Sum of all submatrices approach 2

#1

Please explain how to generate prefix sum submatrix ?

#2

for generating prefix sum submatrix
first you have to sum column wise and then row wise
use this

for(int i=0;i<n;i++){
		for(int j=1;j<n;j++){
			arr[i][j]+=arr[i][j-1];
		}
	}
	for(int j=0;j<n;j++){
		for(int i=1;i<n;i++){
			arr[i][j]+=arr[i-1][j];
		}
	}

now in the array arr[i][j] represent the sum of submatrix starting form (0,0) to (i,j)

i hope this helps
if yes hit a like and don’t forgot to mark doubt as resolved :grinning:
if you have more doubts regarding this feel free to ask

#3

Can we apply the following approach to solve this problem-

  1. Calculate prefix sum from [0, 0] to [x, y] = sum1
  2. Calculate prefix sum from [0, 0] to [i, j] = sum2
  3. Then sum required from [i, j] to [x, y] = sum2 - sum1 + matrix[i][j].

Here I am taking x, y, i, j in reference to matrix that is explained in video.

#4

no it will not work
make a matrix and then try to visiualize this

correct way
bi => bottom most i
bj => bottom most j
ti ,tj => topmost i and j

                    int temp=arr[bi][bj];
                    if(tj>0)temp-=arr[bi][tj-1];
                    if(ti>0)temp-=arr[ti-1][bj];
                    if(ti>0&&tj>0)temp+=arr[ti-1][tj-1];
                    // cout<<temp<<"\n";
                    sum+=temp;
#5

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