<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 <unordered_map>
#include <queue>

class Solution {
public:
    std::unordered_map<int, std::vector<std::vector<int>>> roads = {
        {1, {{0, 1}, {0, -1}}},
        {2, {{-1, 0}, {1, 0}}},
        {3, {{0, -1}, {1, 0}}},
        {4, {{1, 0}, {0, 1}}},
        {5, {{0, -1}, {-1, 0}}},
        {6, {{0, 1}, {-1, 0}}},
    };

    bool hasValidPath(std::vector<std::vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        std::queue<std::pair<int, int>> q;
        q.push({0, 0});
        std::vector<std::vector<bool>> visited(m, std::vector<bool>(n, false));
        visited[0][0] = true;

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

            if (r == m - 1 && c == n - 1) {
                return true;
            }

            for (const auto& dir : roads[grid[r][c]]) {
                int nr = r + dir[0];
                int nc = c + dir[1];

                if (nr >= 0 && nr < m && nc >= 0 && nc < n && !visited[nr][nc]) {
                    for (const auto& backDir : roads[grid[nr][nc]]) {
                        if (nr + backDir[0] == r && nc + backDir[1] == c) {
                            visited[nr][nc] = true;
                            q.push({nr, nc});
                            break;
                        }
                    }
                }
            }
        }

        return false;
    }
};
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