<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:
    int slidingPuzzle(vector<vector<int>>& board) {
        string ini_str;
        for(int i = 0; i < board.size(); i++) {
            for(int j = 0; j < board[0].size(); j++) {
                ini_str.push_back((char) board[i][j] + '0');
            }
        }
        
        queue<string> q;
        q.push(ini_str);
        int ans = 0;
        unordered_set<string> seen;
        while(!q.empty()) {
            int temp_size = q.size();
            for(int i = 0; i < temp_size; i++) {
                string pop_str = q.front();
                q.pop();
                if(pop_str == "123450") return ans;
                int zero_pos = -1;
                for(int i = 0; i < pop_str.size(); i++) zero_pos = (pop_str[i] == '0' ? i : zero_pos);
                vector<string> next_strs = get_swapped_strs(pop_str, zero_pos);
                for(auto& next_str : next_strs) {
                    if(seen.count(next_str)) continue;
                    seen.insert(next_str);
                    q.push(next_str);
                }
            }
            ans++;
        }
        return -1;
    }
private:
    vector<string> get_swapped_strs(string& s, int pos) {
        vector<string> strs;
        if(pos % 3 - 1 >= 0) { // left
            string temp_str(s);
            swap(temp_str[pos], temp_str[pos-1]);
            strs.push_back(temp_str);
        }
        
        if(pos % 3 + 1 < 3) { // right
            string temp_str(s);
            swap(temp_str[pos], temp_str[pos+1]);
            strs.push_back(temp_str);
        }
        
        if(pos - 3 >= 0) { // up
            string temp_str(s);
            swap(temp_str[pos], temp_str[pos-3]);
            strs.push_back(temp_str);
        }
        
        if(pos + 3 < 6) { // down
            string temp_str(s);
            swap(temp_str[pos], temp_str[pos+3]);
            strs.push_back(temp_str);
        }
        return strs;
    }
};
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