<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 {
    int m;
    int n;
    string getStateId(vector<vector<int>>& board){
        string stateId = "";
        for(int i=0; i<m; i++){
            for(int j=0; j<n; j++){
                stateId += to_string(board[i][j]);
            }
        }
        return stateId;
    }
    string getState(int i, int j, string state){
        string ns = state;
        swap(ns[i],ns[j]);
        return ns;
    }
    vector<string> genPosState(string state){
        vector<string> states;
        int zidx = state.find('0');
        switch(zidx){
            case 0:
                states.push_back(getState(0,1,state));
                states.push_back(getState(0,3,state));
                break;
            case 1:
                states.push_back(getState(1,0,state));
                states.push_back(getState(1,2,state));
                states.push_back(getState(1,4,state));
                break;
            case 2:
                states.push_back(getState(2,1,state));
                states.push_back(getState(2,5,state));
                break;
            case 3:
                states.push_back(getState(3,0,state));
                states.push_back(getState(3,4,state));
                break;
            case 4:
                states.push_back(getState(4,1,state));
                states.push_back(getState(4,3,state));
                states.push_back(getState(4,5,state));
                break;
            case 5:
                states.push_back(getState(5,2,state));
                states.push_back(getState(5,4,state));
                break;
        }
        return states;
    }

public:
    int slidingPuzzle(vector<vector<int>>& board) {
        m = board.size();
        n = board[0].size();
        
        unordered_set<string> visited;
        string solved = "123450";
        
        queue<pair<string,int>> q; //{state, moves}
        string initPos = getStateId(board);
        
        if(initPos == solved) return 0;
        
        q.push({initPos,0});
        visited.insert(initPos);
        // cout << initPos << endl;
        while(!q.empty()){
            auto[state, moves] = q.front(); q.pop();
            vector<string> posStates = genPosState(state);
            for(auto &pState : posStates){
                // cout<< pState << endl;
                if(pState == solved){
                    return moves+1;
                }
                if(!visited.count(pState)){
                    visited.insert(pState);
                    q.push({pState, moves+1});
                }
            }
        }
        return -1;
    }
};
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