<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 {
    bool isValid(const vector<vector<int>>& grid, int row, int col, vector<vector<int>>& visited){
        if( row < 0 || row >= grid.size() || col < 0 || col >= grid[0].size() || visited[row][col] == 1) return false;
        return true;
    }

    void pathCheck(int row, int col, vector<vector<int>>& grid, vector<vector<int>>& visited){
        // if(visited[row][col] == 1 || row < 0 ||
        // row >= grid.size() || col < 0 || col >= grid[0].size()) return;
        
        int n = grid.size();
        int m = grid[0].size();

        visited[row][col] = 1;
        int up = 0, down = 0, left = 0, right = 0;
        if(grid[row][col] == 1){
            if(col+1 < m && (grid[row][col+1] == 1 || grid[row][col+1] == 3 || grid[row][col+1] == 5))
             right = 1;
            if(col-1 >= 0 && (grid[row][col-1] == 1 || grid[row][col-1] == 4 || grid[row][col-1] == 6))
             left = 1;
        } 
        else if(grid[row][col] == 2){
            if(row-1 >= 0 && (grid[row-1][col] == 2 || grid[row-1][col] == 3 || grid[row-1][col] == 4))
             up = 1;
            if(row+1 < n && (grid[row+1][col] == 2 || grid[row+1][col] == 5 || grid[row+1][col] == 6))
             down = 1;
        }
        else if(grid[row][col] == 3){
            if(col-1 >= 0 && (grid[row][col-1] == 1 || grid[row][col-1] == 4 || grid[row][col-1] == 6))
             left = 1;
            if(row+1 < n && (grid[row+1][col] == 2 || grid[row+1][col] == 5 || grid[row+1][col] == 6))
             down = 1;
        }
        else if(grid[row][col] == 4){
            if(col+1 < m && (grid[row][col+1] == 1 || grid[row][col+1] == 3 || grid[row][col+1] == 5))
             right = 1;
            if(row+1 < n && (grid[row+1][col] == 2 || grid[row+1][col] == 5 || grid[row+1][col] == 6))
             down = 1; 
        }
        else if(grid[row][col] == 5){
            if(col-1 >= 0 && (grid[row][col-1] == 1 || grid[row][col-1] == 4 || grid[row][col-1] == 6))
             left = 1;
            if(row-1 >= 0 && (grid[row-1][col] == 2 || grid[row-1][col] == 3 || grid[row-1][col] == 4))
             up = 1;
            
        }
        else{
            if(row-1 >= 0 && (grid[row-1][col] == 2 || grid[row-1][col] == 3 || grid[row-1][col] == 4))
             up = 1;
            if(col+1 < m && (grid[row][col+1] == 1 || grid[row][col+1] == 3 || grid[row][col+1] == 5))
             right = 1;
            
        }

        cout <<row<<","<<col<<"   ";
        
        ///----up--
        if(up && isValid(grid, row-1, col, visited)) pathCheck(row-1, col, grid, visited);
        
        //----left---
        if(left && isValid(grid, row, col-1, visited)) pathCheck(row, col-1, grid, visited);

        //--------right---
        if(right && isValid(grid, row, col+1, visited)) pathCheck(row, col+1, grid, visited);

        //---bottom--
        if(down && isValid(grid, row+1, col, visited)) pathCheck(row+1, col, grid, visited);

    }
public:
    bool hasValidPath(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        vector<vector<int>> visited(n, vector<int>(m, 0));
        pathCheck(0, 0, grid, visited);
        return visited[n-1][m-1];
    }
};
74289