<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 {
public:
    int dfs(int x,int y,int m,int n,vector<vector<int>> gr,vector<vector<int>> &vis,int s){
        if(gr[x][y]==2&&s==0){
            return 1;
        }int l=0,r=0,u=0,d=0;
        if(x+1<m&&gr[x+1][y]!=-1&&vis[x+1][y]==-2){
            vis[x][y]=1;
            d=dfs(x+1,y,m,n,gr,vis,s-1);
            vis[x][y]=-2;
        }
        if(y+1<n&&gr[x][y+1]!=-1&&vis[x][y+1]==-2){
            vis[x][y]=1;
            l=dfs(x,y+1,m,n,gr,vis,s-1);
            vis[x][y]=-2;
        }
        if(x-1>=0&&gr[x-1][y]!=-1&&vis[x-1][y]==-2){
            vis[x][y]=1;
            u=dfs(x-1,y,m,n,gr,vis,s-1);
            vis[x][y]=-2;
        }
        if(y-1>=0&&gr[x][y-1]!=-1&&vis[x][y-1]==-2){
            vis[x][y]=1;
            r=dfs(x,y-1,m,n,gr,vis,s-1);
            vis[x][y]=-2;
        }
        return l+r+u+d;
    }
    int uniquePathsIII(vector<vector<int>>& grid) {
      int m=grid.size();
      int n=grid[0].size();
      int x,y;
      vector<vector<int>> vis(m,vector<int>(n,-2));
      int cnt=0;
      for(int i=0;i<m;i++){
        for(int j=0;j<n;j++){
            if(grid[i][j]==1){
                x=i;
                y=j;
            }if(grid[i][j]==-1){cnt++;}
        }
      }
      int ans=dfs(x,y,m,n,grid,vis,m*n-cnt-1);
      return ans;
    }
};
40228