path-with-maximum-gold.md

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

<p>Return the maximum amount of gold you&nbsp;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&nbsp;<code>0</code> gold.</li>
	<li>You can start and stop collecting gold from&nbsp;<strong>any </strong>position in the grid that has some gold.</li>
</ul>

<p>&nbsp;</p>
<p><strong>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>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>1 &lt;= grid.length,&nbsp;grid[i].length &lt;= 15</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 100</code></li>
	<li>There are at most <strong>25&nbsp;</strong>cells containing gold.</li>
</ul>