<p>You are given an <code>m x n</code> integer array <code>grid</code> where <code>grid[i][j]</code> could be:</p>

<ul>
	<li><code>1</code> representing the starting square. There is exactly one starting square.</li>
	<li><code>2</code> representing the ending square. There is exactly one ending square.</li>
	<li><code>0</code> representing empty squares we can walk over.</li>
	<li><code>-1</code> representing obstacles that we cannot walk over.</li>
</ul>

<p>Return <em>the number of 4-directional walks from the starting square to the ending square, that walk over every non-obstacle square exactly once</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/02/lc-unique1.jpg" style="width: 324px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[1,0,0,0],[0,0,0,0],[0,0,2,-1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> We have the following two paths: 
1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2)
2. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2)
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/02/lc-unique2.jpg" style="width: 324px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[1,0,0,0],[0,0,0,0],[0,0,0,2]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> We have the following four paths: 
1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2),(2,3)
2. (0,0),(0,1),(1,1),(1,0),(2,0),(2,1),(2,2),(1,2),(0,2),(0,3),(1,3),(2,3)
3. (0,0),(1,0),(2,0),(2,1),(2,2),(1,2),(1,1),(0,1),(0,2),(0,3),(1,3),(2,3)
4. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2),(2,3)
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/02/lc-unique3-.jpg" style="width: 164px; height: 165px;" />
<pre>
<strong>Input:</strong> grid = [[0,1],[2,0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no path that walks over every empty square exactly once.
Note that the starting and ending square can be anywhere in the grid.
</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;= 20</code></li>
	<li><code>1 &lt;= m * n &lt;= 20</code></li>
	<li><code>-1 &lt;= grid[i][j] &lt;= 2</code></li>
	<li>There is exactly one starting cell and one ending cell.</li>
</ul>

class Solution {
   inline int CalculateUniquePaths(
    const vector<vector<int>>& grid, 
    std::vector<vector<int>>visited, 
    int vsquares, 
    int req,
    int startrow,
    int startcol,
    int goalrow,
    int goalcol
    )
    {
        vsquares++;
        visited[startrow][startcol]=1;

        if(vsquares==req && startrow==goalrow && startcol==goalcol)
        {
            return 1;
        }
        if(startrow==goalrow && startcol==goalcol && vsquares < req)
        {;
            return 0;
        }
        int ans=0;
        if(startrow > 0 && grid[startrow-1][startcol] != -1 && !visited[startrow-1][startcol])
        {
            ans+=CalculateUniquePaths(grid,visited,vsquares,req,startrow-1, startcol,goalrow, goalcol);
        }
        if(startrow < grid.size()-1 && grid[startrow+1][startcol] != -1 && !visited[startrow+1][startcol])
        {
            ans+=CalculateUniquePaths(grid,visited,vsquares,req,startrow+1, startcol,goalrow, goalcol);
        }
        if(startcol > 0 && grid[startrow][startcol-1] != -1 && !visited[startrow][startcol-1])
        {
            ans+=CalculateUniquePaths(grid,visited,vsquares,req,startrow, startcol-1,goalrow, goalcol);
        }
        if(startcol < grid[0].size()-1 && grid[startrow][startcol+1] != -1 && !visited[startrow][startcol+1])
        {
            ans+=CalculateUniquePaths(grid,visited,vsquares,req,startrow, startcol+1,goalrow, goalcol);
        }

        return ans;
    }
public:
    int uniquePathsIII(vector<vector<int>>& grid) {

       int validsquares=0;
       int startrow=0;
       int startcol=0;
       int goalrow=0;
       int goalcol=0;
       std::vector<std::vector<int>>vgrid(grid.size(), std::vector<int>(grid[0].size(),0));
       for(int i=0; i<grid.size(); i++)
       {
        for(int j=0; j<grid[0].size(); j++)
        {
            if(grid[i][j]==1)
            {
                vgrid[i][j]=1;
                startcol=j;
                startrow=i;
                validsquares++;
            }
            else if(grid[i][j]==0)
            {
                validsquares++;
            }
            else if(grid[i][j]==2)
            {
                goalrow=i;
                goalcol=j;
                validsquares++;
            }
        }
       }
       return CalculateUniquePaths(grid, vgrid, 0, validsquares,startrow,startcol,goalrow,goalcol);


        
    }
};
29826