<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:
    vector<vector<int>> target = {{1,2,3},{4,5,0}};
    vector<pair<int,int>> moves = {{0,1},{0,-1},{1,0},{-1,0}};
    int slidingPuzzle(vector<vector<int>>& board) {
        long long tv = encode(target);
        map<long long, int> dp;
        long long v = encode(board);
        if (v == tv) return 0;
        dp[v] = 0;
        queue<long long> q;
        q.push(v);
        while (!q.empty()) {
            v = q.front();
            q.pop();
            for(auto nv: transistions(v)) {
                if (dp.find(nv) == dp.end()) {
                    if (nv == tv) {
                        return dp[v] + 1;
                    }
                    dp[nv] = dp[v] + 1;
                    q.push(nv);
                }
            }
            // cout << "queue size " << q.size() << '\n';
        }
        return -1;
    }

    long long encode(vector<vector<int>>& board) {
        long long base = 1;
        long long ans = 0;
        for(int i=0; i<2; i++) {
            for(int j=0; j<3; j++) {
                ans += base * board[i][j];
                base = base * 6;
            }
        }
        return ans;
    }

    vector<long long> transistions(long long curr) {
        vector<vector<int>> board(2,vector<int>(3));
        int a, b;
        for(int i=0; i<2; i++) {
            for(int j=0; j<3; j++) {
                board[i][j] = curr % 6;
                curr /= 6;
                if (board[i][j] == 0) {
                    a = i;
                    b = j;
                }
                // cout << board[i][j] << ' ';
            }
            // cout << '\n';
        }

        vector<long long> res;
        for(auto mv: moves) {
            int i = a + mv.first;
            int j = b + mv.second;
            if (i >= 0 && i<2 && j >= 0 && j<3) {
                swap(board[i][j], board[a][b]);
                res.push_back(encode(board));
                swap(board[i][j], board[a][b]);
            }
        }
        return res;
    }
};
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