<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 {
public:
    int getMaximumGold(vector<vector<int>>& grid)
    {
        stack<tuple<int, int, int, int>> *stk;
        stack<pair<int, int>> *vstd;
        int dirs[4][2] = { { -1,  0 }, {  0,  1 },
                           {  1,  0 }, {  0, -1 } };
        int d, i, j, k, l, m, n, r, s, t, u, v;
        bool * *g;

        m = grid.size();
        n = grid[0].size();
        g = new bool *[m];
        for (i = 0; i < m; i++) {
            g[i] = new bool[n];
            std::fill(&g[i][0], &g[i][n], false);
        }
        stk = new stack<tuple<int, int, int, int>>();
        vstd = new stack<pair<int, int>>();
        for (i = 0; i < m; i++)
            for (j = 0; j < n; j++)
                if (grid[i][j] > 0)
                    stk->push({ i, j, 0, grid[i][j] });
        r = 0;
        while (!stk->empty()) {
            tie(i, j, l, s) = stk->top();
            while (vstd->size() > l) {
                tie(u, v) = vstd->top();
                vstd->pop();
                g[u][v] = false;
            }
            stk->pop();
            vstd->push({ i, j });
            g[i][j] = true;
            t = stk->size();
            for (k = 0; k < 4; k++) {
                u = dirs[k][0] + i;
                v = dirs[k][1] + j;
                if (u >= 0 && u < m && v >= 0 && v < n &&
                    grid[u][v] > 0 && !g[u][v]) {
                    stk->push({ u, v, vstd->size(), s + grid[u][v]});
                }
            }
            if (stk->size() == t) {
                g[i][j] = false;
                if (r < s)
                    r = s;
            }
        }
        delete vstd;
        delete stk;
        for (i = 0; i < m; i++)
            delete[] g[i];
        delete[] g;

        return r;
    }
};
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