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51008 - Sum of Regional Maxes

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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Question by Ibrahim Mesecan.

Sum of Regional Maxes

You have data in a table (2D matrix r-by-c) and you are asked to calculate sum of regional maxes. 2D array will be divided into square regions with the given dimension (k) starting from the upper left corner. The max of every region is to be determined and the sum of maxes will be calculated. Search max, only within the given matrix (r-by-c).

Question: Write a program which reads information and calculates the sum of regional maxes.

Input specification: You will be given three integers in the beginning:

  • The number of rows (r) and columns (c): two positive integers not greater than 200,
  • The size of square regions (k)
where 1 < k < (r and c) ≤ 200. Then, each of the following r lines contains c integers which are between -2e4 and +2e4.

Output specification: Show one integer.

Sample Input
5 6 3
0 8 1 1 10 6
6 8 7 0 3 9
0 7 6 8 6 5
4 0 2 7 2 0
4 4 5 7 5 1
 		Sample Output
30

Explanation: Max of the first region is 8. And sum of regional maxes is 8 + 10 + 5 + 7 = 30.



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