Facebook Interview Question: Suppose you have a matrix of ... | Glassdoor

Interview Question

Machine Learning Software Engineer Interview Palo Alto, CA

Suppose you have a matrix of numbers. How can you easily

  compute the sum of any rectangle (i.e. a range [row_start, row_end, col_start, col_end]) of those numbers? How would you code this?
algorithm, code

Interview Answer

8 Answers


It can be done in constant time by precalculating sums of some basic rectangles (extending all the way to the border of the matrix). That precalculation times time O(n) by simple dynamic programming.

Interview Candidate on Jan 21, 2010

Please elaborate, which "basic rectangles"? Are you recursively dividing each rectangle into 4 smaller rectangles? Precalc time for doing that is not O(n)?!?

maxzed2k on Feb 10, 2010

Compute the sum of the rectangles, for all i,j, bounded by (i,j), (i,m), (n,j), (n,m), where (n,m) is the size of the matrix M. Call that sum s(i,j). You can calculate s(i,j) by dynamic programming: s(i,j) = M(i,j) + s(i+1,j) + s(i,j+1) - s(i+1,j+1). And the sum of any rectangle can be computed from s(i,j).

Anonymous on Feb 10, 2010


Anonymous on Feb 21, 2010

The answer is already popular in computer vision fields!! It is called integral imaging.
See this page http://en.wikipedia.org/wiki/Haar-like_features

seungwooYoo on Oct 13, 2012

It wasn't 100% clear to me, then I found the Wiki page


Anonymous on Oct 23, 2014

Let a[][] be the 2d array, int i=0; for( j = row_start; j <= row_end; j++) for( k = col_start; k <= col_end; k++) i+=a[j][k];

Anonymous on Mar 4, 2019

Iterate over matrix as an array storing (new sums array) in each position the cumulative sum up to that point. For each row in the desired submatrix we can compute its sum as a difference between its end and start positions. Repeat for other rows. Add up all the row sums.

Edi on Mar 8, 2019

Add Answers or Comments

To comment on this, Sign In or Sign Up.