Print maximum sum square sub-matrix of given size in C Program.

Given a matrix of NxN find a sub matrix of MxM where M<=N and M>=1 such that addition of all the elements of matrix MxM is maximum. Input of matrix NxN can contain zero, positive and negative integer values.

Example

Input:
   {{1, 1, 1, 1, 1},
   {2, 2, 2, 2, 2},
   {3, 3, 3, 3, 3},
   {4, 4, 4, 4, 4},
   {5, 5, 5, 5, 5} }
Output:
   4 4
   5 5

The above problem can be solved by a simple solution in which we can take whole matrix NxN, then find out all possible MxM matrix and find their sum, then print the one matrix of MxM with the maximum sum. This approach is easy but require O(N^2.M^2) time complexity, so we try to find out a way which takes less time complexity.

Algorithm

Start
Step 1 -> Declare Function void matrix(int arr[][size], int k)
   IF k>size
      Return
   Declare int array[size][size]
   Loop For int j=0 and j<size and j++
      Set sum=0
   Loop for int i=0 and i<k and i++
      Set sum=sum + arr[i][j]
   End
   Set array[0][j]=sum
   Loop For int i=1 and i<size-k+1 and i++
      Set sum=sum+(arr[i+k-1]][j]-arr[i-1][j]
      Set arrayi][j]=sum
   End
   Set int maxsum = INT_MIN and *pos = NULL
   Loop For int i=0 and i<size-k+1 and i++)
      Set int sum = 0
      Loop For int j = 0 and j<k and j++
         Set sum += array[i][j]
      End
      If sum > maxsum
         Set maxsum = sum
         Set pos = &(arr[i][0])
      End
      Loop For int j=1 and j<size-k+1 and j++
         Set sum += (array[i][j+k-1] - array[i][j-1])
         IF sum > maxsum
            Set maxsum = sum
            Set pos = &(arr[i][j])
         End
      End
   End
   Loop For int i=0 and i<k and i++
      Loop For int j=0 and j<k and j++
         Print *(pos + i*size + j)
      End
      Print \n
   End
Step 2 -> In main()
   Declare int array[size][size] = {{1, 1, 1, 1, 1}, {2, 2, 2, 2, 2}, {3, 3, 3, 3, 3}, {4, 4, 4, 4, 4}, {5, 5, 5, 5, 5}}
   Declare int k = 2
   Call matrix(array, k)
Stop

Example

#include <bits/stdc++.h>
using namespace std;
#define size 5
void matrix(int arr[][size], int k){
   if (k > size) return;
      int array[size][size];
   for (int j=0; j<size; j++){
      int sum = 0;
      for (int i=0; i<k; i++)
         sum += arr[i][j];
         array[0][j] = sum;
      for (int i=1; i<size-k+1; i++){
         sum += (arr[i+k-1][j] - arr[i-1][j]);
         array[i][j] = sum;
      }
   }
   int maxsum = INT_MIN, *pos = NULL;
   for (int i=0; i<size-k+1; i++){
      int sum = 0;
      for (int j = 0; j<k; j++)
         sum += array[i][j];
      if (sum > maxsum){
         maxsum = sum;
         pos = &(arr[i][0]);
      }
      for (int j=1; j<size-k+1; j++){
         sum += (array[i][j+k-1] - array[i][j-1]);
         if (sum > maxsum){
            maxsum = sum;
            pos = &(arr[i][j]);
         }
      }
   }
   for (int i=0; i<k; i++){
      for (int j=0; j<k; j++)
         cout << *(pos + i*size + j) << " ";
      cout << endl;
   }
}
int main(){
   int array[size][size] = {
      {1, 1, 1, 1, 1},
      {2, 2, 2, 2, 2},
      {3, 3, 3, 3, 3},
      {4, 4, 4, 4, 4},
      {5, 5, 5, 5, 5},
   };
   int k = 2;
   matrix(array, k);
   return 0;
}

Output

if we run above program then it will generate following output

4 4
5 5