<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:
    unordered_map<int,vector<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(vector<vector<int>>& grid) {
        vector<int>prev = {};
        return dfs(grid,0,0,prev);
    }

    bool dfs(vector<vector<int>>& grid, int r, int c, vector<int>& prev)
    {
        // check inbounds or if visited already
        if(r<0 || r>=grid.size() || c<0 || c>=grid[0].size() || grid[r][c]==-1)
            return false;
        vector<vector<int>> dirs = roads[grid[r][c]];
        // check if the current road can connect to the prev road
        if(!prev.empty())
        {
            bool connects = false;
            for(vector<int>& dir : dirs)
            {
                if(dir[0]==-prev[0] && dir[1]==-prev[1])
                {
                    connects = true;
                    break;
                }
            }
            if(!connects)
                return false;
        }
        // check if its m-1, n-1
        if(r==grid.size()-1 && c==grid[0].size()-1)
            return true;
        // search
        grid[r][c]=-1;
        bool res = false;
        for(vector<int>& dir : dirs)
        {
            res = dfs(grid,r+dir[0],c+dir[1],dir) || res;
        }
        return res;
    }
};
120034