<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 solved(vector<vector<int>>& board){
        return  board[0][0]==1&&
                board[0][1]==2&&
                board[0][2]==3&&
                board[1][0]==4&&
                board[1][1]==5&&
                board[1][2]==0;
    }
    pair<int,int> get0(vector<vector<int>>& board){
        if(board[0][0]==0)return {0,0};
        if(board[0][1]==0)return {0,1};
        if(board[0][2]==0)return {0,2};
        if(board[1][0]==0)return {1,0};
        if(board[1][1]==0)return {1,1};
        if(board[1][2]==0)return {1,2};
        return {0,0};
    }
    string getState(vector<vector<int>>& board){
        string ret="";
        for(int i=0;i<2;i++){
            for(int j=0;j<3;j++)ret+=to_string(board[i][j]);
            ret+='\n';
        }
        return ret;
    }
    int slidingPuzzle(vector<vector<int>>& board) {
        deque<vector<vector<int>>> dq{board};
        unordered_set<string> visited{getState(board)};
        int depth=0;
        while(!dq.empty()){
            // cout<<"depth:"<<depth<<endl;
            int n=dq.size();
            for(int i=0;i<n;i++){
                auto b=dq.front();
                auto copy1=b;
                auto copy2=b;
                auto copy3=b;
                auto copy4=b;
                string state=getState(b);
                // cout<<state<<endl;
                dq.pop_front();
                if(solved(b))return depth;
                auto [r,c]=get0(b);
                // cout<<"r:"<<r<<", c:"<<c<<endl;
                // cout<<"creating:"<<endl;
                if(r-1>=0){
                    swap(copy1[r][c],copy1[r-1][c]);
                    string s=getState(copy1);
                    if(!visited.count(s)){
                        visited.insert(s);
                        dq.push_back(copy1);
                        // cout<<"1"<<endl;
                        // cout<<s<<endl;
                    }
                }
                if(r+1<2){
                    swap(copy2[r][c],copy2[r+1][c]);
                    string s=getState(copy2);
                    if(!visited.count(s)){
                        visited.insert(s);
                        dq.push_back(copy2);
                        // cout<<"2"<<endl;
                        // cout<<s<<endl;
                    }

                }
                if(c-1>=0){
                    swap(copy3[r][c],copy3[r][c-1]);
                    string s=getState(copy3);
                    if(!visited.count(s)){
                        visited.insert(s);
                        dq.push_back(copy3);
                        // cout<<"3"<<endl;
                        // cout<<s<<endl;
                    }
                }
                if(c+1<3){
                    swap(copy4[r][c],copy4[r][c+1]);
                    string s=getState(copy4);
                    if(!visited.count(s)){
                        visited.insert(s);
                        dq.push_back(copy4);
                        // cout<<"4"<<endl;
                        // cout<<s<<endl;
                    }
                }
            }
            depth++;
        }
        return -1;

    }
};
20896