Kadane?

#include <iostream>
#include <vector>
using namespace std;

int main()
{
    vector< vector<int> > mat;
    int n, m;

    cin>>n>>m;
    mat = vector< vector<int> > (n, vector<int> (m) );

    for(int i=0; i<n; i++)
        for(int j=0; j<m; j++)
            cin>>mat[i][j];


    vector< vector<int> > DP (n+1, vector<int> (m+1, 0) );

    for(int i=1; i<=n; i++)
    {
        for(int j=1; j<=m; j++)
        {
            DP[i][j] = DP[i-1][j] + DP[i][j-1] - DP[i-1][j-1] + mat[i-1][j-1];
        }
    }

    for(int i=0; i<n; i++)
    {
        for(int j=0; j<m; j++)
            cout<<mat[i][j]<<" ";
        cout<<endl;
    }
    cout<<endl;
    for(int i=1; i<=n; i++)
    {
        for(int j=1; j<=m; j++)
            cout<<DP[i][j]<<" ";
        cout<<endl;
    }

    return 0;
}