<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>

# simulation
# TC: O(m * n)
# SC: O(m * n)
class Solution:
    def hasValidPath(self, grid: List[List[int]]) -> bool:
        m = len(grid)
        n = len(grid[0])

        street = [[0] * (n * 3) for _ in range(m * 3)]
        # 把每个点变成3x3的地图
        for i in range(0, m):
            for j in range(0, n):
                idx_i = i * 3
                idx_j = j * 3
                if grid[i][j] == 1:
                    street[idx_i + 1][idx_j] = 1
                    street[idx_i + 1][idx_j + 1] = 1
                    street[idx_i + 1][idx_j + 2] = 1
                elif grid[i][j] == 2:
                    street[idx_i][idx_j + 1] = 1
                    street[idx_i + 1][idx_j + 1] = 1
                    street[idx_i + 2][idx_j + 1] = 1
                elif grid[i][j] == 3:
                    street[idx_i + 1][idx_j] = 1
                    street[idx_i + 1][idx_j + 1] = 1
                    street[idx_i + 2][idx_j + 1] = 1
                elif grid[i][j] == 4:
                    street[idx_i + 1][idx_j + 1] = 1
                    street[idx_i + 1][idx_j + 2] = 1
                    street[idx_i + 2][idx_j + 1] = 1
                elif grid[i][j] == 5:
                    street[idx_i][idx_j + 1] = 1
                    street[idx_i + 1][idx_j] = 1
                    street[idx_i + 1][idx_j + 1] = 1
                else:
                    street[idx_i][idx_j + 1] = 1
                    street[idx_i + 1][idx_j + 1] = 1
                    street[idx_i + 1][idx_j + 2] = 1
        
        # street built
        # next step
        # check if there is a path from top-left to bottom-right
        start_points = [(0, 1), (1, 0), (1, 1), (1, 2), (2, 1)]
        row = (m - 1) * 3
        col = (n - 1) * 3
        end_points = [(row, col + 1), (row + 1, col), (row + 1, col + 1), (row + 1, col + 2), (row + 2, col + 1)]

        # print(start_points)
        # print(end_points)
        
        for x, y in start_points:
            # 四个方向
            # 哪个方向是1 就往哪个方向走 
            # 经过一个点 就把拿个点在street上set为0
            
            while street[x][y]:
                if (x, y) in end_points:
                    return True
                street[x][y] = 0
                # check left
                if (y > 0 and street[x][y - 1] == 1):
                    y = y - 1
                # check right
                elif (y < n * 3 - 1 and street[x][y + 1] == 1):
                    y = y + 1
                # check up
                elif (x > 0 and street[x - 1][y] == 1):
                    x = x - 1
                # check down
                elif (x < m * 3 - 1 and street[x + 1][y] == 1):
                    x = x + 1
        return False

"""
[[0, 0, 0, 0, 0, 0, 0, 0, 0],
 [0, 1, 1, 0, 1, 1, 1, 1, 0],
 [0, 1, 0, 0, 1, 0, 0, 1, 0], 
 [0, 1, 0, 0, 1, 0, 0, 1, 0], 
 [0, 1, 1, 1, 1, 0, 0, 1, 0], 
 [0, 0, 0, 0, 0, 0, 0, 1, 0]]

"""
24218