<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 solve(int i, int j, int m, int n, int &emptySquares, vector<vector<int>>& grid, unordered_set<int> &pushed, vector<vector<int>> &mp){
        if(grid[i][j]==2){
            return pushed.size()==emptySquares+1;
        }
        
        pushed.insert(mp[i][j]);
        int left = 0, right = 0 , up = 0 , down = 0;
        if(i-1>=0 && grid[i-1][j]!=-1 && pushed.find(mp[i-1][j])==pushed.end())
           up   = solve(i-1, j , m, n, emptySquares, grid, pushed, mp);
        if(i+1 <m && grid[i+1][j]!=-1 && pushed.find(mp[i+1][j])==pushed.end())
           down = solve(i+1, j , m, n, emptySquares, grid, pushed, mp);
        if(j-1>=0 && grid[i][j-1]!=-1 && pushed.find(mp[i][j-1])==pushed.end())
           left = solve(i, j-1 , m, n, emptySquares, grid, pushed, mp);
        if(j+1 <n && grid[i][j+1]!=-1 && pushed.find(mp[i][j+1])==pushed.end())
           right= solve(i, j+1 , m, n, emptySquares, grid, pushed, mp);

        
        pushed.erase(mp[i][j]);
        return left + right + up + down;   
        
    }
    
    int uniquePathsIII(vector<vector<int>>& grid) {
        unordered_set<int> pushed;
        
        int emptySquares = 0, m = grid.size(), n = grid[0].size(), count =0;
        vector<vector<int>> mp(m, vector<int> (n, 0));

        pair<int,int> start;
        for(int i = 0 ; i < m ; ++i){
            for(int j = 0 ; j < n ; ++j){
                if(grid[i][j]==0) emptySquares++;
                else if(grid[i][j]==1) start = {i,j};
                
                mp[i][j] = count++;
            }
        }
   
        return solve(start.first, start.second, m, n, emptySquares, grid, pushed, mp);
        
    }
};
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