<p>You are given an <code>m x n</code> <code>grid</code>. Each cell of <code>grid</code> represents a street. The street of <code>grid[i][j]</code> can be:</p>

<ul>
	<li><code>1</code> which means a street connecting the left cell and the right cell.</li>
	<li><code>2</code> which means a street connecting the upper cell and the lower cell.</li>
	<li><code>3</code> which means a street connecting the left cell and the lower cell.</li>
	<li><code>4</code> which means a street connecting the right cell and the lower cell.</li>
	<li><code>5</code> which means a street connecting the left cell and the upper cell.</li>
	<li><code>6</code> which means a street connecting the right cell and the upper cell.</li>
</ul>
<img alt="" src="https://assets.leetcode.com/uploads/2020/03/05/main.png" style="width: 450px; height: 708px;" />
<p>You will initially start at the street of the upper-left cell <code>(0, 0)</code>. A valid path in the grid is a path that starts from the upper left cell <code>(0, 0)</code> and ends at the bottom-right cell <code>(m - 1, n - 1)</code>. <strong>The path should only follow the streets</strong>.</p>

<p><strong>Notice</strong> that you are <strong>not allowed</strong> to change any street.</p>

<p>Return <code>true</code><em> if there is a valid path in the grid or </em><code>false</code><em> otherwise</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/03/05/e1.png" style="width: 455px; height: 311px;" />
<pre>
<strong>Input:</strong> grid = [[2,4,3],[6,5,2]]
<strong>Output:</strong> true
<strong>Explanation:</strong> As shown you can start at cell (0, 0) and visit all the cells of the grid to reach (m - 1, n - 1).
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/03/05/e2.png" style="width: 455px; height: 293px;" />
<pre>
<strong>Input:</strong> grid = [[1,2,1],[1,2,1]]
<strong>Output:</strong> false
<strong>Explanation:</strong> As shown you the street at cell (0, 0) is not connected with any street of any other cell and you will get stuck at cell (0, 0)
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1,2]]
<strong>Output:</strong> false
<strong>Explanation:</strong> You will get stuck at cell (0, 1) and you cannot reach cell (0, 2).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 300</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 6</code></li>
</ul>

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

class Solution {
public:
    bool hasValidPath(vector<vector<int>>& grid) {
        int m = grid.size(), n = grid[0].size();
        vector<vector<bool>> visited(m, vector<bool>(n, false)); // Corrected initialization
        
        // Directions based on the street type
        vector<vector<pair<int, int>>> directions = {
            {}, // There's no street type 0
            {{0, -1}, {0, 1}},        // Type 1
            {{-1, 0}, {1, 0}},        // Type 2
            {{0, -1}, {1, 0}},        // Type 3
            {{0, 1}, {1, 0}},         // Type 4
            {{0, -1}, {-1, 0}},       // Type 5
            {{0, 1}, {-1, 0}}         // Type 6
        };
        
        queue<pair<int, int>> q;
        q.push({0, 0});
        visited[0][0] = true;
        
        while (!q.empty()) {
            auto [r, c] = q.front();
            q.pop();
            
            if (r == m - 1 && c == n - 1) return true;
            
            for (auto [dr, dc] : directions[grid[r][c]]) {
                int nr = r + dr, nc = c + dc;
                if (nr >= 0 && nr < m && nc >= 0 && nc < n && !visited[nr][nc]) {
                    // Check if the next cell connects back to the current cell
                    for (auto [br, bc] : directions[grid[nr][nc]]) {
                        if (nr + br == r && nc + bc == c) {
                            visited[nr][nc] = true;
                            q.push({nr, nc});
                            break;
                        }
                    }
                }
            }
        }
        
        return false;
    }
};

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