<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 {
    int m, n;

public:
    bool hasValidPath(vector<vector<int>>& grid) {
        m = grid.size(), n = grid[0].size();
        std::vector<std::vector<bool>> visited(m, std::vector<bool>(n, false));
        return dfs(0, 0, grid, visited);
    }
    bool dfs(int curr_x, int curr_y, std::vector<std::vector<int>> const& grid,
             std::vector<std::vector<bool>>& visited) {
        std::cout << curr_x << ' ' << curr_y << std::endl;
        if (curr_x == m - 1 && curr_y == n - 1) {
            return true;
        }
        visited[curr_x][curr_y] = true;
        std::vector<std::array<int, 2>> dirs = {
            {-1, 0}, {1, 0}, {0, -1}, {0, 1}};
        auto const canVisit = [](int src, int dst, int dx, int dy) -> bool {
            if (src == 1) {
                if (dx != 0 || dst == 2) {
                    return false;
                }
                if (dx == 1 && (dst == 4 || dst == 6)) {
                    return false;
                }
                if (dx == -1 && (dst == 3 || dst == 5)) {
                    return false;
                }
            } else if (src == 2) {
                if (dy != 0 || dst == 1) {
                    return false;
                }
                if (dx == 1 && (dst == 3 || dst == 4)) {
                    return false;
                }
                if (dx == -1 && (dst == 5 || dst == 6)) {
                    return false;
                }
            } else if (src == 3) {
                if (dx == -1 || dy == 1) {
                    return false;
                }
                if (dx == 1 && (dst == 1 || dst == 4)) {
                    return false;
                }
                if (dy == -1 && (dst == 2 || dst == 5)) {
                    return false;
                }
            } else if (src == 4) {
                if (dx == -1 || dy == -1) {
                    return false;
                }
                if (dx == 1 && (dst == 1 || dst == 3)) {
                    return false;
                }
                if (dy == 1 && (dst == 2 || dst == 6)) {
                    return false;
                }
            } else if (src == 5) {
                if (dx == 1 || dy == 1) {
                    return false;
                }
                if (dx == -1 && (dst == 1 || dst == 6)) {
                    return false;
                }
                if (dy == -1 && (dst == 2 || dst == 3)) {
                    return false;
                }
            } else {
                if (dx == 1 || dy == -1) {
                    return false;
                }
                if (dx == -1 && (dst == 1 || dst == 5)) {
                    return false;
                }
                if (dy == 1 && (dst == 2 || dst == 4)) {
                    return false;
                }
            }
            return true;
        };
        auto const isInside = [&](int x, int y) -> bool {
            return 0 <= x && x < m && 0 <= y && y < n;
        };
        for (auto [dx, dy] : dirs) {
            auto x = curr_x + dx;
            auto y = curr_y + dy;
            if (isInside(x, y) && !visited[x][y] &&
                canVisit(grid[curr_x][curr_y], grid[x][y], dx, dy) &&
                dfs(x, y, grid, visited)) {
                return true;
            }
        }
        return false;
    }
};
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