<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 hasValidPath(vector<vector<int>>& grid) {
        int rows = grid.size();
        int cols = grid[0].size();

        vector<vector<int>> adj_list(rows*cols, vector<int>());
        for (int r = 0; r < rows; r++) {
            for (int c = 0; c < cols; c++) {
                int node = (r*cols) + c;

                switch (grid[r][c]) {
                    case 6:
                    case 1:
                        if (c + 1 < cols && grid[r][c+1] % 2) {
                            // valid;
                            int next_node = (r * cols) + c + 1;
                            adj_list[node].push_back(next_node);
                            adj_list[next_node].push_back(node);
                        }
                        break;
                    case 2:
                    case 3:
                        if (r + 1 < rows && (grid[r+1][c] == 2 || grid[r+1][c] >= 5)) {
                                int next_node = ((r+1)* cols) + c;
                                adj_list[node].push_back(next_node);
                                adj_list[next_node].push_back(node);
                            }
                        break;
                    case 4:
                        if (c + 1 < cols && grid[r][c+1] % 2) {
                                // valid;
                                int next_node = (r * cols) + c + 1;
                                adj_list[node].push_back(next_node);
                                adj_list[next_node].push_back(node);
                            }
                        if (r + 1 < rows && (grid[r+1][c] == 2 || grid[r+1][c] >= 5)) {
                            int next_node = ((r+1)* cols) + c;
                            adj_list[node].push_back(next_node);
                            adj_list[next_node].push_back(node);
                        }
                        break;
                }

            }
        }


        queue<int> q;

        q.push(0);
        vector<bool> visited(rows*cols, false);
        while (q.size()) {
            int node = q.front(); q.pop();
            if (node == (rows * cols) - 1) return true;

            for (int neigh: adj_list[node]) {
                if (visited[neigh]) continue;
                visited[neigh] = true;
                q.push(neigh);
            }
        }
        return false;
    }
};
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