<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:
    int n,m;
    vector<vector<bool>>vis;
    bool hasValidPath(vector<vector<int>>& grid) 
    {
        n = grid.size();
        m = grid[0].size();
        int row = 0;
        int col = 0;
        vis.resize(grid.size(),vector<bool>(grid[0].size(),false));
        return fun(grid,row,col,n,m);    
    }
    bool fun(vector<vector<int>>&grid,int row,int col,int &n,int &m)
    {
         cout<<"row = "<<row<<" "<<"col = "<<col<<endl;
         if(row == (n-1) and col == (m-1))
         {
             cout<<"hello"<<endl;
             return true;   //condition has fullfilled
         }

         if(row < 0 or row >= n or col < 0 or col >= m)
         {
              return false;  //out of bound condition
         }
        
         int nextrow  = -1;
         int nextcol = -1;

         int num = grid[row][col];
         if(num == 1)    //can move in the left or in the right
         {
             bool a = false;
             bool b = false;
             
             vis[row][col] = true;

             if(isValid(row,col-1) == true and vis[row][col-1] == false and (grid[row][col-1] == 4 or grid[row][col-1] == 6 or grid[row][col-1] == 1))  //4 6 
             a = fun(grid,row,col-1,n,m);   //moving left side

             if(a == true) return true;

             if(isValid(row,col+1) == true and vis[row][col+1] == false and (grid[row][col+1] == 3 or grid[row][col+1] == 5  or grid[row][col+1] == 1)) // 3 5
             b = fun(grid,row,col+1,n,m);   //moving the right side

             vis[row][col] = false;

             if(a == true or b == true)
             return true;
         }

         if(num == 2)    //can move in the left or in the right
         {
             bool a = false;
             bool b = false;

             vis[row][col] = true;

             if(isValid(row-1,col) == true and vis[row-1][col] == false and (grid[row-1][col] == 3 or grid[row-1][col] == 4 or grid[row-1][col] == 2)) // 3 4
             a = fun(grid,row-1,col,n,m);   //moving the upper side

             if(a == true) return true;

             if(isValid(row+1,col) == true and vis[row+1][col] == false and (grid[row+1][col] == 5 or grid[row+1][col] == 6 or grid[row+1][col] == 2))  //5 6
             b = fun(grid,row+1,col,n,m);   //moving the lower side

             vis[row][col] = false;

             if(a == true or b == true)
             return true;
         }

         if(num == 3)    //can move in the left or in the right
         {
             bool a = false;
             bool b = false;
            
             vis[row][col] = true;

             if(isValid(row,col-1) == true and vis[row][col-1] == false and (grid[row][col-1]==1 or grid[row][col-1] == 4 or grid[row][col-1] == 6 or grid[row][col-1] == 3))  //1 4 6
             a = fun(grid,row,col-1,n,m);   //moving left side

             if(a == true) return true;

             if(isValid(row+1,col) == true and vis[row+1][col] == false and (grid[row+1][col] == 2 or grid[row+1][col] == 5 or grid[row+1][col] == 6))  //2 5 6
             b = fun(grid,row+1,col,n,m);   //moving the lower side

             vis[row][col] = false;

             if(a == true or b == true)
             return true;
         }

         if(num == 4)    //can move in the left or in the right
         {
             bool a = false;
             bool b = false;
             

             vis[row][col] = true;

             if(isValid(row,col+1) == true and vis[row][col+1] == false and (grid[row][col+1] == 1 or grid[row][col+1] == 3 or grid[row][col+1] == 5 or grid[row][col+1] == 4))  //1 3 5
             a = fun(grid,row,col+1,n,m);   //moving right side

             if(a == true) return true;

             if(isValid(row+1,col) == true and vis[row+1][col] == false and (grid[row+1][col] == 2 or grid[row+1][col] == 5 or grid[row+1][col] == 6)) // 2 5 6
             b = fun(grid,row+1,col,n,m);   //moving the lower side

             vis[row][col] = false;

             if(a == true or b == true)
             return true;
         }
         
         if(num == 5)    //can move in the left or in the right
         {
             bool a = false;
             bool b = false;
 
             vis[row][col] = true;

             if(isValid(row,col-1) == true and vis[row][col-1] == false and (grid[row][col-1] == 1 or grid[row][col-1] == 4 or grid[row][col-1] == 6)) // 1 4 6
             a = fun(grid,row,col-1,n,m);   //moving left side

             if(a == true) return true;

             if(isValid(row-1,col) == true and vis[row-1][col] == false and (grid[row-1][col]==2 or grid[row-1][col] == 3 or grid[row-1][col] == 4)) // 2 3 4
             b = fun(grid,row-1,col,n,m);    //moving the upper cell

             vis[row][col] = false;

             if(a == true or b == true)
             return true;
         }

         if(num == 6)    //can move in the left or in the right
         {
             bool a = false;
             bool b = false;

              vis[row][col] = true;

              if(isValid(row,col+1) == true and vis[row][col+1] == false and (grid[row][col+1] == 1 or grid[row][col+1] == 3 or grid[row][col+1] == 5)) //1 3 5
              a = fun(grid,row,col+1,n,m);   //moving right side

              if(a == true) return true;

              if(isValid(row-1,col) == true and vis[row-1][col] == false and (grid[row-1][col] == 2 or grid[row-1][col] == 3 or grid[row-1][col] == 4)) //2 3 4
              b = fun(grid,row-1,col,n,m);   //moving the upper cell

              vis[row][col] = false;

             if(a == true or b == true)
             return true;
         }
         
         return false;
    }
    bool isValid(int row,int col)
    {
        if(row < 0 or row >= n or col < 0 or col >= m)
        return false;

        return true;
    }
};
118400