<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 isSolved(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);
    }

    string createHash(vector<vector<int>> &board) {
        string str;
        int n = board.size();
        int m = board[0].size();
        for(int i=0;i<n;i++) {
            for(int j=0;j<m;j++) {
                str += to_string(board[i][j]);
            }
        }
        return str;
    }
    vector<pair<int,int>> adj = {{-1,0},{0,-1},{0,1},{1,0}};
    int solve(vector<vector<int>> &board, int row, int col, unordered_map<string,int> &visited,int steps) {
        int n = board.size();
        int m = board[0].size();
        if(isSolved(board)) {
            return steps;
        }
        string hash = createHash(board);
        if(visited.find(hash) != visited.end()) {
            if(visited[hash] < steps) {
                return INT_MAX;
            }
        }
        visited[hash] = steps;
        int mi = INT_MAX;
        for(int i=0;i<4;i++) {
            int new_row = row + adj[i].first;
            int new_col = col + adj[i].second;
            if(new_row >= 0 && new_row < n && new_col >= 0 && new_col < m) {
                swap(board[row][col],board[new_row][new_col]);
                mi = min(mi, solve(board,new_row,new_col,visited,steps+1));
                swap(board[row][col],board[new_row][new_col]);
            }
        }
        return mi;
    }
    int slidingPuzzle(vector<vector<int>>& board) {
        int n = board.size();
        int m = board[0].size();
        int row = -1,col = -1;
        for(int i=0;i<n;i++) {
            for(int j=0;j<m;j++) {
                if(board[i][j] == 0) {
                    row = i;
                    col = j;
                    break;
                }
            }
            if(row != -1) break;
        }
        unordered_map<string,int> visited;
        int ans = solve(board,row,col,visited,0);
        return (ans == INT_MAX) ? -1 : ans;
    }
};
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