<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>

#include <vector>
#include <queue>
#include <unordered_set>
#include <string>

using namespace std;

class Solution {
public:
    // Function to convert 2D board to a single string for easy comparison and hashing
    string toString(const vector<vector<int>>& board) {
        string result;
        for (const auto& row : board) {
            for (int num : row) {
                result += to_string(num) + ",";
            }
        }
        return result;
    }

    // Function to convert string back to 2D board
    vector<vector<int>> toBoard(const string& s) {
        vector<vector<int>> board(2, vector<int>(3));
        int idx = 0;
        for (int i = 0; i < 2; ++i) {
            for (int j = 0; j < 3; ++j) {
                board[i][j] = s[idx] - '0';
                idx += 2; // Skip comma
            }
        }
        return board;
    }

    // Function to get the position of zero in the board
    pair<int, int> findZero(const vector<vector<int>>& board) {
        for (int i = 0; i < 2; ++i) {
            for (int j = 0; j < 3; ++j) {
                if (board[i][j] == 0) {
                    return {i, j};
                }
            }
        }
        return {-1, -1}; // Should not reach here
    }

    int slidingPuzzle(vector<vector<int>>& board) {
        vector<vector<int>> target = {{1, 2, 3}, {4, 5, 0}};
        string targetStr = toString(target);
        string startStr = toString(board);

        if (startStr == targetStr) {
            return 0;
        }

        queue<pair<string, pair<int, int>>> q;
        unordered_set<string> visited;
        auto zeroPos = findZero(board);
        q.push({startStr, zeroPos});
        visited.insert(startStr);

        vector<pair<int, int>> directions = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
        int steps = 0;

        while (!q.empty()) {
            int size = q.size();
            while (size--) {
                auto [curStr, zero] = q.front();
                q.pop();
                auto [x, y] = zero;
                vector<vector<int>> curBoard = toBoard(curStr);

                for (const auto& dir : directions) {
                    int newX = x + dir.first;
                    int newY = y + dir.second;
                    if (newX >= 0 && newX < 2 && newY >= 0 && newY < 3) {
                        swap(curBoard[x][y], curBoard[newX][newY]);
                        string newStr = toString(curBoard);
                        if (newStr == targetStr) {
                            return steps + 1;
                        }
                        if (visited.find(newStr) == visited.end()) {
                            visited.insert(newStr);
                            q.push({newStr, {newX, newY}});
                        }
                        swap(curBoard[x][y], curBoard[newX][newY]); // Restore the state
                    }
                }
            }
            ++steps;
        }

        return -1; // Return -1 if no solution found
    }
};

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