title: Finding the maximum-sum sub=rectangle within a matrix
body: <blockquote>
    <p><strong>Possible Duplicate:</strong><br>
    <a href="https://stackoverflow.com/questions/2643908/getting-the-submatrix-with-maximum-sum">Getting the submatrix with maximum sum?</a>  </p>
  </blockquote>
  
  
  
  <p>Given a 2-dimensional array of positive and negative integers, find the sub-rectangle with the largest sum. The sum of a rectangle is the sum of all the elements in that rectangle. In this problem the sub-rectangle with the largest sum is referred to as the maximal sub-rectangle. A sub-rectangle is any contiguous sub-array of size 1*1 or greater located within the whole array. As an example, the maximal sub-rectangle of the array:</p>
  
  <pre><code> 0 -2 -7  0
   9  2 -6  2
  -4  1 -4  1
  -1  8  0 -2
  </code></pre>
  
  <p>is in the lower-left-hand corner:</p>
  
  <pre><code> 9  2
  -4  1
  -1  8
  </code></pre>
  
  <p>and has the sum of 15. </p>
  
  <p>So given a rectangle, what will be an efficient algorithm to find the sum of the maximal sub-rectangle (15 in the above example).</p>