<p>In a gold mine <code>grid</code> of size <code>m x n</code>, each cell in this mine has an integer representing the amount of gold in that cell, <code>0</code> if it is empty.</p>

<p>Return the maximum amount of gold you can collect under the conditions:</p>

<ul>
	<li>Every time you are located in a cell you will collect all the gold in that cell.</li>
	<li>From your position, you can walk one step to the left, right, up, or down.</li>
	<li>You can&#39;t visit the same cell more than once.</li>
	<li>Never visit a cell with <code>0</code> gold.</li>
	<li>You can start and stop collecting gold from <strong>any </strong>position in the grid that has some gold.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> grid = [[0,6,0],[5,8,7],[0,9,0]]
<strong>Output:</strong> 24
<strong>Explanation:</strong>
[[0,6,0],
 [5,8,7],
 [0,9,0]]
Path to get the maximum gold, 9 -&gt; 8 -&gt; 7.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,0,7],[2,0,6],[3,4,5],[0,3,0],[9,0,20]]
<strong>Output:</strong> 28
<strong>Explanation:</strong>
[[1,0,7],
 [2,0,6],
 [3,4,5],
 [0,3,0],
 [9,0,20]]
Path to get the maximum gold, 1 -&gt; 2 -&gt; 3 -&gt; 4 -&gt; 5 -&gt; 6 -&gt; 7.
</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;= 15</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 100</code></li>
	<li>There are at most <strong>25 </strong>cells containing gold.</li>
</ul>

class Solution {
    vector<int>delrow = {0 , 0 , 1 , -1};
    vector<int>delcol = {1 , -1 , 0 , 0};
public:
    int getMaximumGold(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        int res = 0;
        vector<vector<bool>> vis(m , vector<bool>(n , false));
        for(int i=0 ; i<m ; i++){
            for(int j=0 ; j<n ; j++){
                if(grid[i][j]!=0){
                    res = max(res , dfs(i , j , m , n , vis , grid));
                }
            }
        } 
        return res;
    }
    int dfs(int row , int col , int& m , int& n , vector<vector<bool>> &vis , vector<vector<int>> &grid){
        if(!isValid(row , col , m , n , vis , grid)) return 0;
        vis[row][col] = true;
        int ans = 0;
        for(int i=0 ; i<4 ; i++){
            int x = row + delrow[i];
            int y = col + delcol[i];
            ans = max(ans , dfs(x , y , m , n , vis , grid));
        }
        vis[row][col] = false;
        return ans + grid[row][col];
    }
    bool isValid(int& row , int& col , int& m , int& n , vector<vector<bool>> &vis , vector<vector<int>> &grid){
        return row>=0 && row<m && col>=0 && col<n && !vis[row][col] && grid[row][col]!=0;
    }
};
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