<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:
    // 0 1 2
    // 3 4 5 
    bool isFinal(vector<int> &state){
        for(int i=1;i<6;i++)
            if(state[i-1] != i)
                return false;
        return (state[5] == 0);
    }
    struct myHash{
    size_t operator() ( const vector<int> &state) const{
        size_t a=0;
        for(int i=0;i<6;i++){
            a += state[i];
            a  = a<<2;
        }
        return a;
    }
    };
    vector<vector<int>> neighbours;
    unordered_set<vector<int>,myHash> S;
    queue<vector<int>> Q;
    bool add_neighbours(vector<int> &state){
        //find zero pos
        int z=0;
        for(z=0;z<6;z++)
        if(state[z] == 0)
            break;
        for(int &p:neighbours[z]){
            swap(state[z],state[p]);
            if(S.find(state) == S.end()){
                if(isFinal(state))
                    return true;
                Q.push(state);
                S.insert(state);
            }
            swap(state[p],state[z]);
        }
        return false;
    }
    //operator must be const member function
    //also need to custom operator == for vector if necessary
    int slidingPuzzle(vector<vector<int>>& board) {
        neighbours = {
            {1,3},
            {0,2,4},
            {1,5},
            {0,4},
            {1,3,5},
            {2,4}
        };
        vector<int> state(6,0);
        int cur=0;
        for(int i=0;i<2;i++)
        for(int j=0;j<3;j++)
          state[cur++] = board[i][j];
        Q.push(state);
        if(isFinal(state))
            return 0;
        int level = 1,m=1;
        vector<int> cur_state;
        S.insert(state);
        while(!Q.empty()){
            m=Q.size();
            while(m>0){
                cur_state = Q.front();
                Q.pop();
                if(add_neighbours(cur_state))
                    return level;
                m--;
            }
            level++;
        }
        return -1;
    }
};
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