<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:
    using State = std::array<std::vector<int>, 2>; 
    
    std::map<State, bool> mVisited;
    //std::map<State, int> mAnswer;
    
    State SolvedState;
    
    int solve(State const & s) {
        
        mVisited[s] = true;
        
        for(int i = 0 ; i < 2; ++i) {
            for(int j = 0 ; j < 3 ; ++j) {
                std::cout << s[i][j] << " ";
            }
            std::cout << std::endl;
        }
        std::cout << "_---" << std::endl;
        
        if(s == SolvedState) {
            std::cout << "Soled state" << std::endl;
            return 0;
        }
        
        
        int zeroRow = 0;
        int zeroCol = 0;
        for(int i = 0; i < 2; ++i) {
            for(int j = 0 ; j < 3; ++j) {
                if(s[i][j] == 0) {
                    zeroRow = i;
                    zeroCol = j;
                    break;
                }
            }
        }
        
        int dx[] = {-1, 0, 1, 0};
        int dy[] = {0, 1, 0, -1};
        
        int ans = std::numeric_limits<int>::max();
        for(int i = 0 ; i < 4; ++i) {
            int ndx = zeroRow + dx[i];
            int ndy = zeroCol + dy[i];
            
            if(ndx >= 0 and ndx < 2 and ndy >= 0 and ndy < 3) {
                State newState = s;
                std::swap(newState[zeroRow][zeroCol], newState[ndx][ndy]);
                
                if(not mVisited[newState]  ) {
                    int v = solve(newState);
                    if(v != std::numeric_limits<int>::max()) 
                        ans = std::min(ans, v+1);
                }
                    
            }
        }
         
        //if(ans == numeric_limits<int>::max()) return -1;
        
        return ans;
    }
    
    int slidingPuzzle(vector<vector<int>>& board) {
        State s;
        s[0] = board[0];
        s[1] = board[1];
        
        
        SolvedState[0] = {1, 2, 3};
        SolvedState[1] = {4, 5, 0};
        
        std::queue<State> q; 
        q.push(s);
        
        std::map<State, int> ans;
        ans[s] = 0;
        
        while(!q.empty()) {
            
            State s = q.front(); 
            q.pop();
            
            mVisited[s] = true;
            
            if(s == SolvedState) break;
            
            int dx[] = {-1, 0, 1, 0};
            int dy[] = {0, 1, 0, -1};
            
            int zeroRow = 0;
            int zeroCol = 0;
            for(int i = 0; i < 2; ++i) {
                for(int j = 0 ; j < 3; ++j) {
                    if(s[i][j] == 0) {
                        zeroRow = i;
                        zeroCol = j;
                        break;
                    }
                }
            }

            //int ans = std::numeric_limits<int>::max();
            for(int i = 0 ; i < 4; ++i) {
                int ndx = zeroRow + dx[i];
                int ndy = zeroCol + dy[i];

                if(ndx >= 0 and ndx < 2 and ndy >= 0 and ndy < 3) {
                    State newState = s;
                    std::swap(newState[zeroRow][zeroCol], newState[ndx][ndy]);

                    if(not mVisited[newState]) {
                        ans[newState] = 1 + ans[s];
                        q.push(newState);
                    }

                }
            }
        }
        
        if(ans.find(SolvedState) != ans.end()) return ans[SolvedState];
        return -1;
       
    }
};
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