<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) {
        unordered_map<int, vector<int>>mymap;
        vector<unordered_set<int>>vdir = {{2,3,4}, {1,3,5}, {2,5,6},{1,4,6}};
        mymap[1] = {0, 1, 0, 1};
        mymap[2] = {1, 0, 1, 0};
        mymap[3] = {0, 0, 1, 1};
        mymap[4] = {0, 1, 1, 0};
        mymap[5] = {1, 0, 0, 1};
        mymap[6] = {1, 1, 0, 0};
        vector<vector<int>>dirs = {{-1, 0}, {0, 1}, {1, 0}, {0, -1}};
        int m = grid.size(); int n = grid[0].size();
        unordered_set<int>vis;
        queue<int>myq;
        myq.push(0); vis.insert(0);
        while (!myq.empty()){
            int cur = myq.front(); myq.pop();
            int x = cur / n; int y = cur % n;
            if (x == m - 1 && y == n - 1){return 1;}
            for (int i = 0; i < 4; i++){
                if(mymap[grid[x][y]][i] == 0){continue;}
                int px = x + dirs[i][0];
                int py = y + dirs[i][1];
                if (px < 0 || py < 0 || px >= m || py >= n){continue;}
                if (!vdir[i].count(grid[px][py]) || vis.count(px*n+py)){continue;}
                vis.insert(px*n+py);
                myq.push(px*n+py);
            }
        }
        return 0;
    }
};
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