<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:
    vector<int>row={-1,0,0,+1};
    vector<int>col={0,-1,+1,0};

    int solvemem(int i,int j,int ex,int ey,int cnt,int &sum,int n,int m,vector<vector<int>>&grid,vector<vector<int>>vis){
        if(i==ex && j==ey && cnt==sum) return 1;

        // if(vis[i][j]!=-1) return vis[i][j];

        int ans=0;
        for(int k=0;k<4;k++){
            int nrow=i+row[k];
            int ncol=j+col[k];

            if(nrow>=0 && ncol>=0 && nrow<n && ncol<m && grid[nrow][ncol]!=-1 && vis[nrow][ncol]==-1){
                vis[nrow][ncol]=1;
                ans+=solvemem(nrow,ncol,ex,ey,cnt+1,sum,n,m,grid,vis);
                vis[nrow][ncol]=-1;
            }   
        }

        return ans;
    }

    int uniquePathsIII(vector<vector<int>>& grid) {
        int sx,sy,ex,ey;
        int n=grid.size();
        int m=grid[0].size();

        int cnt=2;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1){
                    sx=i;
                    sy=j;
                }else if(grid[i][j]==2){
                    ex=i;
                    ey=j;
                }else if(grid[i][j]==0) cnt++;
            }
        }

        vector<vector<int>>vis(n+1,vector<int>(m+1,-1));
        vis[sx][sy]=1;
        int ans=solvemem(sx,sy,ex,ey,1,cnt,n,m,grid,vis);

        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                cout<<vis[i][j]<<" ";
            }
            cout<<endl;
        }
        cout<<endl;

        return ans;
    }
};
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