<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:

// Function to convert the board to a string representation
string boardToString(vector<vector<int>>& board) {
    string s;
    for (int i = 0; i < 2; ++i) {
        for (int j = 0; j < 3; ++j) {
            s += to_string(board[i][j]);
        }
    }
    return s;
}

// Function to get the neighbors of a position in a 1D index of the board
vector<int> getNeighbors(int pos) {
    vector<vector<int>> neighborMap = {
        {1, 3},    // neighbors for index 0
        {0, 2, 4}, // neighbors for index 1
        {1, 5},    // neighbors for index 2
        {0, 4},    // neighbors for index 3
        {1, 3, 5}, // neighbors for index 4
        {2, 4}     // neighbors for index 5
    };
    return neighborMap[pos];
}

int slidingPuzzle(vector<vector<int>>& board) {
    string target = "123450"; // the goal state
    string start = boardToString(board); // convert the starting board to string

    if (start == target) return 0; // if already solved

    // BFS setup
    queue<pair<string, int>> q; // queue stores the current board state and the number of moves
    unordered_set<string> visited; // to keep track of visited states
    q.push({start, 0}); // start from the initial state
    visited.insert(start);

    while (!q.empty()) {
        auto [currBoard, moves] = q.front();
        q.pop();

        int zeroPos = currBoard.find('0'); // find the position of 0 (empty space)
        vector<int> neighbors = getNeighbors(zeroPos);

        for (int neighbor : neighbors) {
            string newBoard = currBoard;
            swap(newBoard[zeroPos], newBoard[neighbor]); // swap 0 with a neighbor

            if (newBoard == target) return moves + 1; // if we reached the goal

            if (visited.find(newBoard) == visited.end()) {
                q.push({newBoard, moves + 1}); // add new state to the queue
                visited.insert(newBoard); // mark it as visited
            }
        }
    }

    return -1; // no solution
}



};
18959