<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:
    int W;
    int H;
    
    bool inbound_y(int pos_y) { return (0<=pos_y) && (pos_y < H); }
    bool inbound_x(int pos_x) { return (0<=pos_x) && (pos_x < W); }
    bool inbound( int pos_y, int pos_x) { return inbound_y(pos_y) && inbound_x(pos_x); }
    bool reachEnd(int pos_y, int pos_x) { return (pos_y == H-1) && (pos_x == W-1); }
    
    bool compat(vector<vector<int>>& g, int del_y, int del_x, int nxt_y, int nxt_x)
    {
        
        int ng_v = g[nxt_y][nxt_x];
        if(del_y == 1 && del_x == 0) // 1, 0-->2,5,6
            return ng_v==2 || ng_v == 5 || ng_v == 6; 
        else if(del_y == -1 && del_x == 0) //-1, 0-->2,3,4
            return ng_v==2 || ng_v == 3 || ng_v == 4;
        else if(del_y == 0 && del_x == 1) // 0, 1-->1,3,5
            return ng_v==1 || ng_v == 3 || ng_v == 5;
        else//if(del_y == 0 && del_x == -1) // 0,-1-->1,4,6
            return ng_v==1 || ng_v == 4 || ng_v == 6;
    }
    
    int getId(int y, int x) { return y*W+x; }
    void condi_q_push(queue<vector<int>>& q, vector<vector<int>>& visited, vector<vector<int>>& g, \
                      int cur_y, int cur_x, int del_y, int del_x)
    {
        int nxt_y = cur_y + del_y;
        int nxt_x = cur_x + del_x;
        if(inbound(nxt_y, nxt_x) && visited[nxt_y][nxt_x]==0 && compat(g, del_y, del_x, nxt_y, nxt_x))
            q.push({nxt_y,nxt_x});
    }
    
    bool hasValidPath(vector<vector<int>>& grid) 
    {
        int cur_y = 0;
        int cur_x = 0;
        H = grid.size();
        W = grid[0].size();
        
        queue<vector<int>> q;
        q.push({0,0});
        
        if(grid[0][0]==5) return false;
        vector<vector<int>> visited(H, vector<int>(W, 0));
        
        unordered_map<int, vector<vector<int>>> del;
        del[1] = {{0,-1}, {0,1}};
        del[2] = {{-1,0}, {1,0}};
        del[3] = {{0,-1}, {1,0}};
        del[4] = {{0, 1}, {1,0}};
        del[5] = {{0,-1}, {-1,0}};
        del[6] = {{0, 1}, {-1,0}};
        
        int del_y, del_x, gval;
        while(!q.empty())
        {
            vector<int> cur_pos = q.front();
            int cur_y = cur_pos[0];
            int cur_x = cur_pos[1];
            q.pop();
            
            visited[cur_y][cur_x]=1;
            if(reachEnd(cur_y, cur_x))
                return true;
            
            gval = grid[cur_y][cur_x];
        
            del_y = del[gval][0][0];
            del_x = del[gval][0][1];
            condi_q_push(q, visited, grid, cur_y, cur_x, del_y, del_x);
            
            del_y = del[gval][1][0];
            del_x = del[gval][1][1];
            condi_q_push(q, visited, grid, cur_y, cur_x, del_y, del_x);
            
            /*if(grid[cur_y][cur_x]==1)
            {
               condi_q_push(q, visited, cur_y  , cur_x-1);
               condi_q_push(q, visited, cur_y  , cur_x+1);
            }
            else if(grid[cur_y][cur_x]==2))
            {
               condi_q_push(q, visited, cur_y-1, cur_x  );
               condi_q_push(q, visited, cur_y+1, cur_x  );              
            }
            else if(grid[cur_y][cur_x]==3))
            {
               condi_q_push(q, visited, cur_y  , cur_x-1);
               condi_q_push(q, visited, cur_y+1, cur_x  );              
            }                      
            else if(grid[cur_y][cur_x]==4))
            {
               condi_q_push(q, visited, cur_y  , cur_x+1);
               condi_q_push(q, visited, cur_y+1, cur_x  );              
            }
            else if(grid[cur_y][cur_x]==5))
            {
               condi_q_push(q, visited, cur_y  , cur_x-1);
               condi_q_push(q, visited, cur_y-1, cur_x  );              
            }
            else if(grid[cur_y][cur_x]==6))
            {
               condi_q_push(q, visited, cur_y  , cur_x+1);
               condi_q_push(q, visited, cur_y-1, cur_x  );              
            }*/
        }
        return false;
    }
};
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