<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 {
    const bool tryLeft(const vector<vector<int>>& grid, vector<vector<bool>>& visited, const int r, const int c)
    {
        if(c > 0 && visited[r][c-1] == false && 
            (grid[r][c-1] == 1 || grid[r][c-1] == 4 || grid[r][c-1] == 6))
        {
            if(bt(grid,visited,r,c-1))
                return true;
        }

        return false;
    }

    const bool tryRight(const vector<vector<int>>& grid, vector<vector<bool>>& visited, const int r, const int c)
    {
        if(c != grid[0].size()-1 && visited[r][c+1] == false && 
            (grid[r][c+1] == 1 || grid[r][c+1] == 3 || grid[r][c+1] == 5))
        {
            if(bt(grid,visited,r,c+1))
                return true;
        }

        return false;
    }

    const bool tryTop(const vector<vector<int>>& grid, vector<vector<bool>>& visited, const int r, const int c)
    {
        if(r > 0 && visited[r-1][c] == false && 
            (grid[r-1][c] == 2 || grid[r-1][c] == 3 || grid[r-1][c] == 4))
        {
            if(bt(grid,visited,r-1,c))
                return true;
        }

        return false;
    }

    const bool tryBtm(const vector<vector<int>>& grid, vector<vector<bool>>& visited, const int r, const int c)
    {
        if(r != grid.size()-1 && visited[r+1][c] == false && 
            (grid[r+1][c] == 2 || grid[r+1][c] == 5 || grid[r+1][c] == 6))
        {
            if(bt(grid,visited,r+1,c))
                return true;
        }

        return false;
    }
    const bool bt(const vector<vector<int>>& grid, vector<vector<bool>>& visited, const int r, const int c)
    {
        if(visited[r][c])
            return false;

        visited[r][c] = true;

        if(r == grid.size() - 1 && c == grid[0].size() - 1)
            return true;

        switch(grid[r][c])
        {
            case 1:
            {
                if(tryLeft(grid,visited,r,c) || tryRight(grid,visited,r,c))
                    return true;
            }
            break;
            case 2:
            {
                if(tryTop(grid,visited,r,c) || tryBtm(grid,visited,r,c))
                    return true;
            }
            break;
            case 3:
            {
                if(tryLeft(grid,visited,r,c) || tryBtm(grid,visited,r,c))
                    return true;
            }
            break;
            case 4:
            {
                if(tryRight(grid,visited,r,c) || tryBtm(grid,visited,r,c))
                    return true;
            }
            break;
            case 5:
            {
                if(tryLeft(grid,visited,r,c) || tryTop(grid,visited,r,c))
                    return true;
            }
            break;
            case 6:
            {
                if(tryRight(grid,visited,r,c) || tryTop(grid,visited,r,c))
                    return true;
            }
            break;
        }
        
        return false;
    }
public:
    bool hasValidPath(vector<vector<int>>& grid) {
        const int rSize = grid.size();
        const int cSize = grid[0].size();
        vector<vector<bool>> visited(rSize,vector<bool>(cSize));
        return bt(grid,visited,0,0);
    }
};
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