<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:
    def hasValidPath(self, grid: List[List[int]]) -> bool:
        if not grid:
            return False

        rows = len(grid)
        cols = len(grid[0])

        def connnectingStreets(row, col):
            match grid[row][col]:
                case 1: # 1 left and right
                    return [(row, col - 1), (row, col + 1)]
                case 2: # 2 up and down
                    return [(row - 1, col), (row + 1, col)]       
                case 3: # 3 left and down
                    return [(row, col - 1), (row + 1, col)]            
                case 4: # 4 right and down
                    return [(row, col + 1), (row + 1, col)]
                case 5: # 5 up and left
                    return [(row - 1, col), (row, col - 1)]   
                case 6: # 6 up and right
                    return [(row - 1, col), (row, col + 1)]

        # loop through streets in grid, populate adjList based on street
        adjList = defaultdict(set)

        for i, row in enumerate(grid):
            for j, col in enumerate(row):
                potentialConnections = connnectingStreets(i, j)
                for potentialConnection in potentialConnections:
                    if 0 <= potentialConnection[0] <= rows - 1 and 0 <= potentialConnection[1] <= cols - 1:
                        adjList[(i, j)].add(potentialConnection)

        # adjList = {
        #     (0,0): [1,0]
        #     (0,1): [1,1],[0,2]
        #     (0,2): [0,1],[1,2]
        #     (1,0): [0,0],[1,1]
        #     (1,1): [1,0],[0,1]
        #     (1,2): [0,2]
        # }

        #perform dfs on adjList using stack

        stack = [(0,0)]
        visited = set()

        while stack:
            node = stack.pop()

            if node == (rows - 1, cols - 1):
                return True

            for nextNode in adjList[node]:
                print(nextNode)
                if nextNode not in visited and node in adjList[nextNode]:
                    stack.append(nextNode)
            
            visited.add(node)

        return False



            




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