<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>

class Solution {
public:
    bool hasValidPath(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();

        bool vis[m][n];
        memset(vis, false, sizeof(vis));

        int dx[] = {1, 0, -1, 0};
        int dy[] = {0, 1, 0, -1};
        bool ar[6][4] = {
            {0, 1, 0, 1},
            {1, 0, 1, 0},
            {1, 0, 0, 1},
            {1, 1, 0, 0},
            {0, 0, 1, 1},
            {0, 1, 1, 0}
        };

        queue<pair<int, int>> Q;
        Q.emplace(0, 0);
        vis[0][0] = true;
        while (!Q.empty()) {
            auto now = Q.front();
            int r = now.first, c = now.second;
            int val = grid[r][c];
            Q.pop();
            for (int i = 0; i < 4; i++) {
                if (!ar[val - 1][i]) continue;
                int nr = r + dx[i], nc = c + dy[i];
                if (nr < 0 || nr >= m || nc < 0 || nc >= n) continue;
                if (vis[nr][nc]) continue;
                if (!ar[grid[nr][nc] - 1][(i + 2) % 4]) continue;
                vis[nr][nc] = true;
                Q.emplace(nr, nc);
            }
        }
        return vis[m - 1][n - 1];
    }
};
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