<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:

    map<string,int>mp;
    pair<int,int>dir[4]={{1,0},{0,1},{-1,0},{0,-1}};

    string make(vector<vector<int>>& s){
        string t;
        t.push_back(s[0][0]+'0');
        t.push_back(s[0][1]+'0');
        t.push_back(s[0][2]+'0');
        t.push_back(s[1][0]+'0');
        t.push_back(s[1][1]+'0');
        t.push_back(s[1][2]+'0');
        return t;
    }
    
    int fun(vector<vector<int>>& s,string &t){
        
        queue<vector<vector<int>>>q;
        q.push(s);
        mp[make(s)]=0;

        while(q.size()>0){
            vector<vector<int>>r=q.front();
            string xx=make(r);
            q.pop();
            // cout<<xx<<endl;
            // for(int i=0;i<=1;i++){
            //     for(int j=0;j<=2;j++){
            //         cout<<r[i][j];
            //     }
            // }
            // cout<<endl;

            for(int i=0;i<=1;i++){
                for(int j=0;j<=2;j++){
                    
                    if(r[i][j]!=0) continue;

                    for(auto z:dir){
                        
                        int a=i+z.first;
                        int b=j+z.second;

                        if(a<0||a>1||b<0||b>2)continue;

                        swap(r[i][j],r[a][b]);

                        string y=make(r);

                        if(mp.count(y)==0){
                            q.push(r);
                            mp[y]=mp[xx]+1;
                        }

                        swap(r[i][j],r[a][b]);
                    }
                }
            }

            // cout<<xx<<endl;
        }

        // cout<<endl;
        // for(auto z: mp){
        //     cout<<z.first<<" "<<z.second<<endl;
        // }

        if(mp.count(t)){
            return mp[t];
        }
        return -1;

    }



    int slidingPuzzle(vector<vector<int>>& s) {
        vector<vector<int>> xx= {{1,2,3},{4,5,0}};
        string tt=make(xx);
        return fun(s,tt);

    }

    
};







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