计算数组矩形区域中的值之和

Question

I have a very big array of many value and store it in an row-major 1d array .

ex:  
   1 2 3  
   4 5 6

will be store in int* array = {1,2,3,4,5,6};

what I have to do is given the row1, row2, column1, column2 , then print out the area's sum, and it will request to caulate different area for many times.

what I have think about it is first use nested loop to traverse the array and store each row's sum in sum_row and store each column's sum in sum_column and store the total element's sum im totalSum .

Then totalSum - the row and the columns that surrond it + the elemnts that has been minus twice .

But it seems fast enough, is there any algorithm that can do faster or some coding style tips that can make the factor little?

Thx in advance.

Answer 1

It seems to me that you have replaced one double iteration with another. The problem is in subtracting " the elemnts that has been minus twice "; unless I'm mistaken, this involves iterating over those elements to sum them.

Instead, just iterate over the rectangular area that you need to sum. I doubt it will be any slower.

A more efficient algorithm can be obtained by generating the matrix of summed upper-left matrices. (See the Wikipedia article on summed area table .) You can then compute any submatrix sum by looking up four area sums.