( mySet.find( resultBoard ) != mySet.end() ){
                                return count;
                            }
                        }
                        swap( top.first[newi][newj], top.first[top.second.first][top.second.second] );
                    }
                }
                size--;
            }
        }


        return -1;


    }
};
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