<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 check_next(int i, int k, vector<vector<int>>& grid, vector<vector<bool>>& old_street, int dir) {
        if (i > grid.size()-1 || k > grid[0].size()-1) return false;
        if (i < 0 || k < 0) return false;
        
        int cur = grid[i][k];
        switch (dir) {          //check if transition was valid 1: from top, 2: from right...
            case 1:
                if (cur == 1 || cur == 3 || cur == 4) return false;
                break;
            case 2:
                if (cur == 2 || cur == 3 || cur == 5) return false;
                break;
            case 3:
                if (cur == 1 || cur >= 5) return false;
                break;
            case 4:
                if (cur % 2 == 0) return false;
                break;
            default :
        }

        // cout << old_street[0][2];
        // cout << old_street[0][1];
        // cout << "Ich bin hier: i = " << i << ", k = " << k << endl;
        if (old_street[i][k]) return false;
        old_street[i][k] = true;
        if (i == grid.size()-1 && k == grid[0].size() -1) return true;


        switch(cur) {
            case 1:
                return (check_next(i, k+1, grid, old_street, 4) || check_next(i, k-1, grid, old_street, 2));
                break;
            case 2:
                return (check_next(i-1, k, grid, old_street, 3) || check_next(i+1, k, grid, old_street, 1));
                break;
            case 3:
                return( check_next(i, k-1, grid, old_street, 2) || check_next(i+1, k, grid, old_street, 1));
                break;
            case 4:
                return (check_next(i, k+1, grid, old_street, 4) || check_next(i+1, k, grid, old_street, 1));
                break;
            case 5:
                return (check_next(i-1, k, grid, old_street, 3) || check_next(i, k-1, grid, old_street, 2));
                break;
            case 6:
                return (check_next(i-1, k, grid, old_street, 3) || check_next(i, k+1, grid, old_street, 4));
                break;
        }

        return true;
    }

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

        vector<vector<bool>> old_street (m, (vector<bool> (n,false)));    
        
        return check_next(0, 0, grid, old_street, 0);
    }
};
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