<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 <iostream>
#include <vector>
#include <queue>
#include <map>
using namespace std;

class Solution {
public:
    int slidingPuzzle(vector<vector<int>>& board) {
        // Target configuration of the sliding puzzle.
        vector<vector<int>> target = {{1, 2, 3}, {4, 5, 0}};
        
        // Map to track visited states.
        map<vector<vector<int>>, int> mp;
        
        // Queue to store board states for BFS.
        queue<vector<vector<int>>> q;
        q.push(board);
        
        int cnt = -1;
        
        // Direction vectors for movement: up, down, left, right.
        vector<pair<int, int>> directions = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
        
        while (!q.empty()) {
            cnt++;
            int size = q.size();
            
            // Iterate over all the current queue elements.
            for (int i = 0; i < size; i++) {
                auto temp = q.front();
                q.pop();
                
                // If the current board configuration matches the target, return the number of moves.
                if (temp == target) {
                    return cnt;
                }
                
                // Find the position of the empty tile (0).
                int zero_row, zero_col;
                for (int j = 0; j < 2; j++) {
                    for (int k = 0; k < 3; k++) {
                        if (temp[j][k] == 0) {
                            zero_row = j;
                            zero_col = k;
                        }
                    }
                }
                
                // Try moving the empty tile in all four possible directions.
                for (auto& dir : directions) {
                    int new_row = zero_row + dir.first;
                    int new_col = zero_col + dir.second;
                    
                    // Check if the new position is within bounds.
                    if (new_row >= 0 && new_row < 2 && new_col >= 0 && new_col < 3) {
                        // Swap the empty tile with the adjacent tile.
                        swap(temp[zero_row][zero_col], temp[new_row][new_col]);
                        
                        // If this state hasn't been visited yet, add it to the queue and mark it visited.
                        if (mp.count(temp) == 0) {
                            mp[temp]++;
                            q.push(temp);
                        }
                        
                        // Swap back to restore the original configuration.
                        swap(temp[zero_row][zero_col], temp[new_row][new_col]);
                    }
                }
            }
        }
        
        // If the target configuration is not reachable, return -1.
        return -1;
    }
};

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