<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(vector<vector<int>>&v,int i,int j){
  
  return i>=0 && i<v.size() && j>=0 && j<v[0].size() ;
}
struct State
{
  State(vector<vector<int>>&state,pair<int,int> loc,pair<int,int> par):state(state),loc(loc),par(par){}
  vector<vector<int>>state;
  pair<int,int> loc;
  pair<int,int> par;
  bool operator ==(State& s){
    return state==s.state;
  }
  bool operator <(State &x){
    return state < x.state;
  }
  bool operator >(State &x){
    return state > x.state;
  }
};
bool checkstate(queue<State>&q,set<vector<vector<int>>>&vis,vector<vector<int>>&state,vector<vector<int>>&Rstate,pair<int,int>loc,pair<int,int>par){
  
  if(state==Rstate)return 1;
  
  if(vis.insert(state).second)
     q.push(State(state,loc,par));
 
  return 0;
}

int slidingPuzzle(vector<vector<int>>& board){
  vector<vector<int>>state{{1,2,3},{4,5,0}};
  if(board==state)return 0;
  queue<State>q;
  set<vector<vector<int>>>vis;
  vis.insert(board);
  pair<int,int> loc={0,0};
  for(int i=0;i<2;i++)
    for(int j=0;j<3;j++)
      if(board[i][j]==0)
        loc={i,j};
  int c=0;
  q.push(State(board,loc,{-1,-1}));
   int dx[]{1,-1,0,0};
   int dy[]{0,0,1,-1};
  while (!q.empty())
  {
     int sz=q.size();
     while (sz--)
     {
        auto cur=q.front();
        q.pop();
        for(int i=0;i<4;i++){
          int x=cur.loc.first+dx[i];
          int y=cur.loc.second+dy[i];
          if(!isvalid(board,x,y)||x==cur.par.first&&y==cur.par.second)continue;
          auto s=cur.state;
          swap(s[cur.loc.first][cur.loc.second],s[x][y]);
          if(checkstate(q,vis,s,state,{x,y},cur.loc))return c+1;
        }     
     }
     c++;

  }
  return -1;
}

};
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